If you saw 12-1 / 16''off a board that is 20-3/4 " long, the length of the remaining board will be
8 -1/4''
8 -11 /16''
11 -1/4''
17 -3/8''

The regression equation is Y=1117.84+73.62X for the data as follows:

(20,3200), (15,3600), (25,3400), (10,1800), (18,2200), (18,2400), (15,2400), (12,1500), (22,2500), (15,2400), (25,3000), (16,2700), (12,2000), (20,2600), (25,2800)

where (x,y) denotes infomercials and sales, respectively.

According to regression equation Y=a+bX,

a = ((Σy) x (Σx^2) - (Σx) x (Σxy)) / (n x (Σx^2) - (Σx)^2)

a = ((36500 x 5126)-(268 x 677000)) / ((15 x 5126)-(268 x 268))

a = 1117.84

and, b = (n(Σxy)-(Σx)(Σy)) / (n(Σx^2)-(Σx)^2)

b = ((15 x 677000)-(268 x 365000)) / ((15 x 5126)-(268 x 268))

b = 73.62

Putting the values of a and b in the regression equation, we get the desired equation Y=1117.84+73.62X.

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At the null hypothesis, it is tested if the mean is of 15 years, that is:

[tex]H_0: \mu = 15[/tex]

At the alternative hypothesis, it is tested if the mean is different of 15 years, that is:

[tex]H_1: \mu \neq 15[/tex]

The equation that gives the test statistic is defined as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which:

The values of these parameters in this problem are given as follows:

[tex]\overline{x} = 17.4, \mu = 15, s = 6.3, n = 75[/tex]

Hence the test statistic is of:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{17.4 - 15}{\frac{6.3}{\sqrt{75}}}[/tex]

t = 3.30.

Considering a two-tailed test, as we are testing if the mean is different of a value, with t = 3.30 and 75 - 1 = 74 df, the p-value of the test is of:

0.0015.

Since the p-value is less than the significance level of 0.05, the null hypothesis is rejected, meaning that there is enough evidence to conclude that prisoners spend a time different of 15 years in the death row.

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The solution of the given inequality 6 - 4( 6 n+7 )  ≥ 122 is given by

n ≤ -6.

As given in the question,

Given inequality is :

6 - 4( 6 n+7 )  ≥ 122

Open the parenthesis of the given inequality we get,

⇒ 6 - 24n - 28 ≥ 122

⇒ 6 - 28 -24n ≥ 122

⇒ -22 -24n ≥ 122

Add 22 on both the side of inequality we get,

⇒ -22 + 22 -24n ≥ 122 + 22

⇒ -24n ≥ 144

Divide both the side by ( -24 ) we get,

⇒ n ≤ -144/ 24

⇒ n ≤ -6.

This shows that n has all the less than or equal to -6.

Therefore, the solution of the given inequality is equal to n ≤ -6.

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The expression (2/15x - 5) - (-0.7x + 2) is simplified to 5/12x - 3

An algebraic expression can be defined as an expression made up of variables, terms, coefficients, factors and constants.

These expressions are also made up of arithmetic operations.

From the information given, we have;

2/15x - 5) - (-0.7x + 2)

expand the bracket

2/15x - 5 + 7/10x - 2

collect like terms

2/15x + 7/10x - 5 + 2

Add the like terms

4x + 21x /30 - 3

Add the numerators

25x/60 - 3

Divide the common terms, we have;

5/12x - 3

Hence, the expression is 5/12x - 3

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The exponential function is  y = 2400(1.78)x

Since 1.78 < 1, the function is an exponential decay function.

The function can also be written as 2400(1 - 0.04)x.

The rate of decrease is 4% (that's 0.04 expressed as a percent)

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Answer:

Step-by-step explanation:

.40x + .65 ≤3.50

(3, 4)  I think it is a solution to the inequality. Because when you graph it (3, 4) looks like it is shaded meaning that it is a solution. (If wrong, I'm sorry)

The inequality that represents the numbers of apples and pears you can buy is 0.40x + 0.65y ≤ 3.50.

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.

Given;

The cost of the apples = $0.40 per apple

So, the cost of x apples is 0.40x.

The cost of the pears = $0.65 per pear

So, the cost of y pears is 0.65y.

The total cost of the apples and pears is the sum of the cost of the apples and the cost of the pears, which is 0.40x + 0.65y;

Since we can spend at most $3.50 at the market, the total cost of the apples and pears must be less than or equal to $3.50;

Therefore, the inequality that represents the numbers of apples and pears you can buy will be 0.40x + 0.65y ≤ 3.50;

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a complete description of simple harmonic motion must take into account several physical quantities and various mathematical relations then the position of a 60 gg oscillating mass is given by x(t) -20 sin 10t

this information is needed to solve oscillation problems of this type

the position of a 60 gg oscillating mass is given by x(t)

x = 2 cos wt = 2 cos 10t ; w = 10

velocity = dx/dt = -2 x 10 sin 10 t.=- 20 sin 10t

t = .4

velocity = -20 sin 10 x .4 = -20 sin 4 = -20 x -0.7568 = 15.136 cm /s

w = √ k / m = 10 = √ k / .05

k = 15.136  N/m

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The height of the rocket in given time using regression equation is 586 feet.

The regression equation is, y =  7.70961x² + 176.30826x - 12.44515

Given,

A rocket is shot off from a launcher. The accompanying table represents the height of the rocket at given times, where x is time, in seconds, and y is height, in feet

That is,

x ; 0.6, 1.3, 1.8, 2.5, 3.1

y ; 108, 218, 285, 368, 436

We have to write a quadratic regression equation for the given set;

The quadratic regression equation is;

y =  7.70961x² + 176.30826x - 12.44515

Now,

We have to find the height at a time of 3 seconds using the equation;

So,

y =  7.70961 x 3² + 176.30826 x 3 - 12.44515

y =  69.38649 + 528.92478 - 12.44515

y = 585.86612

y = 586

Height of the rocket= 586 feet

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To calculate how much Farah must invest today at age 19 to have a cool million dollars when she is 55, we need to know how many years she has until she retires. Since Farah wants to retire at age 55, she has 55-19 = <<55-19=36>>36 years until she retires.

We also need to know the interest rate that the account pays and the frequency at which the interest is compounded. In this case, the interest rate is 8% and the interest is compounded monthly.

To calculate how much Farah must invest, we can use the formula for the future value of an annuity, which is given by:

FV = PMT * (((1 + i)^n - 1) / i)

where FV is the future value that Farah wants to have, PMT is the amount that Farah must invest each period, i is the interest rate per period, and n is the total number of periods.

Since Farah wants to have a cool million dollars, we can set FV equal to $1,000,000. We also know that the interest rate is 8% and that the interest is compounded monthly, so we can set i equal to 8% / 12 = 0.006667. Finally, we know that Farah has 36 years until she retires, so we can set n equal to 36 * 12 = 432, since there are 12 months in a year.

Substituting these values into the formula above, we get:

FV = PMT * (((1 + i)^n - 1) / i)

FV = PMT * (((1 + 0.006667)^432 - 1) / 0.006667)

To solve for PMT, we can divide both sides of the equation by ((1 + 0.006667)^432 - 1) / 0.006667, which gives us:

PMT = FV / (((1 + i)^n - 1) / i)

PMT = $1,000,000 / (((1 + 0.006667)^432 - 1) / 0.006667)

Calculating this value gives us a result of PMT = $176.72, which is the amount that Farah must invest each month to have a cool million dollars when she is 55.

Now, let's consider Sam's situation. Sam also wants to have a cool million dollars when he is 55, but he is willing to put money into his account every year instead of every month. This means that the frequency at which the interest is compounded will be annual instead of monthly.

To calculate how much money Sam must put into his account each year, we can use the same formula as above but with a few changes. In particular, we need to set i equal to 8% / 1 = 0.08, since the interest is compounded annually, and we need to set n equal to 55-21 = <<55-21=34>>34, since Sam has 34 years until he retires.

Substituting these values into the formula above, we get:

FV = PMT * (((1 + i)^n - 1) / i)

FV = PMT * (((1 + 0.08)^34 - 1) / 0.08)

Solving for PMT gives us:

PMT = FV / (((1 + i)^n - 1) / i)

PMT = $1,000,000 / (((

the scalar surface integral ∬T(z+y)dS where T is the triangle (including its interior) with vertices (0,0,2), (0,1,0)( and (1,0,0) is 1

We can compute the scalar surface integral ∬T(z+y)dS using the parametric form of the surface integral.

Let S be the surface of the triangle. We can parameterize S as follows:

S(u,v) = (u, v, 2-u-v)

where 0 ≤ u ≤ 1 and 0 ≤ v ≤ 1-u.

Then, the scalar surface integral ∬T(z+y)dS is defined as:

∬T(z+y)dS = ∬S(u,v) (2-u-v + v) dudv

= ∫0→1∫0→1-u (2-u-v + v) dudv

= ∫0→1 [2u + (1-u)2 - (1-u)2u - u2(1-u)] du

= ∫0→1 (2u + 1 - 2u2 - u3) du

= [u2 + u - u4/4]0→1

= 1/4 + 1 - ¼

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Taylor Series for following parts,

a) f(x) = 7 - (7/2)x² + (7/24)x⁶ +......

b)f(x) = 21 - 18(x+2) + 25(x + 2)² - 8(x+3)³ +......

c)f(x) = 2 + 2log(2)(x -1) +(log2)²(x-1)² + (1/3 (log2)³(x-1)³ + --------

d)f(x) = x² + ----

The Taylor series giving the expansion of the function f(x) in the neighborhood of the point a. If the function is continuous in the neighborhood, all its derivatives exist, and the series converges, then The form f(x) = f(a)+f′(a)/1!(x−a)+(f′′(a)/2!)(x−a)²+⋯+(fⁿ(a)/n! )(x−a)ⁿ --(1) where fⁿ(a) is the nᵗʰ derivative of f(x) evaluated at a.

a) f ( x) = 7 cos(-x) = 7 cos(x) , a = 0

f(a ) = 7 cos(0°) = 7

f'(x) = - 7 sin(x) , f'(a) = 7 sin(0°) = 0

f"(x) = - 7cos(x) , f"(a) = -7 cos(0°) = -7

f"'(x) = 7 sin(x) , f"'(a) = 7 sin(0° ) = 0

....................................

put all the values in above equation (1) we get,

f(x) = 7 + 0/1! (x -0) - (7/2!)(x-0)² )+ 0 +(7/4!) (x-0)⁴-0 + ----------

f(x) = 7 - (7/2)x² + (7/24)x⁶ +......

b) f(x) = x⁴ + x² + 1, a = -2

f(a= -2) = (-2)⁴ +(-2)² +1 = 21

f'(x) = 4x³ + 2x

f'(a= -2) = 4(-2)³ + 2×(-2) = -36

f"(x) = 12x² + 2

f"( a = -2) = 12(-2)² + 2 = 50

.....

put all the values in above equation (1) we get,

f(x) = 21 - (36/2)(x+2) + (50/2!)(x + 2)² - ( 48/3!)(x+3)³ +......

f(x) = 21 - 18(x+2) + 25(x + 2)² - 8(x+3)³ +......

c) f(x) = 2ˣ ; a = 1

f( a= 1) = 2¹ = 2

f'(x) = 2ˣ log(2)

f'(a= 1) = 2 log(2)

f"(x) = 2ˣ ( log(2) )²

f"( a = 1) = 2 ( log(2) )²

................

put all the values in above formula we get,

f(x) = 2 + 2log(2) +( 2/2!)(log2)² + (2/3!)(log2)³

+--------

f(x) = 2 + 2log(2)(x -1) +(log2)²(x-1)² + (1/3(log2)³(x-1)³ + --------

d) f(x) = x tan⁻¹(x²) ; a= 0

f(a=0) = 0

f'(x) = x (1/(1+x⁴) + tan⁻¹(x²)

f'(a = 0) = 0

f"(x) = ((1+x⁴) - x 4x³)/(1+x⁴)² + (1/(1+x⁴)

= (2/(1+x⁴) - 4x⁴/(1+x⁴)²

f"( a = 0) = 2 - 0 = 2

f"'(x) = - 8x³/(1+x⁴)² - 12x³/ (1+x⁴)² + 16x⁷/(1+x⁴)⁴

f"'(a = 0) = 0

..............

f(x) = 0 +0 + 2/2! (x-0)² + 0 +-------

f(x) = x² + ----

Hence, we get all required Taylor Series for

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Answer:

D

Step-by-step explanation:

m^ (-3 · -4) = m^12

n ^ (-2 · -4) = n^8

m^12 n^8

Answer:

0.5a + 0.75p ≤ 23

Step-by-step explanation:

Cost of a apples: 0.5a

Cost of p pears: 0.75p

The total cost must be $23 or less.

0.5a + 0.75p ≤ 23

Answer:

d= 120

Step-by-step explanation:

c+d = 180 degree

d = 180-60 =120 degree

 The arithmetic mean of the three altitudes is equal to 10.1533 or 1523/150

The Arithmetic Mean (AM) or called average is the ratio of the sum of all observations to the total number of observations and is given by   [tex]A= \frac {1}{n} \sum \limits_{i=1}^n a_i[/tex]    

A = arithmetic mean

n = number of values

a₁ = data set values

Given here length of two equal sides is 13 cm and the other side is 10cm

let the Δ be ΔABC with AC=AB= 13 & BC=10cm and the altitudes on sides AC, AB, and BC  with the midpoints P, Q, and R  be AP, BQ, and CR respectively than by Pythagoras theorem we get AP = √13²-5²

                                                                                               = 12

As the altitude of an isosceles triangle bisects the base in this case BC

Then by area of ΔABC is = 1/2×12×10

                                         = 60 cm²

Again BQ is an altitude therefore area ⇒ 60=1/2×BQ×13

                                                                ⇒BQ=9.2307cm

Similarly, we can find  CR = 9.2307 cm

Thus Arithmetic mean of the altitudes is =( 9.2307+9.2307+12)/3        

                                                                  =10.1533 cm

                                                                   = 1523/150 cm

Hence, the answer as a common fraction is 1523/150

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Step-by-step explanation:

it is really a simple concept : instead of the isolated variable x you grab the whole function of g(x) and put that into the place of any x appearance in f(x) : g(x) becomes the input argument for f(x).

so,

f(g(x)) = sqrt(36/(x + 3)) = 6×sqrt(1/(x + 3))

The cubic function is f(x) = x^3 + 8x^2 - 32x + 32, which has a local maximum value of 4 at x = -4 and a local minimum value of 0 at x = 2.

The cubic function f(x) is of the form f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants. In this case, a = 1, b = 8, c = -32, and d = 32. The local maximum value of 4 occurs when x = -4 and the local minimum value of 0 occurs when x = 2.To find the equation, we must use the given information to solve for the constants. The function must equal 4 when x = -4, so f(-4) = 4. Plugging in the values for the constants we have 4 = -4^3 + 8(-4)^2 - 32(-4) + 32. Solving this equation, we find that d = 32, so the equation becomes f(-4) = -64 + 256 + 128 + 32 = 4. Similarly, we set f(2) = 0, so 0 = 8 + 16 - 64 + 32. Solving this equation, we find that c = -32, so the equation becomes f(2) = 8 + 16 - 32 + 32 = 0. Finally, we have the equation f(x) = x

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find a cubic function, in the form below, that has a local maximum value of 4 at -4 and a local minimum value of 0 at 2.f (x) = x^3 + 8x^2 - 32x + 32

Answer: The encrypted number is 25 and this can be determined by using the formula from RSA algorithm.

Given :

Alice has shared that her RSA public key is n = = 33, e = 7.

The formula from the RSA algorithm is used to encrypt the number 16. The formula is given by:

where e = 7, n = 33 and m = 16.

Now, substitute the known values in the above equation.

Now, by using the modulo function the above expression becomes:

c = 25

So, the encrypted number is 25.

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Step-by-step explanation:

Answer:

distance = √17

Step-by-step explanation:

distance = √(y2 - y1)^2 + (x2 - x1)^2

distance = √(1 - 0)^2 + (4 - 0)^2

distance = √17

I hope my answer helps you.

Descartes's number is the 46.989, which is less than 47 and higher than 46.98.

A Descartes number is an odd number with the formula n = m p, where m and p are coprime numbers and 2n = (m) (p + 1). P is regarded as a "spoof" prime in this formula. The only known example is the one that was provided. The invention of Cartesian or analytic geometry, which employs algebra to describe geometry, is one of Descartes's most enduring contributions. In equations, Descartes "introduced the convention of denoting unknowns by x, y, and z, and knowns by a, b, and c." A Descartes number is an odd integer that, if one of its composite elements were prime, would have been an odd perfect number.

Given,

Descartes's number is,

46.989, which is less than 47 and higher than 46.98.

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The system does not have a periodic solution in each of 10 and 11.

A solution of the period depends on the independent variable t is called Periodic Solution. For a periodic solution x(t)( in the case of a system, x is a vector), there is a number T≠0 such that

x(t+T)=x(t)  for t∈R.

The given equations are:

      [tex]\frac{dx}{dt} =-2x-3y-xy^2\\\\\frac{dx}{dt} =y+x^3+x^2y[/tex]

F is the derivative of dx/dt and Gis the derivative of dy/dt:

[tex]F(x,y)=-2x-3y-xy^2\\G(x,y)=y+x^3+x^2y[/tex]

When Fx+Gx has the same sign on the entire domain D, then there are no periodic solutions on the domain D.

Fx+Gx=-2-y^2+1-x^2

          =-1-y^2-x^2

             <for all real numbers x,y[tex]\neq[/tex]0

Fx+Gx have the same sign  for all pairs of real numbers with x[tex]\neq[/tex]0 and y[tex]\neq[/tex]0

Thus, there are no periodic solutions in the system(excluding contact solutions)

Hence proved.

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The position of E as a mixed number is [tex]2\frac{4}{5}[/tex].

What is number line?

A number line is a diagram of a graduated straight line used to represent real numbers in elementary mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.

Let on a number line the position of E is given.

We have to find E as a mixed number.

As we can see there are 5 parts between 2 and 3.

So each part is 0.2 cm.

The position of E is in fourth part.

So, 4 x 0.2 = 0.8 cm

2 + 0.8 = 2.8 is the position of E.

2.8 can be written as.

28/10 = 2 8/10 = 2 4/5

Hence, the position of E as a mixed number is [tex]2\frac{4}{5}[/tex].

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Answer:

this very easy to factorize this because (-+)is- (+-)-

(++)+ (--)+ but the sign which is bigger we have to keep that

Answer:

Step-by-step explanation: A. Prepare journal entries to record the January transactions.

Paid the monthly rental fee, $790.

Debit Credit

Rent Expense 790

Cash 790

Made the monthly payment to Apple Company, $1,700 in order to decrease Accounts Payable.

Debit Credit

Accounts Payable 1,700

Cash 1,700

Purchased additional repair supplies on credit from Pineapple Company, $1,820.

Debit Credit

Supplies 1,820

Accounts Payable 1,820

Received cash for repair service performed, $2,950.

Debit Credit

Service Revenue 2,950

Cash 2,950

Paid cash for an advertisement in the local newspaper, $370.

Debit Credit

Advertising Expense 370

Cash 370

Paid Pineapple Company on account, $1,200.

Debit Credit

Accounts Payable 1,200

Cash 1,200

Collected payment for repair fees earned, $7,460.

Debit Credit

Accounts Receivable 7,460

Cash 7,460

Recorded a dividend paid to stockholders, $8,100.

Debit Credit

Dividends 8,100

Cash 8,100

B. Using the following information, record adjusting entries in the general journal and prepare the T- accounts for all accounts

One month of rent has expired. The rental policy is valid in one year starting from the first day of November 20X0.

Debit Credit

Prepaid Rent 90

Rent Expense 90

The inventory of unused repair supplies is $1,520

Debit Credit

Supplies 1,520

Supplies Expense 1,520

The estimated depreciation on repair equipment is $350.

Debit Credit

Depreciation Expense 350

Accumulated Depreciation - Equipment 350

Accrued one-month interest expense on Note Payable that will be paid on February 1 (Borrowing Note was in 6-month; annual interest rate is 6%).

Debit Credit

Interest Expense 100

Interest Payable 100

Accrued salaries for 2 employees at the end of the month, payment for each person is $500

Debit Credit

Salaries Expense 1,000

Salaries Payable 1,000

Service Revenue still unearned at the end of the period is $3,675

Debit Credit

Unearned Service Revenue 3,675

Service Revenue 3,675

Service revenue earned but not billed is $1,800

Debit Credit

Service Revenue 1,800

Accounts Receivable 1,800

C. Prepare an adjusted trial balance from above T-accounts

Debit Credit

Cash 35,080

Accounts Receivable 63,080

Prepaid Rent 1,510

Supplies 1,300

Equipment 13,900

Accumulated Depreciation - Equipment 3,500

Accounts Payable 2,380

Notes Payable 16,100

Interest Payable 100

Salaries Payable 1,000

Unearned Service Revenue 3,675

Service Revenue 6,475

Rent Expense 870

Answer:

At 12:00 there were 50 riders

Step-by-step explanation:

3 hours after 9 would be noon.  At that time there are 50 riders

The completed Venn Diagram is given by the image shown at the end of the answer.

The percentages are given as follows:

The Venn diagram starts to be filled from the most restrictive conditions, towards the least restrictive.

2% of people answered all three, hence:

V = 2%.

3% of people answered light rail and bus, hence:

IV + V = 3%

IV = 1%.

6% of people answered light rail and carpool, hence:

II + V = 6%

II = 4%.

2% of people answered carpool and bus, hence:

V + VI = 2%

V = 0%.

11% of people answered carpool, hence:

III + II + V + VI = 11

III + 4 + 2 + 0 = 11

III = 5%.

10% of people answered bus, hence:

IV + V + VI + VII = 10

1 + 2 + 0 + VII = 10

VI = 7%.

16% of people answered light rail, hence:

I + II + IV + V = 16

I + 4 + 2 + 1 = 16

I = 9%.

Then the or percentage is given as follows:

9 + 7 + 5 + 1 + 2 + 4 = 28%.

The percentage that uses other mediums is given as follows:

VIII = 100 - 28 = 72%.

Then the missing percentages are given as follows:

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Hello,

I hope you and your family are doing well!

To find the number of students who took Science, Dance, or English, you can add the number of students in each individual category and then subtract the number of students who took all three courses, since those students were counted twice. This gives a total of 1031 + 1058 + 1059 - 218 = 3100 students.

To find the number of students who took Dance and English, but not Science, you can add the number of students in region VII and region VIII, which is 456 + 11 = 467 students.

To find the number of students who took Science or didn't take Dance, you can add the number of students in region I and region III, which is 1031 + 218 = 1249 students.

To find the number of students who took none of the courses, you can add the number of students in region II and region IV, which is 449 + 459 = 908 students.

To find the number of students who took Science or English, but not Dance, you can add the number of students in region V and region VI, which is 1059 + 459 = 1518 students.

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