A survey was given to a random sample of 1350 residents of a town to determine whether they support a new plan to raise taxes in order to increase education spending. Of those surveyed, 26% of the people said they were in favor of the plan. Determine a 95% confidence interval for the percentage of people who favor the tax plan, rounding values to the nearest tenth.

Answer:

  an = (5/16)2^(n -1)

Step-by-step explanation:

The explicit formula for the n-th term of a geometric sequence is ...

  an = a1·r^(n-1)

Filling in the given values, we get two equations in a1 and r:

  a5 = 5 = a1·r^(5 -1)

  a9 = 80 = a1·r(9 -1)

Dividing the second equation by the first gives ...

  80/5 = (a1·r^8)/(a1·r^4)

  16 = r^4

  2 = r . . . . . . . . because we know 2^4 = 16. You could also solve using logarithms

Then we can find a1 from ...

  5 = a1·r^4 = 16·a1

  5/16 = a1

The explicit formula is ...

  an = (5/16)2^(n -1)

__

The above formula matches the form of the equation usually expected. However, we can make the fraction go away by adjusting the exponent:

  an = 5(2^-4)(2^(n-1))

  an = 5·2^(n -5)

Answer:

Step-by-step explanation:

y = mx + c

Here, m is the slope & c is the y-intercept

y = -3x - 1

Slope = -3

y intercept = -1

Answer:

Angle 5

Step-by-step explanation:

Adjacent angles share a common side and a common vertex.

Answer:

The maximum height of the ball is 256m

Step-by-step explanation:

Given the equation of a pathway modelled as pathway can be modeled by h = -16t² + 128t

At maximum height, the velocity of the ball is zero.

velocity = dh/dt

velocity = -32t + 128

Since v = 0 at maximum height

0 = -32t+128

32t = 128

t = 128/32

t = 4seconds

The maximum height can be gotten by substituting t = 4 into the modelled equation.

h = -16t² + 128t

h = -16(4)²+128(4)

h = -16(16)+512

h = -256+512

h = 256m

The maximum height of the ball is 256m.

Since the equation should be [tex]h = -16t^2 + 128t[/tex]

Also we know that at the maximum height, the velocity of the ball should be zero

So,

[tex]velocity = dh/dt[/tex]

velocity = -32t + 128

Now

0 = -32t+128

32t = 128

t = 4seconds

Now

[tex]h = -16t^2 + 128t\\\\h = -16(4)^2+128(4)[/tex]

h = -16(16)+512

h = -256+512

h = 256m

hence, The maximum height of the ball is 256m.

Learn more about height here: https://brainly.com/question/21551182

Considering Ray uses 8 pieces of wood per box, the equation representing how many boxes, y, Ray can make with x pieces of wood is y = x/8. This concept originates from the field of algebra, part of middle school mathematics.

The subject of this question is mathematics as it discusses an equation that needs to be solved, a key component in algebra. The grade level of the student asking this question sits around middle school, as learning to solve these kinds of algebraic problems are typically introduced at this stage.

If Ray uses 8 pieces of wood for each box he makes, we can say that the number of boxes, y, that Ray can make given x pieces of wood is represented by the equation y = x/8. This equation basically says that the number of boxes Ray can make (y) equals the total number of pieces of wood he has (x) divided by the number of pieces each box requires (8). So if Ray has say, 80 pieces of wood, he could make 10 boxes because 80 divided by 8 is 10.

.

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Answer:

1/5 probability

Step-by-step explanation:

1) The total number of jelly beans is 20. This will be your denominator.

2) There are 4 red jelly beans. This is your numerator.

3) Using the numerator and denominator we have, your fraction is 4/20.

4) That can be simplified into 1/5.

Answer:

y-1=2(x-2)

Step-by-step explanation:

Answer:

x (-11/2,0) y (0, 11)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The given function is

[tex]g(x)=10.75+8.14(x-1)[/tex]

The statements that best represent the formula are:

You can deduct that from the formula, because [tex]x[/tex] represents hour, so for [tex]x=1[/tex], we have

[tex]g(0)=10.75+8.14(1-1)=10.75[/tex]

Which means 1 hour costs $10.75.

Then, for [tex]x=2[/tex]

[tex]g(2)=10.75+8.14(2-1)=10.75+8.14=18.89[/tex]

Which means an additional hour cost $8.14 additionally.

The function g(x) = 10.73 + 8.14(x - 1) represents the linear charge for airport parking, with a starting fee of $10.73 and an additional daily rate of $8.14.

The function g(x) = 10.73 + 8.14(x - 1) represents the charge for parking at the airport for x number of days. The initial amount, when x=1, is $10.73, which can be interpreted as the base fee for the first day of parking. Each additional day costs $8.14 more than the previous day. This is a typical example of a linear equation, where the constant term represents a starting value and the coefficient of the variable represents the constant rate of change.

Answer:

936cm

Step-by-step explanation:

204+216=420+240=660+276=936

Answer: 320 m²

Step-by-step explanation:

10m × 8m× 4m = 320

i don't know if the formula is the same in english cause im french but i learned it with the formula long side ×wide side×deep side

Answer:

12 and 13

Step-by-step explanation:

use a calculator ツ

Answer:

12-13

Step-by-step explanation:

Answer:

William Jones was the first Math teacher to use pi

Step-by-step explanation:

Answer:

William Jones

Step-by-step explanation:

Answer:

[tex]\frac{26}{100}[/tex]

Step-by-step explanation:

[tex]\frac{6}{100}[/tex] can stay untouched, but [tex]\frac{2}{10}[/tex] has to be changed to [tex]\frac{20}{100}[/tex]. Now that they have they have the same denominator, you can add them. [tex]\frac{6}{100} + \frac{20}{100} = \frac{26}{100}[/tex], which can be simplified, which is [tex]\frac{13}{50}[/tex].

Answer:

13/50

Step-by-step explanation:

6/100 + ¹⁰⁾2/10 =

6/100 + 20/100

(6 + 20)/100

26⁽²/100

13/50

Answer: 1/5

Step-by-step explanation:

Hi, to answer this question we simply have to divide the amount of bagel left over (4/5) by the number of employees (4)

Mathematically speaking:

4/5 bagel ÷ 4 employees = 1/5 bagel

In conclusion, each employee received 1/5 of bagel.

Feel free to ask for more if needed or if you did not understand something.

Answer:

12.35

Step-by-step explanation:

Plugin value in place of the variables.

Hope this helps! Good luck :-)

Answer:

x = 0, 9/25

Step-by-step explanation:

25x² = 9x

25x² - 9x = 0

x(25x - 9) = 0

x = 0

25x - 9 = 0

x = 9/25

Answer:

The answer is 5 and 4

Step-by-step explanation:

The reason this is the answer is 5*4 is 20 and 5+4 is 9

Answer:

its 1

Step-by-step explanation:

Let's the length of rectangle x cm, then its width is (13-x) cm. since the area is 12 cm^2 we write:

(13-x)Xx=12

we get the width: x=1cm and the length is 13-12=1cm.

good day and be safe

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Answer:

the answer depends on which type of interest we use:

Step-by-step explanation:

the interest rate paid for holding the cards one month 1/50 or 2%.

to convert 2% monthly interest rate to a simple annual rate:

monthly rate x 12 months = 2% x 12 = 24%

now to convert 2% monthly interest rate to an annual rate (using compound interest):

in compound interest, earned interest earns even more interest by itself besides the interest earned by the principal.

Answer:

y=2

Step-by-step explanation:

y= 2x - 2

Let x =2

y = 2(2)-2

y = 4-2

y = 2

Final answer:

To find the value of y when x equals 2 in the equation y = 2x - 2, we substitute 2 for x, giving us y = 4 - 2, which simplifies to y = 2.

Explanation:

The student asks for the value of y when x is equal to 2 in the equation y = 2x - 2. To find the value of y, we replace x with 2 in the equation and solve for y.

So we get:

y = 2(2) - 2

y = 4 - 2

y = 2

Therefore, the value of y when x equals 2 in the given equation is 2.

Answer:

t = 2.5 s

Step-by-step explanation:

Suppose you have a water-balloon launcher. The balloon is 3 ft high when it leaves the launcher. Its equation is :

[tex]16t^2 + 38.8t + 3 =0[/tex]

The above equation is a quadratic equation. The general equation is :

[tex]ax^2+bx+c=0[/tex]

Here, a = 16, b = 38.8 and c = 3

The solution of quadratic equation is given by :

[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}\\\\t=\dfrac{-38.8\pm \sqrt{(38.8)^2-4\times (-16)\times 3} }{2\times (-16)}\\\\t=\dfrac{-38.8+\sqrt{(38.8)^{2}-4\times-16\times3}}{-2\times16}, \dfrac{-38.8-\sqrt{(38.8)^{2}-4\times-16\times3}}{-2\times16}\\\\t=-0.075\ s,2.5\ s[/tex]

So, at t = 2.5 s the balloon is in air.

The water balloon is in the air for approximately 2.51 seconds. We discard the negative solution as time cannot be negative.

To determine the number of seconds t that the balloon is in the air, we need to solve the quadratic equation 0 = -16t² + 38.8t + 3. This can be solved using the quadratic formula:

⇒ t = (-b ± √(b² - 4ac)) ÷ 2a,

where a = -16, b = 38.8, and c = 3.

⇒ Δ = b² - 4ac

⇒ (38.8)² - 4(-16)(3) = 1505.44 + 192

= 1697.44.

⇒ √1697.44 ≈ 41.21.

⇒ t = ( -38.8 ± 41.21 ) ÷ -32.

⇒ t₁ = ( -38.8 + 41.21 ) ÷ -32

≈ -0.076 (discarded because time cannot be negative).

⇒ t₂ = ( -38.8 - 41.21 ) ÷ -32

≈ 2.51 seconds.

The balloon is in the air for approximately 2.51 seconds.

Complete question:

Suppose you have a water-balloon launcher. The balloon is 3 ft high when it leaves the launcher. Use the equation 0 = -16t² + 38.8t + 3 to find the number of seconds t that the balloon is in the air.

Answer:

Step-by-step explanation:

when you break a vector into its parts, those parts are called its components. For example, in the vector (4, 1), the x-axis (horizontal) component is 4, and the y-axis (vertical) component is 1. Typically, a physics problem gives you an angle and a magnitude to define a vector; you have to find the components yourself using a little trigonometry.

Suppose you know that a ball is rolling on a flat table at 15 degrees from a direction parallel to the bottom edge at a speed of 7.0 meters/second. You may want to find out how long the ball will take to roll off the edge 1.0 meter to the right.

Define your axes so the ball is at the origin initially and the x-axis is parallel to the bottom edge of the table (refer to the figure). Therefore, the problem breaks down to finding out how long the ball will take to roll 1.0 meter in the x direction. To find the time, you first need to know how fast the ball is moving in the x direction.

The problem tells you that the ball is rolling at a speed of 7.0 meters/second at 15 degrees to the horizontal (along the positive x-axis), which is a vector: 7.0 meters/second at 15 degrees gives you both a magnitude and a direction. What you have here is a velocity — the vector version of speed. The ball’s speed is the magnitude of its velocity vector, and when you include a direction to that speed, you get the velocity vector v.

To find out how fast the ball is traveling toward the table edge, you need not the ball’s total speed but the x component of the ball’s velocity. The x component is a scalar (a number, not a vector), and you write it like this: vx. The y component of the ball’s velocity vector is vy. Therefore, you can say that

v = (vx, vy)

That’s how you express breaking a vector up into its components. So what’s vx here? And for that matter, what’s vy, the y component of the velocity? The vector has a length (7.0 meters/second) and a direction

And you know that the edge of the table is 1.0 meter to the right.

As you can see in the figure, you have to use some trigonometry to resolve this vector into its components. No sweat. The trig is easy after you get down the angles you see in the figure.

The magnitude of a vector v is expressed as v, and from the figure, you can see that the following is true:

The two vector-component equations are worth knowing because you see them a lot in any beginning physics course. Make sure you know how they work, and always have them at your fingertips.

Of course, if you forget these equations, you can always retrieve them from basic trigonometry. You may remember that the sine and cosine of an angle in a right triangle are defined as the ratio of the opposite side and the adjacent side to the hypotenuse, like so:

By multiplying both sides of these equations by v, you can express the x and y components of the vector as

You can go further by relating each side of the triangle to each other side (and if you know that

you can derive all these from the previous two equations as required; no need to memorize all these):

You know that

so you can find the x component of the ball’s velocity, vx, this way:

Plugging in the numbers gives you

You now know that the ball is traveling at 6.8 meters/second to the right. And because you also know that the table’s edge is 1.0 meter away, you can divide distance by speed to get the time:

Because you know how fast the ball is going in the x direction, you now know the answer to the problem: The ball will take 0.15 seconds to fall off the edge of the table. What about the y component of the velocity? That’s easy to find, too:

Answer:

254

Step-by-step explanation:

The median of a set of data is basically the middle number of the data when placed in least to greater order.

example:

1,2,3,4,5,

in this case (the example) the median is 3 becasue it is the middle number of the 5 numbers (thier are two numbers to the left of 3 and 2 numbers to the right of 3)

Going back to the question being asked if you put that data in order you would get a sequence of

154, 205, 244, 244, 253, 254, 263, 274, 276, 389, 431

now try eliminating a number from each end side one by one (alternating) until you have one number left.

For instance remove 154 and 431, then remove 205 and 389 etc

IF DONE CORRECTLY you would have 254 as the remaining number.

Answer:

254

Step-by-step explanation:

First, put the numbers in order.

431, 154, 254, 244, 244, 276, 263, 389, 253, 274, 205

154, 205, 244, 244, 253, 254, 263, 274, 276, 389, 431

The median of a data set is the middle number.

154, 205, 244, 244, 253, 254, 263, 274, 276, 389, 431

Best of Luck!

Answer:

If repeating 72/99 always create the non repeating and subtract 1 from the denom. now reduce ... subtract the equations with the same digits after the decimal point 72.727272= 100x ... Which numbers from 1 to 10 could be the denominator? THANK YOU! ... Write the fraction in simplest form and equivalent decimal. asked by ...

25 answers

Step-by-step explanation:

Answer:

Step-by-step explanation:

x = 0.7272....  

Two digits are repeating. so, multiply both sides by 100

100x = 72.7272.......

     x =   0.7272........    {Subrtact}

99x = 72

[tex]x=\frac{72}{99}\\\\x=\frac{8}{11}[/tex]

Answer:

D (all real numbers)

Step-by-step explanation:

The domain is the possible input values

The input can be any value of x, so it is all real number

Answer:

-8

Step-by-step explanation:

When we subtract a negative it is like adding

-13 + 5

The signs are different so we subtract and take the sign of the larger

13 -5

8

The 13 is larger so we take its sign, which is negative

-8

Answer:

-8

Step-by-step explanation:

-13 - (-5)

-13 + 5

-8

9514 1404 393

Answer:

  D)  15

Step-by-step explanation:

The Pythagorean theorem is helpful.

  17² = 8² + ?²

  289 = 64 + ?²

  225 = ?²

  √225 = ? = 15

The diameter is 15.

Answer:

44

Step-by-step explanation:

Nothing that's bigger goes into both numbers

Answer:

44

Step-by-step explanation:

220 and 88 greatest common factor is 44