1 Suppose another student says he spends $29 each
week on entertainment. Will the mean and median
increase or decrease?
decreas
2 What is the new mean when the value from problem 1
is included in the data set?
Show your work. For elementary kids

Hence, a person on a 2000 calorie diet  should eat more calories approximate ratio of 200-300 calories from  vegetables and 900-1300 calories from carbohydrates.

A calorie is a measurement,  just like a teaspoon or an inch.  Calories are the amount of energy released when your body breaks down (digests and absorbs) food.  The more calories a food has, the more energy it can provide to your body

The  number of calories a person  should consume from vegetables versus carbohydrates depends on various factors  such as age, gender, activity level, body composition, and overall health status. However, in general, it is recommended that a person on a  2000 calorie diet should  consume more calories from vegetables than from carbohydrates.

The United States Department of Agriculture (USDA) recommends  that adults consume 2.5 to 3 cups of vegetables per day, depending on their age, gender, and level  of physical activity. On a 2000 calorie diet, this would amount to approximately 200-300  calories from vegetables.

For carbohydrates, the recommended  intake varies depending on the individual's energy needs,  but it generally accounts for 45-65% of their total calorie intake. This  equates to 900-1300 calories from carbohydrates on a 2000 calorie diet.

Therefore, a person on a 2000 calorie diet  should eat more calories  from vegetables than from carbohydrates, with an approximate ratio of 200-300 calories from  vegetables and 900-1300 calories from carbohydrates.

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On solving the provided question we can say that As a result, set D denotes a linear function.

The slope of a line indicates how steep it is. The gradient's mathematical equation is known as "gradient overflow" (the change in y divided by the change in x). The slope is defined as the ratio of the vertical change (rise) between two places to the horizontal change (run). The slope-intercept form of an equation is used to express a straight line's equation, which is written as y = mx + b. The y-intercept is found where the slope of the line is m, b is b, and (0, b). For example, consider the slope and y-intercept of the equation y = 3x - 7.The slope of the line is m. b is b at the y-intercept, and (0, b).

The set of ordered pairs expressing a linear function must meet the requirement that any two locations in the set have a constant rate of change (slope).

We can determine the rate of change between the two supplied positions using set D:

slope = (y2 - y1) / (x2 - x1)

slope = (1 - 2) / (2 - (-1))

slope = -1/3

We may use the slope-intercept form of a linear equation to see if the remaining points in set D fulfil the same rate of change: y = mx + b, where m is the slope and b is the y-intercept.

We can solve for b using the first point in D, (-1,2):

2 = (-1/3)(-1) + b

b = 7/3

So the linear equation for set D is: y = (-1/3)x + 7/3

Now we can check if the remaining points in set D satisfy this equation:

(2, 1): 1 = (-1/3)(2) + 7/3 (satisfies the equation)

As a result, set D denotes a linear function.

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You have to find what 0.2 of 132 is

132 x 0.2 = 26.40

The answer [tex]\boxed{\bold{\$26.40}}[/tex]

The expression of 1 picoseconds as a decimal would be = 0.000000000001 picoseconds.

The scientific notation of representation of figures is a systematic way of representation of too large or too small figures encountered in everyday arithmetics.

From the table above, the larger figures are represented with 10 ^ X without a negative sign.

But the smallest figures are represented with 10 ^ -X with a negative sign.

The scientific notation for 1 picoseconds = 10^-12

When converted to decimal

= 0.000000000001 picoseconds.

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Answer:

[tex]x=\pm\sqrt{\frac{2}{7}} \text{ and }x=\pm i\sqrt{\frac{2}{7}}[/tex]

(real solution)       (imaginary solution)

Step-by-step explanation:

For these type of questions, where the exponent is even, it helps to try to rewrite the equation into a quadratic equation as we have a closed formula (quadratic formula) to solve for the zeroes, and it's also just easier to deal with in general.

Let's say that: [tex]u=x^2[/tex], now if we square both sides, [tex]u^2=x^4[/tex], so from here we can substitute in u squared as x to the power of four.

This results in our following equation: [tex]49u^2-4[/tex], from here we could use the quadratic formula, but you may notice a pattern here. We have a difference of squares: [tex]a^2-b^2=(a-b)(a+b)[/tex]

[tex]49u^2[/tex] can be written as [tex](7u)^2[/tex] and [tex]4[/tex] can be written as [tex]2^2[/tex], this gives us our equation: [tex](7u)^2-2^2\implies (7u-2)(7u+2)[/tex]. If we use this definition of the equation on the left side, it gives us: [tex](7u-2)(7u+2)=0[/tex] and this is very convenient as we can solve both of them individually.

Whenever we multiply any number (assuming it's defined) by zero, we should get.... zero. This intuitively makes sense as no matter how many times we add zero up (multiplication is repeated addition), we're always just going to have zero.

So when we have the equation: [tex]a*b=0[/tex], if "a" is zero then regardless of what "b" is (assuming it's defined), then the product will be zero. If "b" is zero then regardless of what "a" is (assuming it's defined), then the product will be zero.

Now if we look back at our equation: [tex](7u-2)(7u+2)=0[/tex], if [tex]7u-2=0[/tex], then regardless of what [tex]7u+2[/tex] is equal to, the product will be zero. Likewise, if [tex]7u+2=0[/tex] then regardless of what [tex]7u-2[/tex] is equal to, the product will be zero, thus making the equation true.

So to find the solutions to this, we find what makes [tex]7u-2=0 \text{ and }7u+2=0[/tex] true. If we work them both out individually we

get:

[tex]7u-2=0\\7u=2\\u=\frac{2}{7}\\\\7u+2=0\\7u=-2\\u=-\frac{2}{7}[/tex]

So now we have our two solutions right? Well remember we started off with a "x" variable, and the "u" is merely a substitution. If you recall, the "u" value is set equal to "x^2", so we can just plug that back in, so we can find the solutions in terms of x.

[tex]x^2=\frac{2}{7} \text{ and } x^2=-\frac{2}{7}[/tex]

If we take the square root of both sides, we get:

[tex]x=\pm\sqrt{\frac{2}{7}} \text{ and }x=\pm\sqrt{-\frac{2}{7}}[/tex]

you'll notice in one of them, we're taking the square root of a negative number. This will result in imaginary solutions, if we factor out a "-1" and take the square root of that, we'll just get an "i" infront, giving us the solutions of: [tex]x=\pm\sqrt{\frac{2}{7}} \text{ and }x=\pm i\sqrt{\frac{2}{7}}[/tex].

The greater angle has a 67.5° degree measurement. When two angles' measurements add up to 90°degrees, they are said to be complimentary.

Call that angle we're looking for "x" for convenience.

The degree that, if added to x, makes x equal 90° degrees is known as the compliment of x.

We now know that 3x, or 3 times x, is the compliment of x.

With this knowledge, we can construct the following equation:

x + 3x = 90°

combining comparable equations;

4x = 90°

x = 22.5°, when both sides are divided by 4.

As a result,

3x = 3(22.5°) = 67.5° degrees is the measurement of the greater angle, which is the complement of x.

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Step-by-step explanation:

AREA = pi r^2

144 = pi r^2     shows      r = 6.77  m       ( or sqrt ( 144/pi)  ) 

        then          diameter = 2 * r = 13.54 m    (or   2 sqrt (144/pi)  )

Answer:

7.64

Step-by-step explanation

This is what I did so I take the root of 144 = 12 and 12/3.14 = roughly 3.82 thats the radius and that times 2 = 7.64 have a great day success to homework yay! Have a great day!!! :D

Answer:

Area of a rectangle = Length x Width

Step-by-step explanation:

Length = 25 cm

Width = 8 cm

25 x 8 = 200

So the area of a rectangle = 60 cm^2

The period of the sinusoidal equation of the graph is 4 months.

The amplitude of the sinusoidal equation of the graph is 84 degrees Celsius.

The period and amplitude are two important characteristics of a wave.

Period: The period of a wave is the time it takes for one complete cycle of the wave to occur. The period of a wave determines its frequency, which is defined as the reciprocal of the period.

Amplitude: The amplitude of a wave is the maximum displacement of the wave from its equilibrium position. In simpler terms, it represents the height or strength of the wave.

In then given graph, the period of the wave = 1 complete cycle in 4 months = 4 months/cycle = 4 months

Amplitude = 84 degrees Celsius.

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Answer:

16.58. my answer needs to be more than 20 characters, soooo... how is your day going?

Answer:

Vertically opposite angles are always same.

Straight angle=180°

Angle MQN=70°

U is located in the plane or vector that A's columns span.

A mathematical concept with both magnitude and direction is a vector. It is frequently used to symbolise forces like the gravitational pull of an object or the electrical forces that exist between charged particles. It can be expressed mathematically as a line segment with two ends, a direction, and a magnitude.

Part 1

To calculate the resulting vector, vector operations including addition, subtraction, multiplication, and division can be used. The individual x, y, and z components of a vector—which stand for its magnitude and direction—can also be determined.

Part 2

Why the answer in Part 1 is correct?

Part 1's answer I gave was A. Yes, writing u as a linear combination of the columns of A after multiplying A by the vector [4, 20, 8]. This is so because the vector [4, 20, 8] may be expressed as a linear combination of the columns of A since it is a solution to the system of linear equations generated by the augmented matrix [A|u]. U is thus in the plane that is covered by the columns of A.

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Answer:

D. 177 ft²

Step-by-step explanation:

the area of a circle is

pi×r²

r is the radius which is half of the diameter, of course.

so, in our case

area = pi×(15/2)² = pi×7.5² = pi×56.25 =

= 176.7145868... ft² ≈ 177 ft²

Step-by-step explanation:

Rate UP stream =  ( s - w) = 106 km / 2 hr  

                                               (  where s = boat speed       w = current speed )

                              (s-w) = 53  km/hr

Rate DOWNstream = ( s+w) = 142 / 2 = 71 kmhr

( s-w) + ( s+w) = 53  + 71   km/hr

2s = 124  

s = 62 km /hr      then   s+w = 71   shows w = 9 km/hr

Row 1 in the matrix multiplied by 1/4 will produce: 1/2, 0, and 3/4 respectively.

A rectangular array of numbers or mathematical objects which are arranged in rows and columns is called a matrix. Each row of a matrix is a horizontal sequence of numbers or objects that are separated by commas and enclosed within square brackets, and it represents a vector in the row space of the matrix.

row 1 of the given matrix are: 2, 0, and 3, multiplying row 1 with 1/4 gives;

1/4 × 2 = 1/2

1/4 × 0 = 0

1/4 × 3 = 3/4

Therefore, row 1 in the matrix multiplied by 1/4 will produce: 1/2, 0, and 3/4 respectively.

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The expressions are solved to give;

1.n = 1

2. h = 1

3. x = -5

4. n = 1/4

5. x = 7/2

6. p = 2/3

7. x = -12

8. n = 3

9. c = -1

10. x = 6

These are expressions that are made up of term, variables, constants, factors and coefficients.

They are also made up of mathematical operations.

From the information given, we have;

1. 5n + n = 2n + 4

collect and add the like terms

4n = 4

Make n subject

n = 1

2. 5h + 2 = h - 2

collect and add the like terms

4h = 4

h = 1

3. 2x - 1 = 3x + 4

collect and add or subtract the like terms

-x = 5

x = -5

4. n = n + 1/5

cross multiply

4n = 1, n = 1/4

5. x + 5 = 3x - 2

collect like terms

-2x = -7

x = 7/2

6. p = p + 2/4

cross multiply

3p = 2

p = 2/3

7. 4(2 + x) = 3x - 4

expand the bracket

8 + 4x = 3x - 4

collect like term

x = -12

8. 5n + 2 = 3n + 4

collect like terms

n = 3

9. 3c - 2 = -3c - 8

collect like terms

6c = - 6

c = -1

10. 3x + 1 = 2x - 5

collect the like terms

x = 6

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(2+3)²=25, base=2+3, exponente=2, (-8)²=64, 3/5 expressed as a percent is 60%, a=7, 20 0/3 = 60/3 = 20/1.

What is percentage?

Percentage is a way of expressing a fraction or decimal as a portion of 100. It is often used to describe proportions or rates in various fields, such as finance, economics, and statistics.

What is exponent?

An exponent is a mathematical operation that involves raising a number to a power. The exponent represents the number of times the base is multiplied by itself. For example, in 2^3, 2 is the base and 3 is the exponent, and it means 2 multiplied by itself three times, resulting in 8.

According to the given information:

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The scale factοr is οne-half. The perimeter οf the mοdel is the prοduct οf the scale factοr and the perimeter οf the οriginal rectangle. The area οf the reduced figure is (1/2)² = 1/4 times the area οf the οriginal figure

The ratiο between cοmparable measurements οf an οbject and a representatiοn οf that οbject is knοwn as a scale factοr in mathematics.

Here,

We have tο cοmpare the perimeter and area οf the οriginal figure tο the perimeter and area οf the reduced figure using the scale factοr.

The ratiο οf the length οf the οriginal rectangle tο that οf the reduced rectangle is 6 tο 3 οr a factοr οf 1/2.

The ratiο οf the width οf the οriginal rectangle tο that οf the reduced rectangle is 2 tο 1, οr, again, a factοr οf 1/2. Sο, because this ratiο οf 1/2 is cοnstant, we knοw the tοtal scale factοr is 1/2, making B cοrrect.

16 ×(1/2) = 8, which means that the perimeter οf the scale-factοred, reduced rectangle is "the prοduct οf the scale factοr and the perimeter οf the οriginal rectangle". Sο, C is cοrrect.

Hence,  The scale factοr is οne-half.

The perimeter οf the mοdel is the prοduct οf the scale factοr and the perimeter οf the οriginal rectangle.

The area οf the reduced figure is (1/2)² = 1/4 times the area οf the οriginal figure.

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The lower limit is 189.331 milligrams per one hundred milliliters, and the upper limit is 195.469 milligrams per one hundred milliliters.

To find the 90% confidence interval for the mean serum cholesterol level of all middle-aged women, we can use the formula:

CI = x' ± t(α/2, n-1) × (s/√n)

where:

x' is the sample mean serum cholesterol level

t(α/2, n-1) is the critical t-value for a two-tailed test with a 90% confidence level and n-1 degrees of freedom

s is the sample standard deviation of the serum cholesterol level

n is the sample size

Substituting the given values, we get:

CI = 192.4 ± t(0.05, 11) × (5.9/√12)

To find the critical t-value, we can use a t-distribution table or calculator. For a two-tailed test with 11 degrees of freedom and a 90% confidence level, the critical t-value is approximately 1.796.

Substituting this value and simplifying, we get:

CI = 192.4 ± 1.796 × 1.707

CI = 192.4 ± 3.069

Therefore, the 90% confidence interval for the mean serum cholesterol level of all middle-aged women is (189.331, 195.469).

This means that we can be 90% confident that the true mean serum cholesterol level for all middle-aged women falls within this interval.

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Therefore, P(z > 0.97) = 0.166 using standard normal distribution table.

A standard normal distribution table, also called a z-score table or a standard normal table, is a table that provides the area under the curve to the left of a specific z-score value in a standard normal distribution. A standard normal distribution is a normal distribution with a mean of zero and a standard deviation of one.

The table usually includes positive z-score values in the right-hand column and the second decimal place in the top row. The intersection of a specific z-score value and decimal place provides the area under the curve to the left of that z-score value.

For example, if we want to find the area under the curve to the left of a z-score value of 1.32, we would locate the row with 1.3 in the top row and the column with 0.02 in the right-hand column. The intersection of this row and column gives the area under the curve to the left of 1.32, which is 0.9066.

Using a standard normal distribution table or calculator, we can find the probability of z being greater than 0.97 is approximately 0.166. Therefore, P(z > 0.97) = 0.166.

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The total amount that Meihua pays for the 36 pencils is  9M - 36n

We know that a set of 4 pencils has a price M, then the price of each single pencil is:

P = M/4

And we also know that Meihua got a discount of n in each pencil, so the price that she pays for each pencil is:

P = M/4 - n

Now we know that she buys 36 of these, so the amount that she pays is given by the product:

amount  = 36*(M/4 - n)

amount = 9M - 36n

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The original numbers multiplied by 10² are:

968

0.002

3.33

When a number is multiplied by 10², the position of the decimal point will move to the right by 2 steps. If the number does not have decimal point, two zeros is added to the back of the number .

6 * 10³  = 6,000

968 * 10² = 96,800

0.002 * 10² = 0.2

70,000 ÷ 10² = 700

3.33 * 10² = 333

Thus, the original numbers multiplied by 10² are 968, 0.002 and 3.33

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1. the APR for this loan is 6%.

2.  the unearned interest is $118.83.

3.  the monthly payment necessary to amortize the $80,000 mortgage at 6% annual interest for 25 years is $506.69.

APR = (finance charge / loan amount) / number of years * 100%

In this scenario, the loan amount is $2400 and the finance charge is $288. Since it's a two-year loan, the number of years is 2

APR = (288 / 2400) / 2 * 100%

APR = 0.06 * 100%

APR = 6%

b.

Number of payments = 4 years * 12 months/year = 48

If the loan is paid off in 3 years instead of 4 years, the number of payments made is:

Number of payments made = 3 years * 12 months/year = 36

Substituting these values into the formula, we get:

Unearned interest = (1426 / 48) * (48 - 36)

Unearned interest = $118.83

3.

To find the monthly payment necessary to amortize a mortgage, we need to use the formula:

M = P * (r / (1 - (1 + r)^(-n)))

where M is the monthly payment, P is the principal (loan amount), r is the monthly interest rate, and n is the total number of payments (in months).

In this scenario, the loan amount is $80,000, the annual interest rate is 6%, and the loan term is 25 years. To find the monthly interest rate, we divide the annual interest rate by 12 (since there are 12 months in a year):

Monthly interest rate = 6% / 12 = 0.005

To find the total number of payments, we multiply the number of years by 12:

Number of payments = 25 years * 12 months/year = 300

Substituting these values into the formula, we get:

M = 80000 * (0.005 / (1 - (1 + 0.005)^(-300)))

M ≈ $506.69

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The cash payback period for the project is 4.7 years.

The cash payback period is a financial metric that calculates the amount of time it takes for a project to generate enough cash flows to recover the initial investment (cost). It is calculated by dividing the initial investment by the estimated annual net cash flows.

Decimal refers to a system of numbers based on the number 10, where each digit represents a different power of 10. It is a way of expressing numbers using a decimal point to separate the whole number from the fractional part.

Given:

Estimated annual net cash flows = $55,800

Initial investment (cost) = $262,260

Cash Payback Period = Initial Investment / Estimated Annual Net Cash Flows

Putting the values:

Cash Payback Period = $262,260 / $55,800

Calculating the cash payback period:

Cash Payback Period = 4.7 years (rounded to one decimal place)

Therefore, the cash payback period for the project is 4.7 years.

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Therefore , the solution of the given problem of test statistic comes out to be 4.0085 is the test statistic for this two-sample t-test.

The Z-statistic, which confirms the precision of the conventional null hypothesis, is the only strategy that's even remotely close to a Z-test. Consider extrapolating a 2.5 E score in a 2 X y examination with a 0.05 threshold of significance. The p-value connected to this Z-value is 0.0124.

Here,

A two-sample t-test's test statistic is calculated as follows:

The formula for

=> t is (mean1 - mean2) / √((s1 / n1) + (s2 / n2)).

where mean1, mean2 represent the sample means for Group 1 (private institutions) and Group 2 (public institutions), respectively; s12, s22 represent the sample variances for

Groups 1 and 2, and n1, n2 represent the sample sizes for Groups 1 and 2, respectively.

Let's compute the test statistic based on the provided information:

The sample mean (mean1) for private institutions (Group 1) is $43,120.

$1,671,699,489.05 is the sample variance (s12).

Sample (n1) size is 37.

Public Institutions: Sample mean (mean2) = $25,469 (Group 2).

$1,682,553,858.66 is the sample variance (s22).

Number of samples

=>  (n2): 39

=> t = (43,120 - 25,469) / √((1,671,699,489.05 / 37) + (1,682,553,858.66 / 39))

=> t = 4.0085

Therefore, 4.0085 is the test statistic for this two-sample t-test.

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Answer: Hi! Read the explanation below:

Brainliest?

Step-by-step explanation:

Student 1 correctly started the proof.

To complete the proof using the law of sines, student 1 should use the fact that the sum of angles in a triangle is 180 degrees to obtain an expression for angle C, and then use the fact that the sum of the lengths of the opposite sides of an angle in a triangle is equal to the length of the third side to obtain an expression for side c in terms of sin(A) and sin(B).

Here's the complete proof:

Starting with Student 1's work:

bsin(A) = h

asin(B) = h

Using the fact that the sum of angles in a triangle is 180 degrees:

C = 180 - A - B

Using the fact that the sum of the lengths of the opposite sides of an angle in a triangle is equal to the length of the third side:

a/sin(A) = b/sin(B) = c/sin(C)

Substituting in the expressions for c and sin(C) in terms of sin(A) and sin(B):

a/sin(A) = b/sin(B) = 2h/(sin(A)+sin(B))

Simplifying:

a = 2hsin(A)/(sin(A)+sin(B))

b = 2hsin(B)/(sin(A)+sin(B))

c = 2hsin(C)/(sin(A)+sin(B)) = 2hsin(180-A-B)/(sin(A)+sin(B)) = 2h*sin(A+B)/(sin(A)+sin(B))

Therefore, the law of sines is:

a/sin(A) = b/sin(B) = c/sin(C) = 2h/(sin(A)+sin(B))

As a result, the triangle formed by the vertices A(0,0), B(3,8), and C(9,0) has an area of 18 square units.

A triangular is a three-sided, tri-geometric shape. It is a double figure that is frequently represented by the character "." A triangle's angles can never add up to more than 180 degrees. Triangles can be categorized into equilateral, elliptic, and scalene varieties according to the length of their sides and the dimensions of their angles. Three equal edges and three equal, 60-degree angles make up an equilateral triangle. Equal size ends and equal size angles make up an isosceles triangle. The sides and angles of a scalene triangle are not equal.

Given a triangle's vertices in the coordinate plane, we can apply the following formula to get its area:

A is equal to [tex]|(x1(y_2 -y_3) + x_2(y_3 -y_1) + x3(y_1 -y_2)) / 2|.[/tex]

where the triangle's vertices' coordinates are [tex](x_1, y_1), (x_2, y_2), and (x_3, y_3).[/tex]

We obtain: by substituting the coordinates of the specified vertices.

[tex]A = |(0(8 - 0) + 3(0 - 0) + 9(0 - 8)) / 2| = |-36| / 2 = 18[/tex]

As a result, the triangle formed by the vertices A(0,0), B(3,8), and C(9,0) has an area of 18 square units.

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Answer:

$525

Step-by-step explanation:

To calculate the sales commission for this employee, we need to first calculate the total sales made by the employee for the week. The employee made sales of 800 on Monday, 600 on Tuesday, 1300 on Wednesday, 800 on Thursday and 800 on Friday. The total sales made by the employee for the week is:

800 + 600 + 1300 + 800 + 800 = 4500

Since the employee does not earn sales commission for the first $1000 of sales but earns a 15% sales commission on all sales made thereafter, we need to calculate the commission earned on sales above $1000.

The total sales above $1000 is:

4500 - 1000 = 3500

The commission earned on sales above $1000 is:

3500 x 15% =$525

Therefore, the employee earned a sales commission of $525 this week.

The correct statement is C. asking questions, identifying problems, and gaining new information is the most accurate option.

The definition of "observation" given by Merriam-Webster is "an act of recognizing and noting a fact or occurrence often involving measurement with instruments," or "a record or description so obtained."

C. asking questions, identifying problems, and gaining new information is the most accurate option.

Making observations often involves the process of asking questions, identifying problems, and gaining new information. Observations are made to gather data and information about a phenomenon or event, which can then be used to answer questions or develop hypotheses for further research.

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The attendance at the movie theatre is;

Children = 142

Students = 44

Adults = 71

What is arithmetic?

Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.

Here, we have

Given:

Seating capacity = 257

Charges: Children = $5.00; Students = $7.00; Adults = $12.00

Total sales of ticket = $1870

A number of children, students, and adults were present in the theatre.

Let A, C, and S represent adults, children, and students respectively.

There are half as many adults as there are children; this means that

A = ½C

If the total seat capacity is 257, then

A + C + S = 257

Also, if the total sales of tickets are $1870, then

12A + 7S + 5C = 1870

So, we have two equations to be solved simultaneously.

A + C + S = 257 --- (1)

12A + 7S + 5C = 1860 --- (2)

Substitute ½C for A in (1) and (2)

½C + C + S = 257

Multiply both sides by 2

2(½C + C + S) = 2 * 257

C + 2C + 2S = 514

3C + 2S = 514 ----- (3)

12(½C) + 7S + 5C = 1870

6C + 7S + 5C ,= 1870

6C + 5C + 7S = 1870

11C + 7S = 1870 --- (4)

Make S the subject of the formula in (3)

2S = 514 - 3C

S = ½(514 - 3C)

S = 257 - 1.5C

Substituton 257 - 1.5C for S in (4)

11C + 7(257- 1.5C) = 1870

11C + 1799 - 10.5C = 1870

Collect like terms

11C - 10.5C = 1870 - 1799

0.5C = 71

Multiply both sides by 2

2 * 0.5C = 2 * 71

C = 142

Recall that

S = 257 - 1.5C

S = 257 - 1.5(142)

S = 257 - 213

S = 44

Also, recall that

A = ½C

A = ½ * 142

A = 71

Hence, the attendance at the movie theatre is;

Children = 142

Students = 44

Adults = 71

To learn more about the arithmetic from the given link

https://brainly.com/question/28369191

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