A study on students drinking habits wants to determine the true average number of alcoholic drinks all FSU graduate students have in a one week period. We know from preliminary studies that the standard deviation is around 1.79. How many students should be sampled to be within 0.5 drinks of population mean with 95% probability?
A. 50
B. 49
C. 24
D. 25

Answer:

x = 2 and x = 1/2.

Step-by-step explanation:

To solve (x-2)(2x-1) = 0, we need to find the values of x that make the left side of the equation equal to 0.

Using the zero product property, we know that if the product of two factors is equal to 0, then at least one of the factors must be equal to 0.

Therefore, we have two possible solutions:

1.x - 2 = 0, which gives us x = 2

2.2x - 1 = 0, which gives us x = 1/2

So, the solutions to the equation (x-2)(2x-1) = 0 are x = 2 and x = 1/2.

Answer:x=(1-sqrt(33))/4=-1.186

x=(1+sqrt(33))/4=1.686

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

 (22x2 -  2x) -  8  = 0

STEP

2

:

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  4x2 - 2x - 8  =   2 • (2x2 - x - 4)

Trying to factor by splitting the middle term

3.2     Factoring  2x2 - x - 4

The first term is,  2x2  its coefficient is  2 .

The middle term is,  -x  its coefficient is  -1 .

The last term, "the constant", is  -4

Step-1 : Multiply the coefficient of the first term by the constant   2 • -4 = -8

Step-2 : Find two factors of  -8  whose sum equals the coefficient of the middle term, which is   -1 .

     -8    +    1    =    -7

     -4    +    2    =    -2

     -2    +    4    =    2

     -1    +    8    =    7

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step

3

:

 2 • (2x2 - x - 4)  = 0

STEP

4

:

Equations which are never true:

4.1      Solve :    2   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Parabola, Finding the Vertex:

4.2      Find the Vertex of   y = 2x2-x-4

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 2 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   0.2500  

Plugging into the parabola formula   0.2500  for  x  we can calculate the  y -coordinate :

 y = 2.0 * 0.25 * 0.25 - 1.0 * 0.25 - 4.0

or   y = -4.125

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = 2x2-x-4

Axis of Symmetry (dashed)  {x}={ 0.25}

Vertex at  {x,y} = { 0.25,-4.12}

x -Intercepts (Roots) :

Root 1 at  {x,y} = {-1.19, 0.00}

Root 2 at  {x,y} = { 1.69, 0.00}

Solve Quadratic Equation by Completing The Square

4.3     Solving   2x2-x-4 = 0 by Completing The Square .

Divide both sides of the equation by  2  to have 1 as the coefficient of the first term :

  x2-(1/2)x-2 = 0

Add  2  to both side of the equation :

  x2-(1/2)x = 2

Now the clever bit: Take the coefficient of  x , which is  1/2 , divide by two, giving  1/4 , and finally square it giving  1/16

Add  1/16  to both sides of the equation :

 On the right hand side we have :

  2  +  1/16    or,  (2/1)+(1/16)

 The common denominator of the two fractions is  16   Adding  (32/16)+(1/16)  gives  33/16

 So adding to both sides we finally get :

  x2-(1/2)x+(1/16) = 33/16

Adding  1/16  has completed the left hand side into a perfect square :

  x2-(1/2)x+(1/16)  =

  (x-(1/4)) • (x-(1/4))  =

 (x-(1/4))2

Things which are equal to the same thing are also equal to one another. Since

  x2-(1/2)x+(1/16) = 33/16 and

  x2-(1/2)x+(1/16) = (x-(1/4))2

then, according to the law of transitivity,

  (x-(1/4))2 = 33/16

We'll refer to this Equation as  Eq. #4.3.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x-(1/4))2   is

  (x-(1/4))2/2 =

 (x-(1/4))1 =

  x-(1/4)

Now, applying the Square Root Principle to  Eq. #4.3.1  we get:

  x-(1/4) = √ 33/16

Add  1/4  to both sides to obtain:

  x = 1/4 + √ 33/16

Since a square root has two values, one positive and the other negative

  x2 - (1/2)x - 2 = 0

  has two solutions:

 x = 1/4 + √ 33/16

  or

 x = 1/4 - √ 33/16

Note that  √ 33/16 can be written as

 √ 33  / √ 16   which is √ 33  / 4

Solve Quadratic Equation using the Quadratic Formula

4.4     Solving    2x2-x-4 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     2

                     B   =    -1

                     C   =   -4

Accordingly,  B2  -  4AC   =

                    1 - (-32) =

                    33

Applying the quadratic formula :

              1 ± √ 33

  x  =    —————

                   4

 √ 33   , rounded to 4 decimal digits, is   5.7446

So now we are looking at:

          x  =  ( 1 ±  5.745 ) / 4

Two real solutions:

x =(1+√33)/4= 1.686

or:

x =(1-√33)/4=-1.186

Two solutions were found :

x =(1-√33)/4=-1.186

x =(1+√33)/4= 1.686

Answer:

x = 1

Step-by-step explanation:

[tex] {4}^{x} + 2 \times {2}^{x} - 8 = 0 [/tex]

[tex] {2}^{2x} + 2 \times {2}^{x} - {2}^{3} = 0[/tex]

[tex]substitute \: {2}^{x} = a[/tex]

[tex]a > 0[/tex]

[tex] {a}^{2} + 2 \times a - 8 = 0[/tex]

According to the Wiet theorem:

[tex]a1 = 2[/tex]

[tex]a2 = - 4[/tex]

[tex]when \: a = 2 \: \: \: \: {2}^{x} = {2}^{1} [/tex]

[tex]x = 1[/tex]

[tex]when \: a = - 4 \: \: \: \: {2}^{x} = - 4 \: \: \\ \: \: \: \: \: \: - 4 < 0[/tex]

[tex]x∈∅[/tex]

Step-by-step explanation:

A. 7

B. 22,5

C. symmetrical, because the mean and the median are not the same

The final amount after 2 years of compounding semiannually at 11% is $31,909.52.

First we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where

Plugging in the given values, we get:

P = $24,700

r = 0.11 (11% annual rate as a decimal)

n = 2 (compounded semiannually, or twice per year)

t = 2 (2 years)

A = $24,700(1 + 0.11/2)^(2*2)

= $31,909.52

Therefore, the final amount after 2 years of compounding semiannually at 11% is $31,909.52.

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Alpha for this confidence interval is approximately 0.021 when rounded to 3 decimals.

We can follow these steps:

Determine the z-score that corresponds to the given margin of error.

Use the z-score to find the alpha level.

Step 1: Determine the z-score
We know the margin of error (M) formula is:

M = z * (population standard deviation / sqrt(sample size)).

We are given M = 0.708219250861584, population standard deviation = 1.92, and sample size = 31. We need to find the z-score.

0.708219250861584 = z * (1.92 / √(31))
To solve for z, divide both sides by (1.92 / √(31)):

z = 0.708219250861584 / (1.92 / √(31))
z ≈ 2.036

Step 2: Use the z-score to find the alpha level

A z-score of 2.036 corresponds to an alpha level of 0.042 (which you can find using a z-table). Since the confidence interval is two-tailed, we need to divide the alpha by 2:

Alpha (α) = 0.042 / 2
α ≈ 0.021

So, the alpha for this confidence interval is approximately 0.021 when rounded to 3 decimals.

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Answer:

1/6

Step-by-step explanation:

theres only 1, 3 and 6 possibilities

Answer:

Possible Outcomes and Sums Just as one die has six outcomes and two dice have 6 2 = 36 outcomes, the probability experiment of rolling three dice has 6 3 = 216 outcomes. This idea generalizes further for more dice.

Therefore, the angle at which the ellipse x² + 3y² = 12 is seen from the point M (0,4) is -30 degrees.

An ellipse is a geometric shape that resembles a stretched or squished circle. It can be defined as the set of all points in a plane, such that the sum of the distances from two fixed points, called the foci, is constant. An ellipse has two axes, a major axis and a minor axis, which intersect at the center of the ellipse. The length of the major axis is twice the distance from the center to one of the foci, while the length of the minor axis is twice the distance from the center to one of the points where the ellipse intersects the major axis. Ellipses have many applications in mathematics, physics, and engineering. They are used to model the orbits of planets and satellites, as well as the paths of objects in electric and magnetic fields. They are also used in optics to describe the shape of lenses and mirrors, and in statistics to model data distributions.

Here,

To determine the angle at which the ellipse x² + 3y² = 12 is seen from the point M (0,4), we first need to find the equation of the tangent line to the ellipse at the point (0,4).

To do this, we take the derivative of the equation of the ellipse with respect to x and evaluate it at the point (0,4):

d/dx (x² + 3y²) = 2x + 6y(dy/dx)

At the point (0,4), we have x = 0 and y = 4, so the equation becomes:

0 + 6(4)(dy/dx) = 0

Solving for dy/dx, we get:

dy/dx = 0

This means that the tangent line to the ellipse at the point (0,4) is a horizontal line passing through the point (0,4).

Now we can find the angle at which the ellipse is seen from the point M (0,4) by finding the angle between the horizontal tangent line and the line connecting the point M to the origin. This angle is given by:

tan θ = (y₂ - y₁)/(x₂ - x₁)

where (x₁, y₁) = (0,4) is the point M and (x₂, y₂) is the point where the tangent line intersects the x-axis.

Since the tangent line is horizontal, it intersects the x-axis at the point (±2√3, 4), which are the x-intercepts of the ellipse. Choosing the positive x-intercept, we have:

x₂ = 2√3

y₂ = 0

Substituting these values into the formula for the tangent, we get:

tan θ = (0 - 4)/(2√3 - 0) = -2/2√3 = -1/√3

Taking the inverse tangent of both sides, we get:

θ = -30 degrees

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A)  120 is 30% percent of 400.

Percent Proportion - 120 : 400 = 3 : 10

Percent Equation - 120 = 30% of 400

Percentage means a number οr a ratiο represented in the fοrm οf fractiοns οf 100. It is represented using the percentage sign ‘%’. The abbreviatiοns used tο represent the percentage are ‘pct’ οr ‘pc’. In οther wοrds, the percentage is defined as hοw much οf οne quantity is made by anοther quantity and it is evaluated in terms οf 100.

A) Let x be the unknown percentage.

We can write:

120 = x % of 400

To solve for x, we can divide both sides by 400:

120/400 = x/100

Simplifying the left side:

0.3 = x/100

To solve for x, we can cross-multiply:

100x = 30

x = 30/100

x = 0.3

Converting to a percentage:

x = 0.3 * 100

x = 30%

Percent Proportion - 120 : 400 = 3 : 10

Percent Equation - 120 = 30% of 400

B) x = 4% of 975

x = 4/100 × 975

x = 39

Percent Proportion - 39 : 975 = 1 : 25

Percent Equation - 39 = 4% of 975

C) x = 12.5% of $100

x = 12.5/100 × 100

x = $12.5

Percent Proportion - 12.5 : 100= 1 : 8

Percent Equation - $12.5 = 12.5% of $100

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There are 15 different 2-member committees that can be formed from the 6 members of the high school student council as per combination.

In mathematics, a combination is a way of selecting objects from a larger group without considering the order in which they are chosen. A combination is also known as a binomial coefficient or a choose function, and is denoted by the symbol "n choose k", where n is the total number of objects and k is the number of objects to be selected.

In mathematics, a permutation is an arrangement of objects in a specific order. The number of possible permutations of a set of n distinct objects is given by n!, which is the product of all positive integers up to n.

The number of different 2-member committees that can be formed from a group of 6 members is given by the combination formula:

C(6, 2) = 6! / (2! * (6 - 2)!) = 15

where C(n, r) represents the number of combinations of r items that can be selected from a group of n items.

Therefore, there are 15 different 2-member committees that can be formed from the 6 members of the high school student council to attend the rally in Washington D.C.

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The temperature of the pizza after 20 minutes will be 25 degrees.

the slope refers to the measure of the steepness or inclination of a line.

We can create a linear model to describe the relationship between time and temperature.

So, slope (m) = [tex]\frac{(y_2 - y_1)}{(x_2 - x_1)}[/tex]

Using the temperature and time values from the first and last data points:

m = [tex]\frac{(145 - 450)}{(16 - 0)}[/tex]

m = -305/16

Using the point-slope form of the equation of a line, we can now ascertain the equation of the line:

y - y₁ = m(x - x₁)

Using the first data point (0, 450);

y - 450 = (-305/16)(x - 0)

Simplifying, y = (-305/16)x + 450

To predict the temperature after 20 minutes, we can plug in x = 20 and solve for y:

y = (-305/16)(20) + 450

y = -950/16 + 450

y = 25

Therefore, we can predict that the temperature of the pizza after 20 minutes will be approximately 25 degrees.

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Answer:

107 hamburgers

Step-by-step explanation:

Let's call hamburgers A and cheese burgers B.

We know that A + B = 321

And that the number of cheeseburgers sold was two times the number of hamburgers sold which means ->  B = 2A

So A + 2A = 321

3A = 321

Now you need to divide both sides of the equation by 3 and you get:

A= 107

Answer:

D

Step-by-step explanation:

The gradient of the line y = -3x+2 is -3 so the gradient of the perp line will be ⅓

Now y=mx+c

8 = (⅓×6) + c

C = 6

Y = ⅓x + 6

Answer:its 4

Step-by-step explanation:

none

Answer:

False.

Step-by-step explanation:

Use Pythagorean theorem.

919681+1022121=1067089

1941802≠1067089

so the triangle is acute, not right.

Since no specific figure or measurements were provided in the student question, it's important to follow these steps for any given 3-dimensional shape.

To find the volume and surface area of a figure, follow these steps:
Identify the type of figure
Determine the shape of the figure, whether it's a sphere, cube, cylinder, or another 3-dimensional shape.
Determine the necessary measurements
Depending on the figure, gather measurements like the length, width, height, or radius.
Calculate the volume
Use the appropriate formula for the figure's volume:
- Cube: [tex]V = L^3[/tex](L = length)
- Rectangular prism: V = L * W * H (L = length, W = width, H = height)
- Sphere: V = (4/3) * π * [tex]r^3[/tex](r = radius)
- Cylinder: V = π *[tex]r^2[/tex] * h (r = radius, h = height)
Calculate the surface area
Use the appropriate formula for the figure's surface area:
- Cube: SA = 6 *[tex]L^2[/tex] (L = length)
- Rectangular prism: SA = 2 * (L * W + L * H + W * H) (L = length, W = width, H = height)
- Sphere: SA = 4 * π * [tex]r^2[/tex] (r = radius)
- Cylinder: SA = 2 * π * r * (r + h) (r = radius, h = height)
Round your answers to the nearest hundredth, if necessary
Use standard rounding rules to round the calculated volume and surface area to the nearest hundredth.

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The slope of the function is 1.

The whole function is simply f(x)=x+3

The co-ordinates of the x and y intercept of the line equation is 2y+ 3x = 1, are (1/2,0) and (0, 1/3) respectively. Gradient of above line is equals to the -3/2.

The X and Y intercepts and the Slope are collectively called the line properties. Gradient is used to measure the steepness of a slope. The formula to determine the gradient of a line is written as, m = Δy/Δx, where m represents the gradient of the line. We have an equation

2y + 3x = 1 --(1)

First, we determine the co-ordinates of x and y intercept of the line (1). For x intercept, substitute y = 0, then

=> 2(0) + 3x = 1

=> 3x = 1

=> x = 1/3

Similarly, for y intercept substitute x = 0 in line (1)

=> 2y + 3(0) = 1

=> 2y = 1

=> y = 1/2

Thus, x and y intercept are 1/3 and 1/2 respectively. Rewrite the equation of line (1) that is in slope-intercept form, 2y + 3x = 1

=> 2y = -3x + 1

dividing by 2

=> y = (-3/2)x + 1/2 --(2)

comparing this equation (2) with y = mx + c, where m is slope of line, so m = -3/2. Therefore, the gradient of line is (-3/2).

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The degree of the polynomial is 2, and the leading coefficient is 3. The polynomial has two terms, so we classify it as a binomial.

What is the polynomial equation?

A polynomial equation is an equation in which the variable(s) are raised to non-negative integer powers and the coefficients are constants. In other words, it is an equation in which the terms involve only addition, subtraction, multiplication, and positive integer exponents.

Assuming that the expression is 7 + 3p²:

To write the polynomial in standard form, we need to arrange the terms in descending order of degree:

3p² + 7

hence, The degree of the polynomial is 2, and the leading coefficient is 3. The polynomial has two terms, so we classify it as a binomial.

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The principal will be outstanding at the halfway time C) p = $3218 & P(180) = 313,722.

Principal is an amount of money borrowed or invested, on which interest is paid. It is the original sum of money that is invested or borrowed and not the interest that accumulates over time. Principal is the amount of money before any interest or other costs are added. Borrowers must pay back the principal plus interest when the loan is due. Investors can earn returns on their principal when an investment is successful.

The payment for a 30 year $400,000 mortgage at 9% compounded monthly is calculated using the following formula:
p = (400000 * (1 + (0.09/12))³⁶⁰)/(360 * (1 - (1 + (0.09/12))^⁻³⁶⁰))
Plugging in the given values, we get:
p = (400000 * (1 + (0.09/12))³⁶⁰)/(360 * (1 - (1 + (0.09/12))^-360)) = $3218
The amount of principal outstanding at the halfway time (180 payments) is calculated using the following formula:
P(180) = 400000 - (p * 180)
Plugging in the given values, we get:
P(180) = 400000 - (3218 * 180) = 313,722
Therefore, the answer is C) p = $3218 & P(180) = 313,722.

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If You take a 30 year $400,000 mortgage at 9% compounded monthy. the paynebt will be $3218 and P(180) = 317,322.  The correct answer is A) p = $3218 & P(180) = 317,322.

What is probability?

Probability is a branch of mathematics that deals with the study of random events or phenomena. It involves the measurement of the likelihood or chance of an event occurring, based on the ratio of the number of favorable outcomes to the total number of possible outcomes.

To calculate the monthly payment for the mortgage, we can use the formula:

P = A / ((1 - (1 + r)^(-n)) / r)

where P is the monthly payment, A is the loan amount ($400,000), r is the monthly interest rate (9%/12 = 0.0075), and n is the total number of payments (30 years x 12 months/year = 360 payments).

P = 400000 / ((1 - (1 + 0.0075)^(-360)) / 0.0075)

P = $3,219.64 (rounded to the nearest cent)

Therefore, the monthly payment is $3,219.

To find the outstanding principal balance at the halfway time (180 payments), we can use the formula for the remaining balance of a loan after t payments:

P(t) = A * ((1 + r)^t - 1) / (r * (1 + r)^t)

where P(t) is the remaining principal balance after t payments.

P(180) = 400000 * ((1 + 0.0075)^180 - 1) / (0.0075 * (1 + 0.0075)^180)

P(180) = $313,721.87 (rounded to the nearest dollar)

Therefore, the correct answer is A) p = $3218 & P(180) = 317,322.

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Answer:

Step-by-step explanation:

The Answer is 203 Fahrenheit.

(95 x 9/5) + 32 = 203

Answer:

see below

Step-by-step explanation:

[tex]\text{Average = total points / total students}[/tex]

[tex]95 = (19\times97 + \text{x}) \div 20[/tex]

[tex]1900 = 1843 + \text{x}[/tex]

[tex]\text{x} = 57[/tex]

[tex]\text{The lowest the last test score can be for the whole class to average a 95 is} \0 \ \bold{57.}[/tex]

The equation of the line with slope 6/5 that passes through the point (0,3) is y = (6/5)x + 3.

The equation of a line with slope m that passes through the point (x₁, y₁) is given by:

y - y₁ = m(x - x₁)

In this case, we know that the slope is 6/5 and the line passes through the point (0,3), so we can substitute these values into the equation:

y - 3 = (6/5)(x - 0)

Simplifying:

y - 3 = (6/5)x

Multiplying both sides by 5 to eliminate the fraction:

5y - 15 = 6x

Adding 15 to both sides:

5y = 6x + 15

Dividing both sides by 5 to solve for y:

y = (6/5)x + 3

Therefore, the equation of the line with slope 6/5 that passes through the point (0,3) is y = (6/5)x + 3.

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Answer:

Step-by-step explanation:

let x be the price of chair and y be the price of table

x = 3+ y/2

3x+y=54

putting the value of x in 2nd equation we get

9+3y/2 +y =54

5y/2=45

y/2=9

y=18

x=12

i hope you find it helpful

The answer is in the picture

No, the idea that water always goes down the drain counterclockwise in the northern hemisphere and clockwise in the southern hemisphere is a myth.

The direction that water drains is actually determined by the shape of the sink or toilet bowl, as well as any other factors such as the water pressure and the motion of the water before it enters the drain. The Coriolis effect, which is often cited as the cause of the supposed clockwise/counterclockwise rotation, only affects large-scale phenomena like weather patterns and ocean currents, and is not noticeable in small-scale phenomena like draining water. So, in reality, the direction that water drains is not determined by the hemisphere in which you are located.

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Complete question

Does water go down the drain counterclockwise in the northern hemisphere and clockwise in the southern hemisphere?

Answer:

1. -3

2. 3

Step-by-step explanation:

Given, a = 1 and b = 2

1. ( 1 + 2 )( 1 - 2 )

= (3) × (-1)

= - 3

2. ( 1 + 2 )( 2 - 1 )

= (3) × (1)

= 3

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To find how many years Napoleon Bonaparte lived, we can subtract his year of birth from his year of death:

Years lived = Year of death - Year of birth

Years lived = 1821 - 1769

Years lived = 52

Therefore, Napoleon Bonaparte lived for 52 years.

Answer: In any right angled triangle , the square of the length of the hypotenuse (longest side) is equal to the sum of square of length of the other two side (i.e. adjacent leg and opposite leg)

Answer:

number A

Step-by-step explanation:

Answer:

I think the answer is x= -0.66 . .. and continuous more 6's

Step-by-step explanation:

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