The height of a curved support can be modeled by

f(x) = x^2/256 + 16

Find the width of the beam​

To calculate the desired sample size with a 98% confidence level and 0.65-hour margin of error, we use the appropriate formula for sample size calculation in statistics, which leads us to a required sample size of 98 bacteria.

In this case, we are trying to determine the appropriate sample size using statistical methodology. To calculate this, we can use the formula for the sample size which is n = (Z∗σ/E)^2. Here, 'Z' is the z-value corresponding to the desired confidence level (for 98% confidence, Z score or z-value is 2.33), σ is the standard deviation (which is 4.8 hours in this case), and 'E' is the desired margin of error (0.65 hours).

Substituting these values into the formula gives: n = (2.33∗4.8/0.65)^2. After simplifying this calculation, we get n = 97.46. However, we can't have a fractional part of a sample, so we round up to the nearest whole number which is 98. So, you would need a sample size of 98 bacteria in order to achieve a 0.65-hour margin of error at a 98% confidence level.

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Answer:

Step-by-step explanation:

This is one of the more interesting motion problems I've seen.  I like it!  If Kelly is driving north (straight up) for 9 miles, then turns east (right) and drives for 12 miles, what we have there are 2 sides of a right triangle.  The hypotenuse is created by Brenda's trip, which originated from the same starting point as Kelly and went straight to the destination, no turns.  We need the distance formula to solve this problem, so that means we need to find the distance that Brenda drove.  Using Pythagorean's Theorem:

[tex]9^2+12^2=c^2[/tex] and

[tex]81+144=c^2[/tex] and

[tex]225=c^2[/tex] so

c = 15.

Brenda drove 15 miles.  Now we can fill in a table with the info:

                d        =        r        x        t

Kelly     12+9               42                t

Brenda    15                45                t

Because they both left at the same time, t represents that same time, whatever that time is.  That's our unknown.

If d = rt, then for Kelly:

21 = 42t

For Brenda

15 = 45t

Solve Kelly's equation for t to get

t = 1/2 hr or 30 minutes

Solve Brenda's equations for t to get

t = 1/3 hr or 20 minutes

That means that Brenda arrived at the destination 10 minutes sooner than Kelly.

Answer:

The estimated weight is in the range:

75.6 pounds [tex]\leq[/tex] Weight [tex]\leq[/tex] 92.4 pounds

Step-by-step explanation:

Since, the maximum error is 10%.

Therefore, the maximum and minimum vales will be 10% more and 10% less than 84 pounds, respectively.

For Maximum Limit:

[tex]Weight_{max}[/tex] = (1.1)(84 pounds)

[tex]Weight_{max}[/tex] = 92.4 pounds

For Minimum Limit:

[tex]Weight_{min}[/tex] = (0.9)(84 pounds)

[tex]Weight_{min}[/tex] = 75.6 pounds

Hence, the estimated weight is in the range:

75.6 pounds [tex]\leq[/tex] Weight [tex]\leq[/tex] 92.4 pounds

Answer:

Explanation:

a). Description of what Brian did wrong.

Brian did not solve the inequality correctly. It seems he made several wrong steps:

b). Your work solving the inequality:

        - x < 3 - 2

        -x < 1

       x > - 1

Then the solution of the inequality is all the real numbers greater than - 1.

c). The correct solution graphed on a number line

d). The correct solution in set notation.

Three valid forms indicating the solution in set notation are:

Both the colon (:) and the straight bar (|) mean "such that".

Answer:The number of the 2- pound bags is 56 and the number of the 5- pound bags is 140

Step-by-step explanation:

Let the number of the 2- pound bags and the 5- pound bags be n since they used the same number.

5n + 2n = 196

7n=196

n= 196/7

n= 28

Therefore the number of the 2- pound bags is 2× 28= 56

and the number if the 5- pound bags is 5×28= 140

Answer:

The correct answer is B. 3 to 2.

Step-by-step explanation:

To solve this problem let suppose

English = E

History = H

Maths = M

so

E = H* 2 (there are twice as many English majors as history majors)

E = M* 3 (three times as many English majors as mathematics majors)

lets suppose E=6 then,

H = 3 and M =2

So

H to M = 3/2.

Using algebra, we establish that if the number of mathematics majors is x, then the number of English majors is 3x and history majors would be 3x/2. The ratio of history majors to mathematics majors simplifies to 3:2.

To determine the ratio of the number of history majors to the number of mathematics majors given the provided relationships among different majors, we must set up the problem with algebra. Let's assume the number of mathematics majors is x. According to the problem, there are three times as many English majors as mathematics majors, so the number of English majors is 3x. It is also stated that there are twice as many English majors as history majors. Since the number of English majors is 3x, the number of history majors must be 3x/2.

Now, we establish the ratio of history majors to mathematics majors using the numbers we have. Since we have 3x/2 for history majors and x for mathematics majors, we can write the ratio as (3x/2):x which simplifies to 3:2 since x cancels out in the ratio.

Therefore, the correct answer is B. 3 to 2.

Answer:

E. 800%

Step-by-step explanation:

Since,

u = 8d/h²      __________ eqn (1)

Now, density (d) is doubled and usage (h) is halved.

Hence the new life (u'), becomes:

u' = 8(2d)/(0.5h)²

u' = 8(8d/h²)

using eqn (1), we get:

u' = 8u

In percentage,

u' = 800% of u

In words, the percentage increase in useful life of the equipment is 800%.

Answer: E. 800%

Step-by-step explanation:

The useful life of a certain piece of equipment is determined by the following formula: u =(8d)/h^2, where u is the useful life of the equipment, in years, d is the density of the underlying material, in g/cm3, and h is the number of hours of daily usage of the equipment.

Assuming d = 1 and h = 1, then

u = (8 × 1)/1^2 = 8

If the density of the underlying material is doubled and the daily usage of the equipment is halved, it means that

d = 2 and h = 1/2 = 0.5, therefore,

u = (8 × 2)/0.5^2 = 16/0.25 = 64

64/8 = 8

The percentage increase in the useful life of the equipment is

8 × 100 = 800%

Answer:

  a.  -1/18

Step-by-step explanation:

Differentiating implicitly, you have ...

  y^2 +2xyy' -2y' +12y^2y' = 0

Solving for y', we get ...

  y'(2xy -2 +12y^2) = -y^2

  y' = -y^2/(2xy -2 +12y^2)

To make use of this, we need to know the value of x at y=1. Filling in y=1 into the given equation, we have ...

  x -2 +4 = 6

  x = 4 . . . . . . . . subtract 2

So, at the point (x, y) = (4, 1), the slope is ...

  y' = -1/(8 -2 +12)

  y' = -1/18

_____

The attached graph shows that the line with slope -1/18 appears to be tangent to the curve at (4, 1).

Answer:

Step-by-step explanation:

[tex]log_{a}(13)=4\\so~ a^{4}=13[/tex]

Answer:

option D

Step-by-step explanation:

Assume number of bulb in the hostel be 100

number of bulb on at 8 p.m.

           = 80 % of total bulb

           = 0.8 x 100 = 80 bulb

Let L be the number of light on and 100 - L be the light that are off

now,

Light on = 40 % of (100 - L) + 90 % of L

80 = 40 - 0.4 L + 0.9 L

40 = 0.5 L

 L = 80 bulb

number of bulbs which were off = 100-80 = 20 bulb

number of bulbs that are on are supposed to be off =  40 % of 20

                = 0.4 x 20 = 8 bulbs

percentage = [tex]\dfrac{8}{80}}\times 100[/tex]

                   = 10 %

Hence, the correct answer is option D

The person can roll the die in 1512 different ways to get 3 fours, 5 sixes, and 1 two in 9 rolls.

When rolling a standard six-sided die, there are 6 possible outcomes for each roll. To find the number of ways the person can get 3 fours, 5 sixes, and 1 two in 9 rolls, we can use the concept of combinations. The number of combinations of getting 3 fours, 5 sixes, and 1 two from 9 rolls is calculated by multiplying the number of ways to choose the positions of the fours, sixes, and two, and then multiplying it by the probability of each outcome.

To calculate this, we can use the formula for combinations:

C(n, r) = n! / ((n - r)! x r!)

Using this formula, we can find the number of ways to choose the positions of the fours, sixes, and two:

Finally, we can multiply these numbers together to find the total number of ways:

Total number of ways = 84 x 6 x 3 = 1512

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Answer:

20hours

Step-by-step explanation:

Jack can complete the painting in 30hours. The fraction he can paint per hour is thus 1/30

Trainee can complete the painting in 45hours, the fraction he can paint per hour is 1/45

If they are working together, the fraction that can paint in an hour is :

1/45 + 1/30 = 5/90 = 1/18

Now we know they can paint 1/18 of the room in an hour, the number of hours needed to completely paint the room is thus 1/1/18 = 18 hours

Rounding up answer to the nearest tenth is 20hours

√57 = 7.549

Round to 7.5

Answer:

7.5

Step-by-step explanation:

7.549

Answer:

A) 15 < x < 24

Step-by-step explanation:

According to the law of the triangle, we know that the lengths of any two sides of a triangle are more significant than the length of the 3rd side. Here A is the answer because 15 is the length of the first side, and 39 is the length of the third side. So the length of the 2nd side is (39-15) = 24. It means that the length of the 2nd side is included between 15<x<24.

Answer:

0.756

Step-by-step explanation:

It is given that a machine has four components, A, B, C, and D.

[tex]P(A)=P(B)=0.93, P(C)=0.95,P(D)=0.92[/tex]

If these components set up in such a manner that all four parts must work for the machine to work properly.

We need to find the probability that the machine works properly. It means we have to find the value of [tex]P(A\cap B\cap C\cap D)[/tex].

If two events X and Y are independent, then

[tex]P(X\cap Y)=P(X)\times P(Y)[/tex]

Assume the probability of one part working does not depend on the functionality of any of the other parts.

[tex]P(A\cap B\cap C\cap D)=P(A)\times P(B)\times P(C)\times P(D)[/tex]

Substitute the given values.

[tex]P(A\cap B\cap C\cap D)=0.93\times 0.93\times 0.95\times 0.92[/tex]

[tex]P(A\cap B\cap C\cap D)=0.7559226[/tex]

[tex]P(A\cap B\cap C\cap D)\approx 0.756[/tex]

Therefore, the probability that the machine works properly is 0.756.

Final answer:

The probability that the machine works properly is found by multiplying the probabilities of all four components working: P(A) * P(B) * P(C) * P(D) = 0.93 * 0.93 * 0.95 * 0.92 = 0.7513, or 75.13%.

Explanation:

To find the probability that the machine works properly, we need to calculate the probability that all four components, A, B, C, and D, are working. Since the functionality of each component is independent, we can find this combined probability by multiplying the individual probabilities together.

The probability of A working is P(A) = 0.93, B working is P(B) = 0.93, C working is P(C) = 0.95, and D working is P(D) = 0.92. So the probability of the machine working is:

P(Machine works) = P(A) * P(B) * P(C) * P(D) = 0.93 * 0.93 * 0.95 * 0.92 = 0.7513

Therefore, the probability that the machine works properly is 0.7513, which is 75.13%.

Answer:

b. Continuous

Step-by-step explanation:

Continuous variable is a variable that can take on any value between its minimum value and its maximum value. A continuous variable is a type of quantitative variable used to describe data that is measurable while Discrete variables are countable in a finite amount of time. Now, justifying whether the gallons of gasoline pumped by a filling station during a day is continuous or discrete. The number of gallons of gasoline pumped by a filling during during a day is a continuous variable because it has a measurable volume which can take value from the minimum to maximum values of the total volume of gasoline the filling station have in the storage tank.

The number of gallons of gasoline pumped by a filling station in a day is a Continuous variable because it can take on an infinite number of values between any two given points.

The number of gallons of gasoline pumped by a filling station during a day is a Continuous variable. Continuous variables are numerical variables that have an infinite number of values between any two values. A continuous variable can be numeric or date/time. For instance, the number of gallons pumped, which can take on possibly infinite values ranging from zero upwards, is a continuous variable.

In contrast, a Discrete variable is a variable whose value is obtained by counting. A Qualitative (or categorical) variable is a variable that can be put into categories, but the numbers placed on the categories have no numerical meaning. An Attribute is a specific domain within qualitative data, like a sub-category.

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Answer:

W = (P - 2L)/2 = (28- 2*8)/2 = 6

Where W is the width, P is the perimeter and L is the length of the garden.

Step-by-step explanation:

Since the equations are not given, i will try to come up with the similar equation than the ne that was the correct option in this exercise.

You can obtain the perimeter of a rectangle by summing the length of its four sides. Thus, the perimeter of the garden, lets call it P, is 2W + 2L, where W denotes the width and L the length. Since Nancy knows the perimeter, in order to calculate the width she can substract from it 2L (which is also known), and divide by 2 to obtain W, thus

W = (P - 2L)/2

If we reemplace P by 28 and L by 8, we obtain

W = (28-8*2)/2 = (28-16)/2 ) = 12/2 = 6.

Answer: $0

Step-by-step explanation:

The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time in years

I = interest after t years

From the information given

T = 1 year

P = $450

R = 4.5%

Therefore

I = (450 × 4.5 × 1)/100

I = 2025/100

I = 20.25

For compound interest,

Initial amount deposited into the account is $450 This means that the principal,

P = 450

It was compounded annually. This means that it was compounded once in a year. So

n = 1

The rate at which the principal was compounded is 4.5%. So

r = 4.5/100 = 0.045

It was compounded for just a year. So

t = 1

The formula for compound interest is

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

A = total amount in the account at the end of t years. Therefore

A = 450 (1+0.045/1)^1×1

A = 450(1.045) = $470.25

Compound interest = 470.25 - 450 = 20.25

The difference is 20.25 - 20.25 = 0

Answer:

$0

Step-by-step explanation:

There is no difference between the simple interest and compound interest at the end of one year.

Answer:

11. ∠ABC = 96°

12. (x – 2)² + (y + 3)² = 4

Step-by-step explanation:

11. The inscribe angle (the angle inside the circle, ∠ABC) is equal to half of the outer circle.

∠ABC = 1/2∠AC

∠ABC = 1/2(192°) = 96°

12. The general equation for a circle is: (x – h)² + (y – k)² = r², where

h and k are the center of the circle (h, k), and r is the radius.

Look at the graph, the circle is centered at (2, -3), so

h=2

k=-3

and the radius of the circle is 2, so

r=2

Plug it all back into the equation:

(x – h)² + (y – k)² = r²

(x – (2))² + (y – (-3))² = (2)²

(x – 2)² + (y + 3)² = 4

First, convert the APR to the periodic interest rate by dividing it by the number of compounds in a year. Then, determine the number of periods by multiplying the number of years by the number of compounds per year. Finally, use these values in the compound interest formula to find the balance.

To solve this, we first need to switch from Annual Percentage Rate (APR) to the periodic interest rate. APR is an annual measure, but interest is compounded quarterly in this case. The periodic interest rate is the APR divided by the number of compounds in a year. So 2.6% APR converted to a periodic interest rate is 0.026/4 = 0.0065.

Next we determine the total number of periods. Since we have 6 years and interest is compounded quarterly, we have 4 compounds/year * 6 years = 24 periods.

Now we can use the compound interest formula: A=P(1+r/n)^(nt), where:

Substitute these values into the formula, we get: A = 3200(1 + 0.0065)^(24), calculate this to get the balance.

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Answer:

D because x is what you subtract/add to get zero in (x − 6). x - 6 + 6 = 0

That is how the class taught me.

Answer:

The Inequality [tex]s > 768\ mi/hr[/tex] is true at which a moving object creates a sonic boom.

Step-by-step explanation:

Given:

Speed of Sound = 768 miles per hour

Also Given:

When an object travels faster than the speed of sound, it creates a sonic boom.

We need to find the inequality which is true only for speeds (s) at which a moving object creates a sonic boom

So We can say;

When;

[tex]s < 768\ mi/hr[/tex]  ⇒ Normal sound no sonic boom (false)

[tex]s = 768\ mi/hr[/tex]  ⇒ speed of sound but no sonic boom (false)

[tex]s > 768\ mi/hr[/tex]  ⇒ sonic boom is created (True)

Hence The Inequality [tex]s > 768\ mi/hr[/tex] is true at which a moving object creates a sonic boom.

Answer:

v(b)   = 4,5  mil/h      speed of the barge in still water

Step-by-step explanation:

d = v*t      barge going upstream       12 miles  and 4 hours trip

                barge returning back         12 miles  and 2 hours trip

let call   v(b) barge velocity   and

v(w)   water velocity

d  =  12 (Mil)  =  4 (h)* [(v(b) - v(w)]

  3   =  v(b)  - v(w)       (1)

d  =  12 (mil)  =  2 (h) * [ (v(b) + v(w)]

        6     =   v(b) + v(w)   (2)

Equations (1)  and (2)  is a two system equation. Solving

      from equation  (1)     v(w)  =  v(b)  - 3

By subtitution in equation (2)

         6   =  v(b)  + v(b)  - 3

         9   =  2v(b)

   v(b)   =  9/2      ⇒     v(b)   = 4,5  mil/h

This is right angle trig. We know that...

cos(18°) x hypotenuse = 100

hypotenuse = 100/cos(18°)

hypotenuse = 105.15 meters approx.

Because they want the height of the tree we want "sin(18°) x hypotenuse".

sin(18°) x 105.15 = 32.5 meters approx.

answer: 32.5 meters approx.

The required height of the tree is 32.5 meters.

Given that,
A person 100 meters from the base of a tree, observes that the angle between the ground and the top of the tree is 18 degrees.  To estimate the height h of the tree to the nearest tenth of a meter.

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.

Here,
let the height of the tree be x, and the slant height from the foot of the person to the top of the tree be h,
according to the question,
base length = 100
cos 18 = 100 / h
h = 105.14
Now,
sin 18 = x / h
sin 18 = x / 105.14
x = 32.5 meters

Thus, the required height of the tree is 32.5 meters.

Learn more about trigonometry equations here:

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Answer: c) 0.75

Step-by-step explanation:

Given : The probability of choosing a black marble is P(Black)= 0.36.

The probability of choosing a black and then a white marble is P( Black and white) = 0.27.

Then by conditional probability ,

The probability of the second marble being white if the first marble chosen is black = [tex]P(\text{white }|\text{Black})=\dfrac{\text{P( Black and white)}}{\text{P(Black}}[/tex]

[tex]=\dfrac{0.27}{0.36}=\dfrac{27}{36}=0.75[/tex]

Therefore , the probability of the second marble being white if the first marble chosen is black = 0.75

Final answer:

The probability of the second marble being white given that the first marble is black is calculated using conditional probability. By dividing the joint probability of choosing a black and then a white marble (0.27) by the probability of choosing a black marble (0.36), we find that the probability is 0.75.

Explanation:

The question asks to find the probability of the second marble being white given that the first marble chosen is black. The probability of choosing a black marble is given as 0.36, and the probability of choosing a black and then a white marble is 0.27. To find the probability of choosing a white marble after a black one, we use the concept of conditional probability, given by:

P(White | Black) = P(Black and White) / P(Black)

Here P(White | Black) is the probability of the second marble being white given that the first marble is black, P(Black and White) is the probability of choosing a black marble and then a white marble, and P(Black) is the probability of choosing a black marble. Substituting the given values:

P(White | Black) = 0.27 / 0.36 = 0.75

This means that the probability of the second marble being white, given that the first marble chosen is black, is 0.75, which corresponds to option (c) in the provided selections.

Answer:

AD is congruent to RS

Step-by-step explanation:

we know that

If two figures are congruent, then its corresponding sides and its corresponding angles are congruent

In this problem

If

ABCD≅PQRS

then

Corresponding angles

∠A≅∠P

∠B≅∠Q

∠C≅∠R

∠D≅∠S

Corresponding sides

AB≅PQ

BC≅QR

CD≅RS

AD≅PS

To find the length of the curve defined by $y=\dfrac{1}{3}(x^2+2)^{3/2}$ over the interval $1\leq x\leq 4$, we must integrate the square root of the sum of 1 and the square of the derivative of our function from 1 to 4.

To begin with, we want to find the derivative of our function. In other words, we need to compute $dy/dx$.

The derivative, with the Chain Rule gives us:
$y' = \dfrac{1}{3} \cdot \dfrac{3}{2} \cdot 2x \cdot (x^2+2)^{1/2}$
Simplifying gives:
$y' = x \cdot (x^2+2)^{1/2}$

Next, we substitute $y'$ into the formula for finding the length of a curve:

$L = \int_{a}^{b}\sqrt{1+(y')^2}dx$

We should note that $a = 1$ and $b = 4$ here. We substitute $y'=x \cdot (x^2+2)^{1/2}$ and obtain:

$L = \int_{1}^{4}\sqrt{1+(x \cdot (x^2+2)^{1/2})^2}dx$

We can now evaluate the integral, where we will square the entire derivative and add 1 as being under the square root.

So, finally, evaluating this integral gives us the length of the curve, which in this case is 24.

Therefore, the length of the curve $y=\dfrac{1}{3}(x^2+2)^{3/2}$ over the interval $1\leq x\leq 4$ is 24.

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Answer:

[tex]Sin(Cos^{-1} (14x))=\sqrt{1-196x^2}[/tex]

Step-by-step explandation:

First of all, from the figure we can define the cosine and sine functions as

[tex]Cos(theta)=\frac{adjacent }{hypotenuse }[/tex]

[tex]Sin(theta)=\frac{Opposite}{hypotenuse }[/tex]

And by analogy with the statement:

[tex]14x=\frac{adjacent }{hypotenuse }[/tex]

Which can be rewritten as:

[tex]\frac{14x}{1}=\frac{adjacent }{hypotenuse }[/tex]

You have then that, for the given triangle, the values of the adjacent and hypotenuse sides, are then given by:

:

Adjacent=14x

Hypotenuse=1

And according to the Pythagorean theorem:

[tex] Opposite=\sqrt{1-(14x)^2}[/tex]

Finally, by doing:

[tex]Cos^-1(14x)=theta[/tex]

We have that:

[tex]Sin(Cos^{-1} (14x))=Sen(theta)=\frac{Opposite}{hypotenuse}=\frac{\sqrt{1-(14x)^2}}{1}=\sqrt{1-(14x)^2}[/tex]

The expression [tex]\( \sin(\cos^{-1}(14x)) \)[/tex] is equivalent to the expression [tex]\[ \sqrt{1 - 196(x)^2} \][/tex].

To express [tex]\( \sin(\cos^{-1}(14x)) \)[/tex] using a right triangle, we proceed as follows:

1. Understand the expression:

[tex]\( \cos^{-1}(14x) \)[/tex] denotes the angle [tex]\( \theta \)[/tex] such that [tex]\( \cos(\theta) = 14x \)[/tex].

We are required to find [tex]\( \sin(\theta) \)[/tex].

2. Use a right triangle:

Let's consider a right triangle where:

One of the acute angles is [tex]\( \theta \)[/tex].

Assume [tex]\( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{14x}{1} \)[/tex]

To find the opposite side (let's call it [tex]\( \sqrt{1 - (14x)^2} \))[/tex], we use the Pythagorean identity:

[tex]\[ \sin(\theta) = \sqrt{1 - \cos^2(\theta)} = \sqrt{1 - (14x)^2} \][/tex]

[tex]\[ \sin(\cos^{-1}(14x)) = \sqrt{1 - (14x)^2} \][/tex]

[tex]\[ \sin(\cos^{-1}(14x)) = \sqrt{1 - 196(x)^2} \][/tex]

Answer:

correct option is D. 54

Step-by-step explanation:

given data

product of digits = 210

integers = 10000

to find out

How many positive integers less than 10,000

solution

we know product of digits 210 are = 1 × 2× 3×5×7

210 = 1 × 6 × 5 × 7

here 2 × 3 = 6 ( only single digit )

here 4 digit numbers with combinations of the digits are = {1,6,5,7} and {2,3,5,7}

3 digit numbers with combinations of digits are = {6,5,7}

and product of their digits =  210

so combination will be

combinations of {1,6,5,7} is  4! = 4 × 3 × 2 × 1 =   24

combinations of {2,3,5,7}  is 4! =  4 × 3 × 2 × 1 = 24

combinations of {6,5,7} is 3! = 3 × 2 × 1 =  6

so total is = 24 + 24 + 6

total is = 54

so correct option is D. 54

Answer:

the individual price of a popcorn is $8.

Step-by-step explanation:

p+2d=14 is the price with deal

p+2d=14+4 if there was no deal

plug 5 into the equation as d

2(5)+p=18

solve for p.

p=8

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