If 4 out of 21 people prefer diet soda to regular soda, about how many regular sodas should be bought to serve 864 people, if each person
receives one soda?

The answer is d.

Finding area of ABCD :

    2. Apply formula to find area

Finding area of GHIA :

Finding area of DEFG :

Now, let's see whether is true.

∴ Hence, it is proved √

The two solutions to the given quadratic equation are 2i/3, -2i/3 and they are both complex solutions.

Hence, option C is the correct answer.

Given the equation; 9x² + 4 = 0

First, we subtract 4 from both sides.

9x² + 4 = 0

9x² = -4

x² = -4/9

Take the square roots of both sides

x = ±√(-4/9)

Rewrite -4/9 as (2i/3)²

x = ±√(2i/3)²

x = ±(2i/3)

Hence,

x = 2i/3, -2i/3

Therefore the two solutions to the given quadratic equation are 2i/3, -2i/3 and they are both complex solutions.

Hence, option C is the correct answer.

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Answer:

but it says ill get 10 only

Step-by-step explanation:

I assume you're asked to compute

[tex]\displaystyle \int \frac{30x^2}{\sqrt{x-4}} \, dx[/tex]

using both of the substitutions provided.

With [tex]u=x-4[/tex], we have [tex]x=u+4[/tex] and [tex]dx=du[/tex]. Then

[tex]\displaystyle \int \frac{30x^2}{\sqrt{x-4}} \, dx = \int \frac{30(u+4)^2}{\sqrt u} \, du \\\\ ~~~~~~~~ = 30 \int \frac{u^2 + 8u + 16}{\sqrt u} \, du \\\\ ~~~~~~~~ = 30 \int \left(u^{3/2} + 8u^{1/2} + 16u^{-1/2}\right) \, du \\\\ ~~~~~~~~ = 30 \left(\frac25 u^{5/2} + \frac{16}3 u^{3/2} + 32 u^{1/2}\right) + C \\\\ ~~~~~~~~ = 12 u^{5/2} + 160 u^{3/2} + 960 u^{1/2} + C \\\\ ~~~~~~~~ = 12 (x-4)^{5/2} + 160 (x-4)^{3/2} + 960 (x-4)^{1/2} + C \\\\ ~~~~~~~~ = 4 \sqrt{x-4} \left(3 (x-4)^2 + 40 (x-4) + 240\right) + C \\\\ ~~~~~~~~ = \boxed{4 \sqrt{x-4} \left(3x^2 + 16x + 128\right) + C}[/tex]

With [tex]u=\sqrt{x-4}[/tex], we have

[tex]u^2 = x-4 \implies x^2 = (u^2+4)^2[/tex]

and [tex]2u\,du=dx[/tex]. Then

[tex]\displaystyle \int \frac{30x^2}{\sqrt{x-4}} \, dx = \int \frac{60u \left(u^2+4\right)^2}u \, du \\\\ ~~~~~~~~ = 60 \int \left(u^4 + 8u^2 + 16\right) \, du  \\\\ ~~~~~~~~ = 60 \left(\frac15 u^5 + \frac83 u^3 + 16u\right) + C  \\\\ ~~~~~~~~ = 12 (x-4)^{5/2} + 160 (x-4)^{3/2} + 960 (x-4)^{1/2} + C \\\\ ~~~~~~~~ = 4 \sqrt{x-4} \left(3 (x-4)^2 + 40 (x-4) + 240\right) + C \\\\ ~~~~~~~~ = \boxed{4\sqrt{x-4} \left(3x^2 + 16x + 128\right) + C}[/tex]

Answer:

5)

rise over run so

5/5 = 1

6)

-2/4 = -0.5

A Ferris wheel with a diameter of 10 m and makes one complete revolution every 80 seconds. Assuming that at time t = 0, the Ferris Wheel is at its lowest height above the ground of 2 m, the cosine equation of the graph drawn is, y = 5 cos [( π/40)(x - (π/2))] + 3.  Here, amplitude of the graph is 5, value of k is  π/40, d is π/2 and c is 3.

Developing the Equation of a Cosine Graph

The given information constitutes the following,

Diameter = 10 m

⇒ Radius, r = 5 m

Time, t = 80 s

Height above the ground, h = 2 m

Thus, we can infer that,

Amplitude, A = 5 m

Period, T = 80 s

Minimum height = 2 m

The cosine function is given as,

a cos [k(x − d)] + c

Here, A is amplitude

B is cycles from 0 to 2π and thus period = 2π/k

d is horizontal shift

c is vertical shift (displacement)

Now, 2π/k = 80

⇒ k = 2π/80 = π/40

The value of c is given as,

c = Amplitude - Minimum height

c = 5 - 2

c = 3

For a shift to the left by π/2 gives, we have,

d = π/2

Thus, the desired equation of the drawn cosine graph is,

y = 5 cos [( π/40)(x - (π/2))] + 3

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The  NPV of this investment if the discount rate is 10 percent is: 1.58%.

Year Cash flow  PVIF 10%  Present value

0         ($11.86)     1.000           ($11.86)

1           1.90          0.909           $1.73

2          1.90          0.826           $1.57

3          1.90           0.751           $1.43

4          1.90           0.683          $1.30

5          1.90           0.621           $1.18

6          1.90           0.564          $1.07

7          1.90            0.513          $0.98

8          1.90           0.467          $0.89

9          1.90           0.424          $0.81

10         6.45          0.386         $2.49

NPV                                          $1.58

1.9+5.25-2×35%=6.45

Hence, the NPV is $1.58.

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Answer:

males = 7

females = 43

Step-by-step explanation:

whilst it may seem intuitive to simply subtract 36 from 50, it is not saying "there are 36 males, how many females?" but instead, "the difference between the number of males and females is 36".

You can solve this equation most easily algebraically. For example:

Number of males = x

number of females = y

the question states that the total number of people = 50

therefore we can say that the total number of males (x) + the total number of females (y) = 50 people

therefore: x + y = 50

similarly, the question says that the number of males (x) + 36 = the total number of females (y)

therefore: x + 36 = y

we now have two equations:

x + y = 50

x + 36 = y

whilst both equations have two unknowns (x and y), therefore we can't simple solve for x or y, with the combination, we can see a pattern.

focusing on the second equation: x + 36 = y

we can add x to both sides, because you can pretty much do anything to the equation as long as you do it to both sides.

x + 36 + x = y + x

now this may seem very random, but you now see that one side of the equation equals y + x, and remember from the other equation, x + y = 50. Therefore we can substitute x + y in the second equation for 50.

our two equations:

x + 36 + x = y + x

x + y = 50

therefore:

x + 36 + x = 50

for the sake of clarity, we can combine like terms...

x + x = 2x

therefore:

x + 36 + x = 50

2x + 36 = 50

solve for x by subtracting 36 from both sides, then dividing both sides by 2

2x + 36 - 36 = 50 - 36

2x = 14

2x / 2 = 14 / 2

x = 7

now remember:

Number of males = 7 (we now know x = 7)

now that we've solved for x, we can go back to our original equation:

x + 36 = y

and substitute x...

7 + 36 = y

43 = y

Now remember:

Number of females = 43 (we now know y = 43)

therefore there are 7 males and 43 females. we can proof this by adding 7 and 43, and you'll see you reach 50, which is the correct total number of people.

hope this helps :)

The first ten terms of the sequence are 1, 2, 8, 33, 148, 765, 4626, 32431, 259512, 2335689.

The n-th term of the sequence is aₙ ₊ ₁ = (aₙ + 1) · n.

A sequence is a set of elements generated by at least one condition, usually an equation. In this case, the sequence is generated by a recurrence formula:

a₁ = 1, aₙ ₊ ₁ = (aₙ + 1) · n        (1)

The first ten terms of the sequence are:

n = 1

a₂ = (a₁ + 1) · 1

a₂ = 2

n = 2

a₃ = (a₂ + 2) · 2

a₃ = 4 · 2

a₃ = 8

n = 3

a₄ = (a₃ + 3) · 3

a₄ = 11 · 3

a₄ = 33

n = 4

a₅ = (a₄ + 4) · 4

a₅ = 37 · 4

a₅ = 148

n = 5

a₆ = (a₅ + 5) · 5

a₆ = 153 · 5

a₆ = 765

n = 6

a₇ = (a₆ + 6) · 6

a₇ = (765 + 6) · 6

a₇ = 4626

n = 7

a₈ = (a₇ + 7) · 7

a₈ = 4633 · 7

a₈ = 32431

n = 8

a₉ = (a₈ + 8) · 8

a₉ = 32439 · 8

a₉ = 259512

n = 9

a₁₀ = (a₁₀ + 9) · 9

a₁₀ = 259521 · 9

a₁₀ = 2335689

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If Sam had Rs. 350000 and invested Rs.175000 in house, in bank Rs.175000 and getting 3000 pension then the monthly income was Rs. 6750.

Given that Sam had Rs.350000,investment in house Rs.175000 at a rent of Rs.2000 per month and Rs.175000 in bank at rate of 12%, getting pension of Rs.3000 per month.

We are required to find the monthly income in 1996.

We have assumed that Sam was retired on 1st January, 1996 so the amount of rent, investment in bank and pension did not increase because they had to be increase in a year and we have to calculate the monthly income in which he was retired.

Monthly income=Rent of 1 month+Simple interest of 1 month+Pension per month

=2000+175000*1/100+3000

=2000+1750+3000

=Rs.6750

Hence if Sam had Rs. 350000 and invested Rs.175000 in house, in bank Rs.175000 and getting 3000 pension then the monthly income was Rs. 6750.

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Jeremiah has to sell 5000 dollars worth of computers to get paid $130 on a given day. Using the linear equation, the required value is calculated.

An equation in which if the highest degree of the variable is 1(one), then that equation is said to be a linear equation.

General form: ax + b = c; where the power of the variable x is 1.

It is given that,

Jeremiah makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from his sales that day.

Consider,

P - as total pay on a day, x - as the number of dollars worth of computers, B - as basic pay, and C - as commission percentage.

So, the linear equation that relates x and P is,

P = Cx + B   ...(i)

On substituting the values from the given table we get,

122.5 = C(4500) + B ...(ii)

160 = C(7000) + B ...(iii)

175 = C(8000) + B ...(iv)

By solving equations (iii) and (iv), we get

C = 15/1000 = 0.015

B = 55

Finding x value when P = $130:

We have P = Cx + B. Then for P = 130,

130 = Cx + B

We know C = 0.015 and B = 55

On substituting these values,

130 = (0.015) x + 55

⇒ 0.015x = 130 - 55 = 75

∴ x = 75/0.015 = 5000

Therefore, the required computers are 5000 dollars worth.

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Disclaimer: The given question on the portal was incomplete. Here is the complete question.

Question: Jeremiah is a salesperson who sells computers at an electronics store. He makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from his sales that day. Let P represent Jeremiah's total payments on a day on which he sells x dollars worth of computers. The table below has select values showing the linear relationship between x and P. Determine how many dollars worth of computers Jeremiah would have to sell to get paid $130 on a given day.

Table:

x: 4500, 7000, 8000

P: 122.5, 160, 175

respectively.

The fraction computed shows that the total inches the infant grew over the three months is 3 3/4 inches.

First month = 2/4 inches

Second month = 1 inch

Third month = 7/4 inches.

The total inches the infant grew over the three months will be;

= 2/4 + 1 + 7/4

= 3 1/4 inches.

The difference in the infants from the second month to the third month will be:

= 7/4 - 1

= 3/4 inches.

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The events E and F are not independent

The given parameters are:

P(E n F) = 0.036

P(E|F) = 0.09

P(F|E) = 0.1

To calculate P(E), we use:

P(F|E) = P(E n F)/P(E)

This gives

P(E) = P(E n F)/P(F|E)

So, we have:

P(E) = 0.036/0.1

Evaluate

P(E) = 0.36

To calculate P(F), we use:

P(E|F) = P(E n F)/P(F)

This gives

P(F) = P(E n F)/P(E|F)

So, we have:

P(F) = 0.036/0.09

Evaluate

P(F) = 0.4

To calculate P(E U F), we use

P(E U F) = P(E) + P(F) - P(E n F)

So, we have:

P(E U F) = 0.36 + 0.4 - 0.036

Evaluate

P(E U F) = 0.724

The events E and F are independent if

P(E n F) = P(E) * P(F)

This gives

0.036 = 0.36 * 0.4

Evaluate

0.036 = 0.144 --- false

Hence, the events E and F are not independent

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Answer:

Yes

Step-by-step explanation:

All sides and angles look equal and appears to be a regular hexagon

Hope this helped and have a good day

Answer:

Yes.

Step-by-step explanation:

Hello!

A regular polygon is a closed shape with sides of equal length, and angles of equal degree. A regular polygon also forms around a general center.

This seems to be a regular polygon as all side lengths and angles seem to be equivalent, and there is a center point to the .

This shape is a hexagon, so the measure of the angles are 120°.

It would Julia 0.60 years more to double the initial investment.

What is future value?

Future value means the initial investment multiplied by 2 since the future value is meant to double.

The formula for future value of a continuously interest rate is provided below:

FV=PV*e^(rt)

FV=future value=$4,200*2=$8,400

PV=initial investment=$4,200

e=exponential constant=2.7182818

r=interest rate=9.5%

t=number of years it takes for the investment to double=unknown

$8,400=$4,200*2.7182818^(9.5%*t)

$8,400/$4,200=2.7182818^(0.095t)

2=2.7182818^0.095t

take log of both sides

ln(2)=0.095t* ln(2.7182818)

0.095t=ln(2)/ln(2.7182818)

0.095t=0.69314718781684800

t=0.69314718781684800/0.095

t=7.30 years

The future value when interest is compounded quarterly is shown thus:

FV=PV*(1+r/4)^(N*4)

FV=$8,400

PV=$4,200

r=8 7/8%

r=8.875%

N=the number of years it would take for the initial investment to double=unknown

$8,400=$4,200*(1+8.875%/4)^(N4)

$8,400=$4,200*(1+0.0221875)^(N4)

$8,400/$4,200=(1+0.0221875)^(N4)

2=(1+0.0221875)^(N4)

2=(1.0221875)^(N4)

take log of both sides

ln(2)=N4*ln(1.0221875)

N4=ln(2)/ln(1.0221875)

N4=31.5857423180125

N=31.5857423180125/4

N=7.90

Difference in years=7.90-7.30

difference in years=0.60 years

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Answer:

1/2

Step-by-step explanation:

This is an independent event.  It does not matter what happened before the chances of getting a tail on one toss will always be what I want/all outcomes.  There are only 2 outcomes:  heads or tails.  I am only looking for one of those outcomes, so 1/2.

Answer:

y= 2x -6

Step-by-step explanation:

The slope-intercept form of a line is given by y= mx +c, where m is the slope and c is the y-intercept.

To find the equation of a line, two information are needed:

Given that the slope is 2, m= 2. Substitute m= 2 into y= mx +c:

y= 2x +c

Let's find the coordinate in which the line intersects the line 2x -3y= 6. Point of intersection refers to the point at which two lines cuts through each other i.e., the point lies on the graph 2x -3y= 6 and the line of interest.

2x -3y= 6

When x= 3,

2(3) -3y= 6

6- 3y= 6

3y= 6 -6

3y= 0

Divide both sides by 3:

y= 0

Coordinate that lies on the graph is (3, 0).

Substitute the point into the equation and solve for c:

y= 2x +c

When x= 3, y= 0,

0= 2(3) +c

0= 6 +c

c= -6

Substitute the value of c back into the equation:

Thus, the equation of the line in slope-intercept form is y= 2x -6.

Additional:

For a similar question on slope-intercept form, do check out the following!

Answer:

x=75 degrees

Step-by-step explanation:

since the shape is quadrilateral, all the angles added together should equal 360 degrees so you use 360 to subtract all the given angles on the shape and you can find X

360-131-107-47=75

We know that,

slope = [tex] \rm{\frac{(y2 - y1)}{(x2 - x1)} }[/tex]

Let (0,1)=(x 1 ,y 1 ) and (1,2)=(x 2,y 2 )

So,

Slope of line = [tex] \frac{(2 - 1)}{(1 - 0)} = 1[/tex]

Now,

The required line equaqtion is given by,

==> y−y 1 = m(x-x1)

==> y−1=1(x−0)

==> y−1=x

==> y=x+1

Answer:

30 km

Step-by-step explanation:

Distance = rate x time

Distance = 20 x 1.5

Distance = 30

[tex]20*1.5=30[/tex] [tex]km[/tex]

Correct answer:-

Avg. speed = [tex]20km/h[/tex]

Time = [tex]1.5 hour[/tex]

Distance traveled in 1.5 hours is Distance = Speed x Time

So,

[tex]D = 20 * 1.5 = 30.[/tex]

reference link-

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The polynomial is quadratic trinomial

The polynomial function is given as:

4x^2+ 8x +16

The highest power in the above polynomial is 2.

This represents quadratic

The number of terms in the above polynomial is 3

This represents trinomial

Hence, the polynomial is quadratic trinomial

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The volume within the spherical compression wave increasing in t = 4 seconds is:64000000π cubic ft/sec.

Given:

dr/dt=100 ft/sec

When: t=4 seconds, radius(r)=400ft

Hence:

Volume of a sphere (V)=4/3πr³

dv/dt=4/3π.3r² dr/dt

dv/dt=4πr²dt/dr

When t=4 seconds

dv/dt=4π×(100×4)²×100 cubic ft/sec

dv/dt=4π×(400)²×100 cubic ft/sec

dv/dt=64000000π cubic ft/sec

Therefore the volume within the spherical compression wave increasing in t = 4 seconds is:64000000π cubic ft/sec.

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Answer:

x=8   y=2

Step-by-step explanation:

solve for x

1. 4x+4y=40

2. subtract 4y from both sides

3. 4x=40-4y

4. divide both sides by 40

5. [tex]\frac{4x}{4} = \frac{40-4y}{4}[/tex]

6. dividing by four undoes the multiplication by four

7.    [tex]x=\frac{40-4y}{4}[/tex]

8. divide 40 - 4y by 4

9. x=10-y

10. use the last equation to solve the rest

The additional information needed to calculate ORS are the measures of SPR and PSR

The lines are given as:

Lines a, b, c and d

The special names of the lines are as follows:

The angle is given as:

OPS= 139 degrees

Start by calculating SPR using

SPR = 180- 139

SPR = 41 degrees

So, the additional information needed to calculate ORS are the measures of SPR and PSR

The theorem 65 is not stated.

So, the question cannot be answered

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The actual roots of f(x) are -4 and 3

The function is given as:

f(x) = 2x^2 + 2x – 24.

Expand the function

f(x) = 2x^2 + 8x- 6x – 24.

Factorize the function

f(x) = 2x(x + 4) - 6(x + 4)

Factor out x + 4

f(x) = (x + 4)(2x - 6)

Set to 0

(x + 4)(2x - 6) = 0

Solve for x

x = -4 and 2x = 6

This gives

x = -4 and x = 3

Hence, the actual roots of f(x) are -4 and 3

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Answer:

A

Step-by-step explanation:

Got 100 on test

Answer:

Step-by-step explanation:

8x + 2(x - 7) = 7x + 3x - 14

8x + 2x - 14 = 7x + 3x - 14                 Distributive property.

10x - 14 = 10x - 14                              Combine the like terms.

-14 = -14                                             Subtraction.

0 = 0                                                  Addition.

Since the statement 0 = 0 is true regardless of the value of x, there is infinitely many solutions.

The answers to the questions are:

a. p = { t, v, c, q}

b. {2, 6} ⊂  {2,6,8,12}

c. {0, 3} ⊄ {3,2,4,6}

To represent sets we use

p = { }

Hence

a. p = { t, v, c, q}

b. If 2 and 6 is a proper subset of  [ 2,6,8,12},

This can be represented as

{2, 6} ⊂  {2,6,8,12}

c. the set consisting of the elements 0 and 3 is not a subset of {3,2,4,6} is written as

{0, 3} ⊄ {3,2,4,6}

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No pair of lines can be proven to be parallel considering the information given, therefore, the answer is: D. None of the options are correct.

Two lines that are cut across by a transversal can be proven to be parallel to each other if:

Thus, given the following information:

m∠2 = 115°

m∠15 = 115°

With only these two angles given, we can't use any of the theorems to prove that any of the two lines are parallel because angle 2 and angle 15 are located entirely on two different transversals that crosses two lines.

In summary, we can conclude that:

D. None of the options are correct.

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Using a system of equations, the amounts of cholesterol in each item are given as follows:

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

The variables for this problem are given as follows:

By eating 1​ egg, 1​ cupcake, and 1 slice of​ pizza, a child consumes 303 mg of cholesterol, hence:

x + y + z = 303.

3 cupcakes and 4 slices of​ pizza, he or she takes in 90 mg of cholesterol, hence:

3y + 4z = 90

y + 1.33z = 30.

By eating 2 eggs and 1​ cupcake, a child consumes 570 mg of cholesterol, hence:

2x + y = 570.

Then, writing y and z as functions of x:

Then, replacing on the first equation:

x + y + z = 303.

x + 570 - 2x + 1.5x - 406 = 303.

0.5x + 164 = 303.

x = (303 - 164)/0.5

x = 278.

The amounts for the cupcake and the slice of pizza are given as follows:

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