the mayor of a town has proposed a plan for the construction of a new community. a political study took a sample of 1100 voters in the town and found that 25% of the residents favored construction. using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 22%. determine the decision rule for rejecting the null hypothesis, h0, at the 0.01 level.

Answer:

3/500

Step-by-step explanation:

6/1000 ÷2 =

3/500

Answer: Let's assume that the zeros of the given quadratic equation are a and 1/a, since they are reciprocals of each other. By the sum-product relationships for zeros of a quadratic equation, we have:

a + 1/a = -b/a1 = -4/(1-3k) (where b = 4 and a1 = 1-3k)

Multiplying both sides by a1, we get:

a1(a + 1/a) = -4

Expanding the left-hand side, we get:

a1a + a1/a = -4

Multiplying both sides by a, we get:

a1a² + a1 = -4a

Substituting a1 = 1-3k, we get:

(1-3k)a² + (1-3k) = -4a

Rearranging, we get:

(1-3k)a² + 4a + (3k-1) = 0

Since a is one of the zeros of the quadratic, we know that the quadratic can be factored as:

(1-3k)(a - r)(a - s) = 0

where r and s are the other two roots of the quadratic. By expanding the left-hand side, we get:

(1-3k)(a² - (r+s)a + rs) = 0

Comparing with the expanded form of the quadratic, we see that:

r + s = -4/(1-3k)

rs = (3k-1)/(1-3k)

By Vieta's formulas, we know that rs = c/a1, where c is the constant term of the quadratic. Substituting c = -5 and a1 = 1-3k, we get:

rs = -5/(1-3k)

Equating this with the expression we obtained earlier for rs, we get:

-5/(1-3k) = (3k-1)/(1-3k)

Multiplying both sides by 1-3k and simplifying, we get:

-5 = (3k-1)(3k-2)

Expanding the right-hand side, we get:

-5 = 9k² - 15k + 2

Simplifying, we get:

9k² - 15k - 7 = 0

Using the quadratic formula, we get:

k = (15 ± sqrt(15² + 497))/18

k = (15 ± sqrt(429))/18

Therefore, the two possible values of k are:

k = (15 + sqrt(429))/18 ≈ 1.57

k = (15 - sqrt(429))/18 ≈ -0.24

Note that both of these values of k satisfy the condition that the zeros of the quadratic are reciprocals of each other.

Step-by-step explanation:

Answer:

domain: [- ∞ , ∞]

range: (8 , -∞]

Step-by-step explanation:

- ∞ < x < ∞

y < 8

Answer:

4 is the answer is this equation

Answer:  I have provided a screenshot of what your graph should look like so uh yeah you got this!

The graph of the line with the equation y = 4/5x + 2 is given in below attachment.

To graph the line with the equation y = (4/5)x + 2, we can use the slope-intercept form, which is y = mx + b.

where "m" represents the slope and "b" represents the y-intercept.

In this case, the slope (m) is 4/5, and the y-intercept (b) is 2.

To plot the line, we can start by plotting the y-intercept, which is the point (0, 2).

From there, we can use the slope to find additional points and connect them to form the line.

Let's plot a few more points:

When x = 5:

y = (4/5)(5) + 2

= 4 + 2 = 6

So we have the point (5, 6).

When x = -5:

y = (4/5)(-5) + 2

= -4 + 2

= -2

So we have the point (-5, -2).

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h(6) = 11

Hi there !

h(t) = t + 2 + 3

= t + 5

replace t = 6

h(6) = 6 + 5

= 11

Good luck !

Answer:

f(g(2)) = 50

Step-by-step explanation:

evaluate g(2) then substitute the result obtained into f(x)

g(2) = 3(2) - 2 = 6 - 2 = 4 , then

f(4) = 2(4 + 1)² = 2(5)² = 2(25) = 50

Answer:

f[g(2)] = 50

Step-by-step explanation:

Given functions:

\(f(x)=2(x+1)^2\)

\(g(x)=3x-2\)

We are asked to determine f[g(2)], which is known as a composite function. When solving composite functions, you always work inside out.

Step 1: Find the value of g(2) by substituting 2 for x in function g(x).

\(\implies g(2)=3(2)-2\)

\(\\\implies g(2)=6-2\Rightarrow g(2)=\boxed{4}\)

Step 2: Substitute the found value into the composite function.

\(\\\implies f[g(2)]= 2(4+1)^2\)

\(\implies f[g(2)] = 2(5)^2 \Rightarrow 2(25) \Rightarrow \boxed{50}\)

Hence, the value of the composite function f[g(2)] is 50.

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The correct answers are options b. LM ≅ ON and d. ∠L ≅ ∠N as they verify that LMNO is an isosceles trapezoid.

To verify that LMNO is an isosceles trapezoid, we need to check if the following conditions are met:
1. One pair of opposite sides must be parallel (base angles are equal).
2. The non-parallel sides (legs) are congruent.
From the given options:
a. LN ≅ MO - This does not verify LMNO as an isosceles trapezoid, as it only shows congruence between the parallel sides.
b. LM ≅ ON - This verifies LMNO as an isosceles trapezoid, as it shows that the non-parallel sides (legs) are congruent.
c. LO ≅ MN - This does not verify LMNO as an isosceles trapezoid, as it only shows congruence between the diagonals.
d. ∠L ≅ ∠N - This verifies LMNO as an isosceles trapezoid, as it shows that the base angles are congruent, indicating that the opposite sides are parallel.
e. ∠L ≅ ∠M - This does not verify LMNO as an isosceles trapezoid, as it only shows congruence between adjacent angles.
Thus, options b and d are the correct answers that verify LMNO is an isosceles trapezoid.

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Answer:

Step-by-step explanation:

10

Given:

P = $10000

r= 5%

Find:

we have to find the time for which initial bank deposit of $10,000 grow to $23,750 at 5% annual compound interest.

Explanation:

The formula for compound interest is

First, convert R as a percent to r as a decimal

r = R/100

r = 5/100

r = 0.05 per year,

Then, solve the equation for t

t = ln(A/P) / n[ln(1 + r/n)]

t = ln(23,750.00/10,000.00) / ( 1 × [ln(1 + 0.05/1)] )

t = ln(23,750.00/10,000.00) / ( 1 × [ln(1 + 0.05)] )

t = 17.729 years

Summary:

The time required to get a total amount of $23,750.00 with compounded interest on a principal of $10,000.00 at an interest rate of 5% per year and compounded 1 times per year is 17.729 years.

(about 17 years 9 months)

Use analytic methods,

(a) The local extrema,

1) If f'(x) > 0 for all x on (a , c) and f'(x)<0 for all x on (c , b), then f(c) is a local maximum value.

2) If f'(x) < 0 for all x on (a , c) and f'(x)>0 for all x on (c , b), then f(c) is a local maximum value.

(b) The intervals on which the function is increasing

Write properties of function :

Increasing interval : ( - ∞ , 0 )

(c) The intervals on which the function is decreasing

Write properties of function :

Decreasing interval : ( 0 , ∞ )

Given that,

Use analytic methods (a) the local extrema, (b) the intervals on which the function is increasing, and (c) the intervals, then the function is,

A function's growing (or decreasing) periods match the periods when its derivative is positive (or negative). As a result, we can easily determine the intervals where a function increases or decreases by taking its derivative and analyzing it to determine if it is positive or negative.

Let f be continuous on an open interval (a , b) that contains a critical x-value.

1) If f'(x) > 0 for all x on (a , c) and f'(x)<0 for all x on (c , b), then f(c) is a local maximum value.

2) If f'(x) < 0 for all x on (a , c) and f'(x)>0 for all x on (c , b), then f(c) is a local maximum value.

(b) The intervals on which the function is increasing

Write properties of function :

Increasing interval : ( - ∞ , 0 )

(c) The intervals on which the function is decreasing

Write properties of function :

Decreasing interval : ( 0 , ∞ )

Therefore,

Use analytic methods,

(a) The local extrema,

1) If f'(x) > 0 for all x on (a , c) and f'(x)<0 for all x on (c , b), then f(c) is a local maximum value.

2) If f'(x) < 0 for all x on (a , c) and f'(x)>0 for all x on (c , b), then f(c) is a local maximum value.

(b) The intervals on which the function is increasing

Write properties of function :

Increasing interval : ( - ∞ , 0 )

(c) The intervals on which the function is decreasing

Write properties of function :

Decreasing interval : ( 0 , ∞ )

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Answer:

Step-by-step explanation:

Total surface area comprises one rectangular base and two pairs of diferent triangles.

Area of rectangle

Area of triangle

Substitute and find

Area of base rectangle

Area of rest triangles

Now

TSA

Answer:

d.90l

Step-by-step explanation:

The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

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Jamal would need approximately 7.9 gallons of gas to travel 296.25 miles.

We can use the concept of direct variation to solve this problem. Direct variation means that two quantities are related by a constant ratio. In this case, the number of miles driven is directly proportional to the number of gallons used.

To find the constant of proportionality, we can use the given data. From the table, we can see that when Jamal used 14 gallons, he drove 525 miles. So we can write:

14/525 = k

where k is the constant of proportionality.

Solving for k, we get:

k = 14/525

Now we can use this value of k to find how many gallons Jamal would need to travel 296.25 miles. Let x be the number of gallons he would need. Then we can write:

x/296.25 = k

Substituting the value of k, we get:

x/296.25 = 14/525

Solving for x, we get:

x = (296.25 × 14) / 525

x ≈ 7.9

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Answer:

Step-by-step explanation:

To find the value of x, solve the equation. Do this by rearranging the equation to make x the subject.

Answer:

x=32761 /4

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

4x+7=32768

Step 2: Subtract 7 from both sides.

4x+7−7=32768−7

4x=32761

Step 3: Divide both sides by 4.

Answer:

29.4444

Step-by-step explanation:

Answer:

I've attached the answer below.

Step-by-step explanation:

did it tell you what x and y equal

the values of x in [0, 2π] where the graph of f(x) has a horizontal tangent are x = 2π/3, x = 4π/3, and x = π.

To find the values of x in [0, 2π] where the graph of f(x) = x + 2sin(x) has a horizontal tangent, we need to find where the derivative of the function is zero or undefined.

The derivative of f(x) is:

f'(x) = 1 + 2cos(x)

For the derivative to be zero, we need:

1 + 2cos(x) = 0

Solving for cos(x), we get:

cos(x) = -1/2

This is true when x = 2π/3 or x = 4π/3.

Now we need to check if the derivative is undefined at any point in the interval [0, 2π]. The derivative is undefined when cos(x) = -1, which occurs at x = π.

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Answer:

Step-by-step explanation:

The point on the x-axis is 2

The point on the y - axis is -3

Answer:

it should take 70 mins to fill all 5

hope this helps!! :)

Step-by-step explanation:

14 x 5 = 70

Answer:

70

Step-by-step explanation:

14 minutes = 1 cavity

x minutes = 5 cavities

70= x

Answer:

m = 3/4

Step-by-step explanation:

Start in (- 2,1) up three and four to the right. Positive slope. (Going uphill positive +, and downhill is negative - )

The term which is used for describing the number of voters who casted their votes using the ballots is called as voter turnout.

The process of selecting a candidate for a suitable post who takes care of the policies which will be framed for the people is called as voting. In this process, the members/ citizens casts their vote in the favor of their suitable candidate. Many times voters are not valid and their votes are considered as null and void.

The voter turnout is either the percentage of registered voters, eligible voters, or all voting-age people ( this varies from place to place depending upon the minimum voting age required). The voter turnout is also referred to the number of people who go to it or take part in it. High voter turnout is generally considered a sign of a healthy democracy.

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The measures of the other two angles in the parallelogram are both 143 degrees.

A parallelogram is a quadrilateral with two sides that are parallel to one another. A parallelogram has equal-length opposite sides and equal-length opposite angles. The internal angles that are extra to the transversal on the same side. A parallelogram's total interior angles add up to 360 degrees.

A parallelogram is formed by the junction of two parallel lines, and its opposite angles are equal.

Then, there are two 35 degree angles. Two further angles that are equivalent are noted: A parallelogram's angles add up to 360 degrees. Following that, x+x+37+37=360

2x=360-74

2x=286

x=143.

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Answer:

35 in

Step-by-step explanation:

Answer: f(x) = -1/2(x+3)

Example: g(x) = -1/2(-x-3)

This function is a dilation and a reflection of the parent function f(x) because when graphed, the two functions have the same shape but are reflected over the y-axis and are half the size of the original.

The maximum price Matthew can pay for the car, considering his repayment capability and the loan terms, is approximately $126,318.29.

To determine the maximum price Matthew can pay for the car, we need to consider his repayment capability and the terms of the loan.

Matthew can make annual repayments of $35,000. Since the loan term is six years, the total amount he can repay over the loan period is $35,000 multiplied by six, which equals $210,000.

To calculate the maximum price of the car, we need to account for the interest rate of 9.25%. The interest rate represents the cost of borrowing and is applied to the loan amount.

Let's assume the loan amount is denoted by P.

The formula to calculate the future value of a loan with interest is:

FV = P(1 + r)^n

Where:

FV = Future value (total amount repaid)

P = Principal amount (maximum price of the car)

r = Interest rate per period (9.25% or 0.0925)

n = Number of periods (six years)

Since Matthew can repay a total of $210,000 over the loan period, we can set up the equation:

$210,000 = P(1 + 0.0925)^6

Now we can solve for P:

P = $210,000 / (1 + 0.0925)^6

Evaluating this expression, we find:

P ≈ $126,318.29

Therefore, the maximum price Matthew can pay for the car, considering his repayment capability and the loan terms, is approximately $126,318.29.

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