Election polling Gloria Chavez and Ronald Flynn are the candidates for mayor in a large city. We want to estimate the proportion p of all registered voters in the city who plan to vote for Chavez with 95% confidence and a margin of error no greater than 0.03. How large a random sample do we need? Show your work.

The number of terms in the polynomial (2·x + 5·y)¹² are 1 thirteen terms

A polynomial is the sum of terms that contains different powers of the variables.

The number of terms in a polynomial in a polynomial of degree n can be found from the expansion of the polynomial as follows;

(2·x + 5·y)¹² = 4096·x¹² + 122880x¹¹·y + 1689600·x¹⁰·y² + 14080000·x⁹·y³ + 79200000·x⁸·y⁴ + 316800000·x⁷·y⁵ + 924000000·x⁶·y⁶ + 1980000000·x⁵·y⁷ + 3093750000·x⁴·y⁸ + 3437500000·x³·y⁹ + 2578125000·x²·y¹⁰ + 1171875000·x·y¹¹ + 244140625·y¹²

The number of terms in the above polynomial are 13 terms, therefore the number of terms in the polynomial (2·x + 5·y)¹² is 13 terms

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The proof to show that ∆AEC and ∆BDC are similar in the blanks is below;

<BDC and <AEC are right angles by the definition of perpendicular lines and all right angles are congruent, So, <BDC≅AEC. Both ∆AEC and ∆BDC share <C, and <C ≅ <C by the reflexive property. Therefore, ∆AEC ~ ∆BDC by the SAS criterion for proving similar triangles.

A triangle is a three sided polygon. The type of triangles includes:

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Answer:

9

Step-by-step explanation:

4-x = 5(16-x)

44-x = 80-5x

4x = 36

x = 9

The calculated slopes of the relations are -5, 9, -1/3 and 3

The table 1

The slope is calculated as

Slope = change in y/x

So, we have

Slope = (13 - 18)/(-2 + 3)

Evaluate

Slope = -5

Ordered pair 2

The slope is calculated as

Slope = change in y/x

So, we have

Slope = (9 + 27)/(1 + 3)

Evaluate

Slope = 9

Graph 3

The slope is calculated as

Slope = change in y/x

So, we have

Slope = (0 - 1)/(3 - 0)

Evaluate

Slope = -1/3

The table 4

The slope is calculated as

Slope = change in y/x

So, we have

Slope = (2 + 1)/(-2 + 3)

Evaluate

Slope = 3

Hence, the values of the slopes are -5, 9, -1/3 and 3

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Answer:

The 15th term is 103

Step-by-step explanation:

Arithmetic Sequence

An arithmetic sequence is a list of numbers with a definite pattern by which each term is found by adding or subtracting a fixed quantity to the previous term. If n is the number of the term, then:

\(a_n=a_{n-1}+d\)

Where d is called the common difference. If we know the first term, the nth term is calculated by:

\(a_n=a_1+(n-1)*d\)

The question asks us to find the term n=15 of an arithmetic sequence with a common difference d=7 and first term a1=5.

Applying the formula above:

\(a_{15}=5+(15-1)*7\)

\(a_{15}=5+14*7\)

\(a_{15}=5+98=103\)

The 15th term is 103

The number of employees that must be included in the sample to be 95% confident that the sample mean is within 1.5 hours of the population mean is 107 employees.

To estimate the mean number of hours worked by all grocery store employees in the county with 95% confidence and a margin of error of 1.5 hours, we can use the sample size formula:

n = (Z * σ / E)²

where:
- n is the required sample size
- Z is the critical value (1.96 for a 95% level of confidence)
- σ is the population standard deviation (7.9 from the previous study)
- E is the margin of error (1.5 hours)

Plugging in the given values:

n = (1.96 * 7.9 / 1.5)²

n ≈ 106.56

Since you cannot have a fraction of an employee, you need to round up to the nearest whole number. Therefore, the researcher must include 107 employees in the sample to be 95% confident that the sample mean is within 1.5 hours of the population mean.

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Answer:

1 ) alternate interior angle

2) corresponding part of congruent triangle

3) vertically opposite angle

4)∆HED congruent to ∆FEG

5) parallel lines and alternate interior angle

The sum of the given polynomials is -3x^2 + 11x - 3. A polynomial is a mathematical expression consisting of variables and coefficients, where the exponents of the variables are all non-negative integers.

To add two polynomials, we need to combine the like terms. Like terms have the same variable raised to the same power.

We can rewrite the two polynomials by placing the terms with the same variable and exponent together. We get:

(-3x^2 + 4x + 2) + (7x - 5) = -3x^2 + (4x + 7x) + (2 - 5)

The given expression is:

(-3x^2 + 4x + 2) + (7x - 5)

To add these polynomials, we group the like terms together:

(-3x^2) + (4x) + (2) + (7x) + (-5)

We can simplify the expression by adding the coefficients of like terms:

-3x^2 + 11x - 3

Therefore, the sum of the polynomials is -3x^2 + 11x - 3.

In other words, if we add the polynomial -3x^2 + 4x + 2 and 7x - 5, we get the polynomial -3x^2 + 11x - 3.

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Brandon rode his bike 8.35 miles further than Randy.

To find out how much further Brandon rode his bike last month than Randy, you'll need to subtract Randy's miles from Brandon's miles using the given values.

Step 1: Identify the miles ridden by both Brandon and Randy.
- Brandon rode 56.28 miles.
- Randy rode 47.93 miles.

Step 2: Subtract Randy's miles from Brandon's miles.
- 56.28 miles (Brandon's miles) - 47.93 miles (Randy's miles) = 8.35 miles.

So, last month, Brandon rode his bike more than Randy.

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Answer:

Point form:

(2, 9)

Equation form:

x = 2,y = 9

Step-by-step explanation:

Answer:

Below in bold.

Step-by-step explanation:

9x^2 - 16

Comparing this with the standard form

ax^2 + bx + c

ac = 9*-16 = -144

b = 0

-12 and 12 multiply to get ac and add to get b.

Factored form is

(3x - 4)(3x + 4).

The value of ac is,

⇒ - 144

The value of b is,

⇒ b = 0

And, The factored form is,

⇒ (3x - 4) (3x + 4)

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The quadratic equation is,

⇒ 9x² - 16

Now, We know that;

General form of quadratic equation is,

⇒ ax² + bx + c

Here, The quadratic equation is,

⇒ 9x² - 16

Hence, By comparing,

⇒ a = 9

⇒ b = 0

⇒ c = - 16

Thus, The value of ac is,

⇒ ac = 9 × - 16

        = - 144

And, The factored form is,

⇒ 9x² - 16

⇒ (3x)² - 4²

⇒ (3x - 4) (3x + 4)

Thus, The value of ac is,

⇒ - 144

The value of b is,

⇒ b = 0

And, The factored form is,

⇒ (3x - 4) (3x + 4)

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The probability that Ella's 10th roll is her last roll is 31/108, or approximately 0.2870.

To find the probability that Ella's 10th roll is her last roll, we need to consider the following:

The last roll must be a repeat of the previous roll, so the previous roll cannot be the first roll or the 6th roll, because there is no previous roll in those cases.

Ella must not have rolled the same number on consecutive rolls before her 10th roll.

The probability of rolling the same number on consecutive rolls is 1/6, so the probability of not rolling the same number on consecutive rolls is 5/6.

Let's break down the probability of Ella's 10th roll being her last roll by considering the different cases:

Case 1: Ella's 8th roll is the first roll of a pair, and her 9th roll is the second roll of that pair.

In this case, Ella cannot roll the same number on consecutive rolls, so the probability of her 10th roll being her last roll is simply 1/6.

Case 2: Ella's 8th roll is the first roll of a pair, but her 9th roll is not the second roll of that pair.

In this case, Ella must roll a number different from her 9th roll, and then roll the same number as her 9th roll on her 10th roll.

The probability of rolling a different number on her 9th roll is 5/6, and the probability of rolling the same number on her 10th roll is 1/6.

Therefore, the probability of her 10th roll being her last roll in this case is (5/6)*(1/6) = 5/36.

Case 3: Ella's 8th roll is not the first roll of a pair, but her 9th roll is the second roll of a pair.

In this case, Ella must roll a number different from her 8th roll, and then roll the same number as her 8th roll on her 9th roll.

The probability of rolling a different number on her 8th roll is 5/6, and the probability of rolling the same number on her 9th roll is 1/6.

Therefore, the probability of her 10th roll being her last roll in this case is (5/6)*(1/6) = 5/36.

Case 4: Ella's 8th roll is not the first roll of a pair, and her 9th roll is not the second roll of a pair.

In this case, Ella must roll a number different from both her 8th and 9th rolls, and then roll the same number as her 9th roll on her 10th roll.

The probability of rolling a different number on her 8th roll is 5/6, the probability of rolling a different number on her 9th roll, given her 8th roll, is 4/6, and the probability of rolling the same number as her 9th roll on her 10th roll is 1/6.

Therefore, the probability of her 10th roll being her last roll in this case is (5/6)(4/6)(1/6) = 5/54.

To find the total probability, we need to sum the probabilities from each case:

1/6 + 5/36 + 5/36 + 5/54 = 31/108.

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The volume of the triangular solid is 128/3 cubic units.

The cross-sections of the triangular solid along the y-axis are equilateral triangles with side length equal to the width of the triangular base at that y-coordinate. The width of the triangular base at y = h is equal to 8 - 4h/4. So, the side length of the equilateral triangle at y = h is 8 - 4h/4.

Let's call the height of the equilateral triangle at y = h as "x". Then, using the Pythagorean theorem, we can find the relationship between x and the side length:

x^2 = (8 - 4h/4)^2 - (x/2)^2

Expanding and simplifying the right-hand side:

x^2 = 64 - 16h + h^2/16 - x^2/4

Multiplying both sides by 4:

4x^2 = 256 - 64h + h^2 - x^2

Solving for x^2:

3x^2 = 256 - 64h + h^2

Taking the square root of both sides:

x = √(256 - 64h + h^2)/√3

So, the height of the equilateral triangle at y = h is equal to x = √(256 - 64h + h^2)/√3.

The volume of the triangular solid can be found by integrating the cross-sectional area over the height of the triangular base:

V = (1/3) ∫[0, 4] x^2(y) dy

= (1/3) ∫[0, 4] (√(256 - 64h + h^2)/√3)^2 dh

= (1/3) ∫[0, 4] (256 - 64h + h^2)/3 dh

Evaluating the definite integral:

V = (1/3) * [(256h/3 - 32h^2/2 + h^3/3) |_0^4]

= (1/3) * [(256/3 * 4 - 32/2 * 4^2 + 4^3/3) - (256/3 * 0 - 32/2 * 0^2 + 0^3/3)]

= (1/3) * (256 - 128 + 64/3)

= 128/3.

Correct Question :

The base of s is the triangular region with vertices (0, 0), (8, 0), and (0, 4). Cross-sections perpendicular to the y-axis are equilateral triangles. What is the volume of the triangular solid.

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A scientific theory is a validated explanation of some aspect of the natural world, based on multiple facts that have been frequently verified through research and experimentation. Fact theories are not "guesses" but reliable accounts of the real world.

The point (2,-5) will be in the function f⁻¹(x). The solution has been obtained using range and domain.

What is range and domain?

The domain of a function is made up of all input values, and the range is made up of all output values.

We are given that a point (5,-2) is in the function f(x).

We know that the range and domain in the inverse function are the reverse of what is in the original function.

This means that

f⁻¹(x) range = f(x) domain  

f⁻¹(x) domain = f(x) range

So, we get that out of the points, (2,-5) will be in the function f⁻¹(x).

Hence, the point (2,-5) will be in the function f⁻¹(x).

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Answer:

The last one 4x4

Step-by-step explanation:

Answer:

last one, D.

Step-by-step explanation:

Answer: its a negative slope and its -4/3

Step-by-step explanation:

hope this helped you

The value of x from the given figure is 12 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

From the given figure,

Consider ΔADC and ΔABC,

∠C=∠C (Reflex property)

AC=AC (Reflex property)

∠BAC=∠CDA=90°

By AA similarity, ΔADC ~ ΔABC

So, AC/BC = DC/AC

x/36 = 4/x

x²=36×4

x²=144

x=12 units

Therefore, the value of x from the given figure is 12 units.

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Answer:

the second

Step-by-step explanation:

refers to well-founded standards of right and wrong that prescribe what humans should do, usually in terms of rights, obligations, benefits to society, justice

Answer:

19 degrees

Explanation:

The tangent ratio is opposite/adjacent. To find the angle however you need to take the inverse so the answer will be tan^-1(17/50).

Answer:

The equation of a basic sine function is f(x)=sinx. In this case b, the frequency, is equal to 1 which means one cycle occurs in 2π. If b=12, the period is 2π12 which means the period is 4π and the graph is stretched.

Step-by-step explanation:

Answer:

5%

Step-by-step explanation:

Solving our equation

r = 75 / ( 750 × 2 ) = 0.05

r = 0.05

converting r decimal to a percentage

R = 0.05 * 100 = 5%/year

The interest rate required to

accumulate simple interest of $ 75.00

from a principal of $ 750.00

over 2 years is 5% per year.

Answer:

1600

Step-by-step explanation:

1200 + 400 = 1600

Answer:

C. 2.01,1.48,1.237,1.234,1.2

Step-by-step explanation:

Step-by-step explanation: i think it is 5000

Adam Vinatieri made 14 field goals and 7 extra points.

Given that,

a field goal is 3 points and the field goal after a touchdown is only 1 point.

Adam Vinatieri made 21 field goals and extra point kicks for 49 points.

Let x be the number of field goals and y be the extra point kicks.

So we get,

x + y = 21 -------------(1)

3x + y = 49 -----------(2)

Subtracting equation (1) from equation (2),

2x = 28

 x = 14

putting the value of x in equation (1),

14 + y = 21

       y = 7

Therefore Adam Vinatieri made 14 field goals and 7 extra points.

Field goal means a score of three points in football made by drop kicking or placekicking the ball over the crossbar from ordinary play. A field goal is a successful kick of the ball by a kicker through the goalpost. It is an offensive play that can score three points for a team.

Adam Vinatieri is an American former football placekicker who played in the National Football League.

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By using the perimeter of the kite, we will see that the value of n is:

n = 23.25

We assume that the measures of the 4 sides of the kite are:

n + 3cm

n cm

n + 3cm

n + 3cm

So we have 3 equal sides and one shorter. And we know that the perimeter is equal to 102cm.

Then we can write the equation:

(n + 3) + n + (n + 3) + (n + 3) = 102

4n + 9 = 102

4n = 102 - 9 = 93

n = 93/4 = 23.25

The value of n is 23.25

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Answer:

12,090

Step-by-step explanation:

multiply 31*19.5*20

Answer:

12,090 inches

Step-by-step explanation:

volume is length x width x height, so all you have to do is multiply all the numbers by each other (31 x 19.5 x 20)

Answer:

h(5) = 20

Step-by-step explanation:

Assume that '2' is an exponent.

So the question for you should be:-

\( \displaystyle \large{h(x) = {x}^{2} - x}\)

We want to find h(5); we substitute x = 5 in.

\( \displaystyle \large{h(x) = {5}^{2} - 5}\)

5^2 is 5•5 = 25.

\( \displaystyle \large{h(x) = 25 - 5} \\ \displaystyle \large{h(x) = 20}\)

Therefore, h(5) is 20.

The linear equation of Johnny's charges is C(x) = 10 + 7.5x

From the question, we have the following parameters that can be used in our computation:

Initial charge = $10

Hourly rate = $7.50

Let the number of hours be x and the total cost be C(x)

So, we have the following representation

C(x) = Initial charge + Hourly rate * x

Substitute the known values in the above equation, so, we have the following representation

C(x) = 10 + 7.5x

Hence, the function is C(x) = 10 + 7.5x

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Complete question

Johnny charges $10 plus $7.50 per hour to mow lawns.

Determine the linear equation