A poll is taken in which 387 out of 500 randomly selected voters indicated their preference for a certain candidate.
(a) find a 99% confidence interval for p.
____________ ≤p≤ _________
(b) find the margin of error for this 98% confidence interval for p _______

The values of x in f(x) = 2x² - 10x + 18 using the quadratic formula are \(x = \frac{10 + \sqrt{-44}}{2 * 2}\) and \(x = \frac{10 - \sqrt{-44}}{2 * 2}\)

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

f(x) = 2x² - 10x + 18

The value of x using the quadratic formula can be calculated using

\(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

Using the above as a guide, we have the following:

\(x = \frac{10 \pm \sqrt{(-10)^2 - 4 * 2 * 18}}{2 * 2}\)

Evaluate

\(x = \frac{10 \pm \sqrt{-44}}{4}\)

Expand and evaluate

\(x = \frac{10 + \sqrt{-44}}{2 * 2}\) and \(x = \frac{10 - \sqrt{-44}}{2 * 2}\)

Hence, the values of x using the quadratic formula are \(x = \frac{10 + \sqrt{-44}}{2 * 2}\) and \(x = \frac{10 - \sqrt{-44}}{2 * 2}\)

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Answer: 900.24

Step-by-step explanation:

Perimeter=L•W•H

Answer:

y = -.4x+107

Here you go! Have a wonderful day!

Answer:

B. a×1

Step-by-step explanation:

This is because a×1 gives a result of a thus,a multiplying the identity element of multiplication

Step-by-step explanation:

one side.

as each tile is guaranteed an equilateral triangle, all sides are equally long. measuring 1 side clarifies therefore the overall size of the tile.

the angles are the same in any case, as every equilateral triangle (no matter its size) has only angles of 60°.

so, if any side has the same length as the side lengths of the other triangles, then the checked triangle is congruent with the others.

The probability of the frequency of an event in repeated trials under comparable circumstances is a statistical analysis.

The study of statistics is the field that deals with the gathering, structuring, analyzing, interpreting, and presenting of data. In order to apply statistics to an issue in science, business, or society, it is customary to start with a statistical population or a statistical model that will be investigated.

Finding the distribution hidden in your data is the aim of a statistical analysis. What do you mean by the distribution that lies underlying my data? "The distribution of your data describes the peaks and valleys of its characteristics in relation to a target population.

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Step-by-step explanation:

30 is the answer for this question

No, not all square numbers have an odd number of factors. In fact, square numbers can have either an odd or an even number of factors, depending on their prime factorization.

A square number is a number that can be expressed as the product of an integer multiplied by itself. For example, 4 is a square number because it can be written as 2 * 2.

When we analyze the factors of a square number, we find that each factor has a corresponding pair that multiplies to give the square number. For instance, the factors of 4 are 1, 2, and 4. We can see that the pairs are (1, 4) and (2, 2). Thus, 4 has an even number of factors.

However, there are square numbers that have an odd number of factors. Consider the square number 9, which is equal to 3 * 3. The factors of 9 are 1, 3, and 9. In this case, 9 has an odd number of factors.

In conclusion, while some square numbers have an odd number of factors (like 9), others have an even number of factors (like 4). The determining factor is the prime factorization of the square number.

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Answer:

\(-6 <f (x)\legslant 3\)

Step-by-step explanation:

If you examine the diagram you can know

\(y=\dfrac {1}{x}\)

\(\setlength{\unitlength}{2.5mm}\begin{picture}(10,10)\linethickness{0.45mm}\put(20,20){\vector(2,0){18}}\put(20,20){\vector(-2,0){18}}\put(20,20){\vector(0,2){18}}\put(20,20){\vector(0,-2){18}}\multiput(19.35,6)(0,2){15}{\line(1,0){1.3}}\multiput(6,19.35)(2,0){15}{\line(0,1){1.3}}\put(20,20){\circle*{1}}\qbezier(20.5,35)(20,20)(35,20.5)\qbezier(19.5,5)(20,20)(5,19.5)\end{picture}\)

Answer:

up me is right :) so get his answer :)

Answer:

-3/17

Step-by-step explanation:

4/17 times -3/4 - divide both fours by 4 gets as 1

1/17 times -3/1-----      -3/17

Answer:

-3/17

Step-by-step explanation:

4x3 is 12

17x3 is 68

Divide both by 4 and you get -3/17

i hope this is helps!

Each equation should be matched to the situation it represents as follows;

"Leilah has not yet studied 600 of her 2400 flashcards. She studies 40 new cards each day." ⇒ 2400 - 40x = 600

"Stetson rents studio space for $600 a month for music lessons. He charges his students $40 per hour and earned a profit of $2400 this month." ⇒ 40x - 600 = 2400

"A kit contains 600 letter tiles and 40 number tiles. Each tile has the same mass, and the kit has a total mass of 2400 g." ⇒ (600 + 40)x = 2400.

In this scenario and exercise, the independent variable (domain or input value) would be represented by the variable x, and then each of the situations described by the word sentence (problem) would be translated into an algebraic equation or linear function as follows;

Since Leilah studies 40 new cards per day, but hasn't studied 600 of her 2400 flashcards yet, a linear function to model or represent this situation is given by;

2400 - 40x = 600

The rent for Stetson's studio space is $600 per month and he charges his students $40 each hour while earning a profit of $2400 this month, a linear function to model or represent this situation is given by;

40x - 600 = 2400

Since this kit with a total mass of 2400rams contains 600 letter tiles and 40 number tiles, and each of the tiles have the same mass, the required linear function is given by;

(600 + 40)x = 2400.

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Answer: 8.39233038348

Step-by-step explanation:

Answer:

8.39233038348

Step-by-step explanation:

569/67.8=8.39233038348

Answer: 4020

Step-by-step explanation: u cute ash

The consumption next year for Ms. Anderson will be approximately $56,363.64 which is not in options, and the debt-equity ratio, based on a total debt ratio of 0.5, so the answer is option d.

To answer the first question, we need to calculate the consumption next year based on the given information. We can use the concept of present value to determine the amount.

The present value formula is:

Present Value = Future Value / (1 + Interest Rate)^n

Where:

Future Value is the amount to be received in the future

Interest Rate is the rate of return or interest rate per period

n is the number of periods

Given that Ms. Anderson has an income of $40,000 next year and the market interest rate is 10 percent, we can calculate the present value of $40,000:

Present Value = $40,000 / (1 + 0.10)^1

Present Value = $40,000 / 1.10

Present Value ≈ $36,363.64

Since Ms. Anderson consumes $80,000 this year and her present income next year is approximately $36,363.64, her consumption next year will be the sum of her present income and the remaining amount:

Consumption next year = Present income + Remaining amount

Consumption next year = $36,363.64 + ($80,000 - $60,000)

Consumption next year = $36,363.64 + $20,000

Consumption next year = $56,363.64

Therefore, the consumption next year will be approximately $56,363.64. None of the provided options match this amount, so it seems there might be an error in the answer choices.

Given that the total debt ratio is 0.5, it implies that the total debt is half of the total equity.

The debt-equity ratio is calculated by dividing the total debt by the total equity:

Debt-Equity Ratio = Total Debt / Total Equity

Substituting the given information, we have:

Debt-Equity Ratio = 0.5 * Total Equity / Total Equity

The term "Total Equity" cancels out, resulting in:

Debt-Equity Ratio = 0.5

Therefore, the correct answer is option d. 0.5.

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The given parabola , the direction of the focus from the vertex will show which way it opens. The one opens down.

What is parabola?

A conic may be a U-shaped plane curve wherever any purpose is at an equal distance from a hard and fast purpose (known because the focus) and from a hard and fast line that is thought because the directrix.

Main body:

Point (x , y) on the parabola, focus of (4, 8) and a directrix of y= 4

√(x-4)²+(y- 8)² = √(y- 4)²

(x-4)² + (y-8)² = (y-4)²

(y-8)² - (y-4)² = (x-4)²

(y²-16y+64) - (y²-8y+16) = (x-4)²

y²-16y+64 - y²+8y+16 =  (x-4)²

-8y = (x-4)² - 80

y = -1/8 (x-4)² + 10

standard formula of parabola: y = a(x-h)² + k  

 (h,k): vertex (4,10)

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490

472 <490<500

it fits the criteria

Taking into account the definition of a system of linear equations, the price of one order of chicken nuggets and one chicken sandwich is $2.98 and $4 respectively.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

A solution to a system is an assignment of values to the unknowns that makes each of the equations true. Solving a system means finding all the solutions of the system.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

2x +3y= 17.96

4x + 2y= 19.92

It is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable "y" from the first equation:

3y= 17.96 -2x

y= (17.96 -2x)÷3

y= 17.96÷3 - 2÷3x

y= 449/75 - 2/3x

Substituting the expression in the second equation:

4x + 2×(449/75 - 2/3x)= 19.92

Solving:

4x + 2×449/75 - 2×2/3x= 19.92

4x + 898/75 - 4/3x= 19.92

4x - 4/3x= 19.92 - 898/75

8/3x= 596/75

x= 596/75÷ 8/3

x= 2.98

Remembering that y= 449/75 - 2/3x, you get:

y= 449/75 - 2/3×2.98

y= 4

Finally, the price of one order of chicken nuggets is $2.98 and the price of one chicken sandwich is $4.

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Answer:

8/15

Step-by-step explanation:

To divide by a fraction, change the division to a multiplication, and flip the fraction.

2/5 / 3/4 = 2/5 * 4/3 = 8/15

Answer:

I only know number 7 sorry

Step-by-step explanation:

Anyways.....

The solution she has in the bucket has 80% water (as you found out), including 14.4 fl oz. water in a total of 18 fl oz. solution.

Barbara will need to add ammonia, but only after removing some (x fl oz.) of the solution she has in the bucket.

If Barbara wants an 18 fl oz. bucket full of 25% ammonia, she will need to have in that bucket 18 × 0.25=4.5 fl oz. ammonia (25% ammonia) and

18 × 0.75=13.5 fl oz. water (75% water).

Barbara will have to start by removing some of that 80% water solution to end up with just 13.5 fl oz. water in the bucket. Removing x fl oz. of solution, gets rid of 0.8x fl oz. of water, leaving 14.4 - 0.8x fl oz.  of water. since the amount of water needed is 13.5 fl oz. Our equation is

13.5 = 14.4 - 0.8x

13.5= 14.4 - 0.8x →→ 0.8x = 14.4 - 13.5 →→ 0.8x = 0.9 →→ \(x= \frac{0.9}{0.8}\) →→ x=1.125 fl. oz

Therefore 1.125 (may need to round) fl. oz should be replaced with ammonia.

Hope this helps some of your stress.

A = (-7,-6)

B = (8,-9)

Find the slope of line AB

m = (y2-y1)/(x2-x1)

m = (-9-(-6))/(8-(-7))

m = (-9+6)/(8+7)

m = -3/15

m = -1/5

The slope of line AB is -1/5.

Flip the fraction and the sign to go from -1/5 to +5/1 = 5. The perpendicular slope is 5.

Let m = 5.

Use the coordinates of point C (2,12) along with the perpendicular slope to get

y - y1 = m(x - x1)

y - 12 = 5(x - 2)

y - 12 = 5x - 10

y = 5x - 10+12

y = 5x + 2

Lastly, convert this to standard form

y = 5x + 2

5x+2 = y

5x+2-y = 0

5x-y = -2

Choice A is the closest match, but the -56 should be -2 instead. It seems like your teacher made a typo somewhere.

Answer:

5x - y = -2.

Step-by-step explanation:

The equation of this altitude line has a slope = -1/m where m is the slope of line AB . It will also pass through the point C.

The slope of line AB = (-9 - (-6)) / (8 - (-7))

= -3/15

= -1/5

So the slope  of the required line = -1 / -1/5 = 5.

Using the point C and the point-slope form of a line:

y - y1 = m(x - x1)

y - 12 =  5(x - 2)

y - 5x = -10 + 12

y - 5x = 2

5x - y = -2.

2 is the numerical expression when  2 to the power of five sixths.

What are power and exponent?

 \(2^{5/6} * 2^{1/6}\)

 \(2^{6/6}\)

  2¹

 = 2

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The rate of change (slopes) and initial value (y-intercepts) are as follows:

A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.

A line of best fit is also referred to as a trend line and it can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.

By critically observing the graph which models the given data, we can logically deduce the following rate of change (slopes) and initial value (y-intercepts):

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It takes 16 seconds for the unexploded shell to return to the ground.

The given function that models the height of a firework shell fired from a mortar is h(t) = -16(t - 8)² + 1024, where t is the time in seconds. We want to find out how long it will take for the shell to return to the ground when it doesn't explode.

To find the time it takes for the shell to reach the ground, we set the height function h(t) equal to zero and solve for t.

So, we have:

-16(t - 8)² + 1024 = 0

Dividing both sides of the equation by -16, we get:

(t - 8)² = 64

Taking the square root of both sides, we have:

t - 8 = ±8

Solving for t, we have two solutions:

t - 8 = 8, which gives t = 16

t - 8 = -8, which gives t = 0

The shell hits the ground when t = 0, which is the starting time.

In summary, it takes 16 seconds for the unexploded shell to return to the ground.

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When enlarging the triangle, given the scale factor of - 2, the new vertices become A'(4, 5), B'(2, 5), C'(4, 1).

Work out the vector from the center of enlargement to each point (subtract the coordinates of the center of enlargement from the coordinates of each point).

For A (7, 8), vector to center of enlargement (6, 7) is:

= 7-6, 8-7 = (1, 1)

For B (8, 8), vector to center of enlargement (6, 7) is:

= 8-6, 8-7 = (2, 1)

For C (7, 10), vector to center of enlargement (6, 7) is:

= 7-6, 10-7 = (1, 3)

Multiply each of these vectors by the scale factor -2, and add these new vectors back to the center of enlargement to get the new points:

For A, new point is:

=  6-2, 7-2 = (4, 5)

For B, new point is:

= 6-4, 7-2

= (2, 5)

For C, new point is:

= 6-2, 7-6

= (4, 1)

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The measure of each angle formed by the three support beams for a bridge is 45 degrees.

The question states that three support beams for a bridge form a pair of complementary angles. Complementary angles are two angles that add up to 90 degrees.

Let's denote the angles as Angle A and Angle B. Since the angles are complementary, we can set up the following equation:

Angle A + Angle B = 90 degrees.

To find the measure of each angle, we need to divide 90 degrees by 2 since there are two angles.

Angle A = Angle B = 90 degrees / 2 = 45 degrees.

Therefore, each angle measures 45 degrees.

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The measure of each angle is 45 degrees.

To find the measure of each angle, we need to understand what complementary angles are. Complementary angles are two angles that add up to 90 degrees.

In this case, we have three support beams for a bridge that form a pair of complementary angles. Since the angles are complementary, their sum is 90 degrees.

Let's assume the measure of one angle is x degrees. The other angle will be (90 - x) degrees, as their sum is 90 degrees.

Since the three support beams form a pair of complementary angles, we can set up the equation:

x + (90 - x) = 90

By simplifying the equation, we have:

90 - x + x = 90

90 = 90

This equation is true for any value of x. Therefore, the measure of each angle can be any value, as long as their sum is 90 degrees.

So, the measure of each angle is not fixed, but it will always add up to 90 degrees.

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For a quadrilateral with one diagonal  = 9 cm, the sum of perpendiculars from opposite vertices on it is 12 cm, area of quadrilateral = (9/2) × √(2BC² + (12 – p2 – p4)²) + (12 – p2 – p4)/2.

Formula used: Area of quadrilateral = [d1d2 + (p1 + p2 + p3 + p4)]/2, Where,d1 and d2 are diagonals p1, p2, p3 and p4 are perpendiculars from opposite vertices on it.

To find: Area of quadrilateralSolution: Let ABCD be a quadrilateral in which diagonal AC = 9 cmLet p1 and p3 be perpendiculars from vertices A and C on diagonal BD respectively, and p2 and p4 be perpendiculars from vertices B and D on diagonal AC respectively.

By using Pythagoras' theorem, we can calculate the length of BD.

BD² = AB² + AD²BD² = BC² + CD².

From right triangles ABC and ADC, we can get AB² + p2² = 9² ….. (1)AD² + p4² = 9² ….. (2)

From right triangles BCD and ABD, we can get BC² + p3² = BD² ….. (3)

AB² + p1² = BD² ….. (4)

Adding (3) and (4), we get: 2AB² + p1² + p3² = 2BD²

From equations (1) and (2), we get: 2AB² + p1² + p3² = AB² + p2² + AD² + p4²

Substituting AB² + AD² = BD² – BC² in the above equation, we get:

p1² + p3² = p2² + p4² + 2BC²

Using the formula of area of quadrilateral, we have area of quadrilateral = [d1d2 + (p1 + p2 + p3 + p4)]/2= [9 × BD + (p1 + p2 + p3 + p4)]/2= [9 × √(2BC² + p1² + p3²) + (p1 + p2 + p3 + p4)]/2= (9/2) × √(2BC² + p1² + p3²) + (p1 + p2 + p3 + p4)/2

The sum of perpendiculars from opposite vertices on a diagonal is 12 cm.

Therefore,p1 + p3 = 12 – p2 – p4

We substitute this in the above equation to get:

Area of quadrilateral= (9/2) × √(2BC² + (12 – p2 – p4)²) + (12 – p2 – p4)/2.

This is the required solution.

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The volume of the given shape is  392.7hr² sq. units.

Given, the base of S is a circular disk with radius 5r.

Parallel cross-sections perpendicular to the base are isosceles triangles with height 5h and unequal side in the base.

we have to find the volume of the shape we are given,

As, Volume = area × height

Now, area = πr²

area = 3.14×(5r)²

area = 78.54r²

as, height = 5h

then, Volume = 78.54r²×5h

Volume = 392.7hr²

Hence, the volume of the given shape is  392.7hr² sq. units.

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