Aisling runs 2km on Monday and three times that many on Tuesday. If she wants to run 20km this week. How many km does she need to run

a. 39 work sampling observations. b. By selecting a random time and a random employee to observe. c. The 95% confidence interval for the population standard is approximately 83.56 +/- (2 * 22.83), or 37.9 to 129.2 hours per hundred beak adjustments.

a. To determine the number of work sampling observations necessary to achieve a 95% confidence level with a margin of error of +10%, we need to use the following formula:

n = (Z^2 * p * (1-p)) / E^2

Where:

n = sample size

Z = Z-score for the desired confidence level (1.96 for 95% confidence level)

p = proportion of beak adjustments estimated from preliminary investigation (0.3)

E = margin of error (0.1)

Plugging in the values:

n = (1.96^2 * 0.3 * 0.7) / 0.1^2

n = 38.15

Rounding up, we need at least 39 work sampling observations.

b. The random observations should be made by selecting a random time of day, and then selecting a random employee to observe. This should be repeated until the required number of observations has been made. This method ensures that all employees have an equal chance of being observed and that the observations are not biased towards certain times or individuals.

c. To determine the standard in hours per hundred beak adjustments, we need to use the following formula:

Standard = (Total time worked / Total number of beak adjustments) * 100

For the six employees summarized in the table:

Granny:

Standard = (82 / 164) * 100

Standard = 50 hours per hundred beak adjustments

Tweety:

Standard = (80 / 161) * 100

Standard = 49.69 hours per hundred beak adjustments

Item:

Standard = (200 / 185) * 100

Standard = 108.11 hours per hundred beak adjustments

Total:

Standard = (82 + 80 + 200 + 121 + 161 + 185) / (164 + 161 + 185) * 100

Standard = 83.56 hours per hundred beak adjustments

The calculated error is the difference between the estimated standard and the true population standard. Since we do not have the population data, we cannot calculate the error. However, we can calculate the variability in the sample data using the following formula:

Standard Error = Standard Deviation / √(n)

Where:

Standard Deviation = √((Σ(x - x-bar)^2) / (n - 1))

n = sample size

Using the data provided in the table, we can calculate the standard deviation and standard error as follows:

Standard Deviation = √(((82-73.5)^2 + (80-73.5)^2 + (200-119)^2 + (121-82.5)^2 + (161-119)^2 + (185-82.5)^2) / (6-1))

Standard Deviation = 55.88

Standard Error = 55.88 / √(6)

Standard Error = 22.83

This means that there is a 95% chance that the true population standard falls within + or - 2 standard errors of the estimated sample standard. Therefore, the 95% confidence interval for the population standard is approximately 83.56 + or - (2 * 22.83), or 37.9 to 129.2 hours per hundred beak adjustments.

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The complete question goes thus:

ACME Corp has hired Daffy Duck to conduct a work sampling project to establish standards. 25 employees are part of the operations under scrutiny. The operations include scenery making, coloring, animation, joke writing, duck beak adjustment, and carrot sourcing. A preliminary investigation resulted in the estimate that 30 percent of the time of the group was spent adjusting duck beaks (this is equal to 17,614 beak adjustments). a. How many work sampling observations would be necessary to conduct if a 95 percent confidence that the observed data were within a +10 percent of the population data? b. Describe how the random observations should be made and justify why (Assume that all random observations need to be conducted over a three-week period or 15 working days). c. The Following table illustrates summary data gathered from 6 out of the 25 employees. From this data, determine a standard in hours per hundred beak adjustments. What is the calculated error? Granny 82 164 Tweety 80 Item Total hours worked Total observations (all elements) Observations involving cataloguing Average rating Operators Speedy Taz Glez 78 76 200 121 Foghorn Leghorn 68 Yosemite Sam 81 161 185 144 51 57 29 42 47 55 78 95 120 85 95 99

Moving the ladder 1 foot towards the building will not be enough to raise it by 1 foot, and moving it 2 feet away from the building will not be enough to lower it by 2 feet.

The relationship between the distance the ladder is moved along the ground (run) and the resulting change in height (rise) is determined by the ladder's angle of inclination, which is constant. This angle can be calculated using trigonometry, specifically the tangent function:

[tex]angle = arctan(rise/run)[/tex]

For a 20-foot ladder, the angle of inclination is approximately 75.96 degrees. If the painter moves the ladder 1 foot towards the building, the run will decrease from 20 feet to 19 feet, which means the rise will decrease proportionally according to the tangent function:

[tex]new rise = tan(angle) * new run[/tex]

[tex]new rise = tan(75.96) * 19[/tex]

new rise ≈ 18.7 feet

So, moving the ladder 1 foot towards the building will only raise it by about 0.3 feet, not enough to achieve the desired 1-foot increase. Similarly, moving the ladder 2 feet away from the building will increase the run from 20 feet to 22 feet, causing the rise to increase proportionally according to the tangent function:

new rise = tan(angle) x new run

new rise = tan(75.96) x 22

new rise ≈ 21.3 feet

Therefore, moving the ladder 2 feet away from the building will only lower it by about 1.3 feet, not enough to achieve the desired 2-foot decrease.

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Answer:

y= -1/4x+b

Step-by-step explanation:

see image

The sample space for choosing one card from the set of eight cards labeled m, u, t, i, p, l, y is 8.

An assortment or set of potential results from a random experiment make up a sample space. With the letter "S," the sample space is denoted. Events are a subset of the possible results of an experiment. Depending on the experiment, a sample space could have several different outcomes. Discrete sample spaces, often known as finite sample spaces, are those that have a finite number of outcomes.

The sample space for choosing 1 card is given as:

Sample space = 8C1 = 8! / (1!)(8 - 1)!

Sample space = 8.

Hence, the sample space for choosing one card from the set of eight cards labeled m, u, t, i, p, l, y is 8.

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The expressions that are equivalent to 2x - 3y = 12 are B and D.

We can modify the equation algebraically and simplify 2x - 3y = 12 to find the expressions that are equal to that number:

2x - 3y = 12

2x - 12 = 3y (subtract 12 from both sides) (subtract 12 from both sides)

(2/3)x - 4 = y (divide both sides by 3) (divide both sides by 3)

As a result, the equation can also be written as y = (2/3)x – 4.

We can now determine which expressions have the same meaning as this form:

A. y = 4 - (2/3)x

This expression is simplified to give y = (-2/3)x + 4. This isn't the same as y = (2/3)x – 4.

B. y = (2/3)x - 4

This formula already equals y = (2/3)x - 4 in terms of value.

C. 2x - 3y = -12

2x - 3y + 12 = 0 is the result of adding 12 to both sides of the equation. y = (2/3)x - 4 is not the same form as this.

D. y = (3/2)x - 6

This expression can be simplified to y = (2/3)x - 4 by doing so. The formula for this is y = (2/3)x – 4.

Hence, the formulas B and D are the same as 2x - 3y = 12.

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Answer:

144

Step-by-step explanation:

To show that d/dx (csc(x)) = −csc(x)cot(x), we will use the chain rule and the derivative of the inverse function.

The chain rule states that the derivative of a composite function is the product of the derivatives of the individual functions. The derivative of the inverse function is the reciprocal of the derivative of the original function. Here are the steps:

1. Start with the given function: d/dx (csc(x))
2. Rewrite csc(x) as 1/sin(x): d/dx (1/sin(x))
3. Use the chain rule to find the derivative: (d/dx 1)(d/dx sin(x))
4. The derivative of 1 is 0, so the first term becomes 0: (0)(d/dx sin(x))
5. The derivative of sin(x) is cos(x), so the second term becomes cos(x): (0)(cos(x))
6. Simplify the expression: 0
7. Use the derivative of the inverse function to find the derivative of 1/sin(x): -1/sin^2(x)
8. Rewrite sin^2(x) as (sin(x))(sin(x)): -1/(sin(x))(sin(x))
9. Simplify the expression by canceling out one of the sin(x) terms: -1/sin(x)
10. Rewrite 1/sin(x) as csc(x): -csc(x)
11. Rewrite -1/sin(x) as -cot(x): -cot(x)
12. Combine the two terms to get the final answer: −csc(x)cot(x)

Therefore, d/dx (csc(x)) = −csc(x)cot(x).

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Answer:₹14.40

Step-by-step explanation:

36x2=72

24x2=48

72+48=120x12=1440/100 =14.40

The equation for the graph that passes through (4,-5) and (7,10) is: y = 5x - 25

What is equation ?

An equation is a mathematical statement that shows that two expressions are equal. It contains an equal sign (=) between two expressions, one on each side. An equation can contain variables, constants, numbers, and mathematical operations like addition, subtraction, multiplication, and division

To write an equation for the graph that passes through the points (4,-5) and (7,10), we can use the slope-intercept form of a linear equation:

y = mx + b

where m is the slope of the line and b is the y-intercept.

To find the slope of the line passing through the two points, we can use the slope formula:

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

where (x1, y1) = (4,-5) and (x2, y2) = (7,10).

m = (10 - (-5)) / (7 - 4)

m = 15 / 3

m = 5

Now that we know the slope of the line, we can use either point to solve for the y-intercept, b. Let's use the point (4,-5):

y = mx + b

-5 = 5(4) + b

-5 = 20 + b

b = -25

Therefore, the equation for the graph that passes through (4,-5) and (7,10) is: y = 5x - 25

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The answer of another zero - polynomial function with real coefficient at 1+2i is 1-2i

The other zero of the polynomial function  with real coefficients and a zero at 1+2i is 1-2i.

This is because if a polynomial function with real coefficients has a complex zero,

then the conjugate of that zero is also a zero of the function. The conjugate of a complex number is obtained by changing the sign of the imaginary part.

Therefore, the conjugate of 1+2i is 1-2i. So, if 1+2i is a zero of the polynomial function, then 1-2i is also a zero of the function.

In summary, the other zero of the polynomial function with real coefficients and a zero at 1+2i is 1-2i.

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The ratio of strawberries to bananas in the basket is 12:18 or 2:3. To find this ratio, you simply take the number of strawberries and place it over the number of bananas. In this case, there are 12 strawberries and 18 bananas, so the ratio is 12:18.

However, this ratio can be simplified by dividing both numbers by their greatest common factor, which is 6. So, the simplified ratio of strawberries to bananas is 2:3. This means that for every 2 strawberries, there are 3 bananas in the basket.

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Triangle IJK is an isosceles triangle.

The slope of IJ is -2, the slope of JK is 1, and the slope of IK is 2. The length of IJ is 8, the length of JK is 4, and the length of IK is 6. Triangle IJK is an isosceles triangle.
√Correct

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The simplified expression is (3x^(4)-12x^(3)-26x^(2)+21x-44)/((x^(2)+1x-6)*(2x^(2)-5x+2)), or (f(x))/(g(x)), where f(x)=3x^(4)-12x^(3)-26x^(2)+21x-44 and g(x)=(x^(2)+1x-6)*(2x^(2)-5x+2).

To simplify the expression (2x^(2)+5x+2)/(x^(2)+1x-6)-:(x^(2)+6x+8)/(2x^(2)-5x+2), we need to find a common denominator and then subtract the numerators. The common denominator in this case is (x^(2)+1x-6)*(2x^(2)-5x+2).

So, the expression becomes:

((2x^(2)+5x+2)*(2x^(2)-5x+2)-(x^(2)+6x+8)*(x^(2)+1x-6))/((x^(2)+1x-6)*(2x^(2)-5x+2))

Simplifying the numerator, we get:

(4x^(4)-5x^(3)-4x^(2)+27x+4-1x^(4)-7x^(3)-14x^(2)-6x-8x^(2)-48x-48)/((x^(2)+1x-6)*(2x^(2)-5x+2))

Combining like terms, we get:

(3x^(4)-12x^(3)-26x^(2)+21x-44)/((x^(2)+1x-6)*(2x^(2)-5x+2))

So, the simplified expression is (3x^(4)-12x^(3)-26x^(2)+21x-44)/((x^(2)+1x-6)*(2x^(2)-5x+2)), or (f(x))/(g(x)), where f(x)=3x^(4)-12x^(3)-26x^(2)+21x-44 and g(x)=(x^(2)+1x-6)*(2x^(2)-5x+2).

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The polynomial in factored form whose solutions are x = -3, 5/2, and -5i is 2(x + 3)(2x - 5)(x² + 25).

Given the solutions;

To have the solutions at x = -3 and x = 5/2, the polynomial must have factors of (x + 3) and (2x - 5), respectively.

Also, to have a solution at x = -5i, there must be a factor of (x+5i) and its complex conjugate (x-5i):

Hence;

(x + 3)(2x - 5)(x + 5i)(x - 5i)

Multiplying out these factors gives:

(x + 3)(2x - 5)(x + 5i)(x - 5i)

(x + 3)(2x - 5)(x² + 25)

= (2x² + x - 15)(x² + 25)

= 2x⁴ + x³ - 15x² + 50x² + 25x - 375

= 2x⁴ + x³ + 35x² + 25x - 375

So the polynomial in factored form is:

= 2(x + 3)(2x - 5)(x + 5i)(x - 5i)

= 2(x + 3)(2x - 5)(x² + 25)

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The annual interest rate.

To find the annual interest rate r that will allow your balance to reach $2000 in 10 years, we need to use the formula for continuously compounded interest: A = Pert, where A is the final amount, P is the principal amount, r is the annual interest rate, and t is the time in years.

We are given that P = $1000, A = $2000, and t = 10 years. Plugging these values into the formula, we get:

$2000 = $1000e10r

Dividing both sides by $1000, we get:

2 = e10r

Taking the natural logarithm of both sides, we get:

ln(2) = 10r

Dividing both sides by 10, we get:

r = ln(2)/10 ≈ 0.0693

Therefore, the annual interest rate r that will allow your balance to reach $2000 in 10 years is approximately 6.93%.

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For each of the given , we need to use the Law of Sines to determine whether the given information results in two triangles, one triangle, or no triangles. The Law of Sines states that for any triangle, the ratio of the length of a side to the sine of the opposite angle is the same for all three sides:

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

Let's look at each scenario and apply the Law of Sines:

Scenario 1: a = 7, b = 10, A = 50°

Using the Law of Sines, we can find the value of angle B:

7/sin 50° = 10/sin B

sin B = 10*sin 50°/7

sin B = 0.918

B = sin^-1(0.918) = 66.4°

Since the sum of the angles in a triangle must equal 180°, we can find the value of angle C:

C = 180° - 50° - 66.4° = 63.6°

Since all three angles add up to 180° and are positive, we can conclude that this scenario results in one triangle.

Scenario 2: a = 5, b = 7, A = 120°

Using the Law of Sines, we can find the value of angle B:

5/sin 120° = 7/sin B

sin B = 7*sin 120°/5

sin B = 1.209

Since the sine of an angle cannot be greater than 1, this scenario does not result in a triangle.

Scenario 3: a = 9, b = 12, A = 30°

Using the Law of Sines, we can find the value of angle B:

9/sin 30° = 12/sin B

sin B = 12*sin 30°/9

sin B = 0.667

B = sin^-1(0.667) = 41.8°

Since the sum of the angles in a triangle must equal 180°, we can find the value of angle C:

C = 180° - 30° - 41.8° = 108.2°

Since all three angles add up to 180° and are positive, we can conclude that this scenario results in one triangle.

In conclusion, scenario 1 and scenario 3 result in one triangle, while scenario 2 does not result in a triangle. We can determine this by using the Law of Sines and checking whether the values of the angles are valid and add up to 180°.

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Answer:

see explanation

Step-by-step explanation:

the x- intercepts are the values of x on the x- axis where the graph crosses the x- axis.

On the x- axis the y- coordinate of any point is zero.

Set the factored form of the polynomial to zero and solve for x

x(x - 3)(x + 3)(x - 2) = 0

equate each factor to zero and solve for x

x = 0

x - 3 = 0 ⇒ x = 3

x + 3 = 0 ⇒ x = - 3

x - 2 = 0 ⇒ x = 2

the x-intercepts are then x = - 3, x = 0, x = 2, x = 3

these can be confirmed from the graph of the polynomial

cost = 3/√34,  csct = √34/5, sect =√34/3 , and cott = 3/5

explanation:-

The given equation is: tant = 5/3, so, cot t = 3/5 as cot t= 1/tan t

we know sec² t - tan² t = 1

or, sec²t= 1 + tan²t = 1+(25/9) = 34/9

or, sect = √(34/9) = √34/3

or, cos t=√(9/34) = 3/√34 as cos t= 1/sec t

now, also, csc²t - cot²t = 1

or, csc²t = 1+cot²t = 1+ 9/25 = 34/25

or, csc t= √34/5

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A package that weighs 5 pounds will cost $15 for both options.

The equation can be used to symbolize the price, y: Y is equal to 5 plus 2 times the weight of the package, x.

Another choice is for the buyer to pay a one-time price of $15, which is represented by the equation y = 15, in order to send the package.

We'll compare the equation as a whole.

In this case,

5 + 2x = 15

Compile similar terms,

2x = 15 - 5

2x = 10

x = 10 / 2

x = 5

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Answer:

To determine who has a greater mean, we need to calculate the mean (average) number of miles ridden by Liz and Sara and compare them.

Day Liz Sara

1 7 6

2 12 8

3 10 5

4 8 10

5 5 7

To find the mean for Liz, we add up the miles she rode and divide by the number of days:

Mean for Liz = (7 + 12 + 10 + 8 + 5) / 5 = 8.4 miles per day

To find the mean for Sara, we add up the miles she rode and divide by the number of days:

Mean for Sara = (6 + 8 + 5 + 10 + 7) / 5 = 7.2 miles per day

Therefore, Liz has a greater mean than Sara by 1.2 miles per day (8.4 - 7.2 = 1.2).

a. False
b. True
c. False
d. False

In order to answer this question, it is important to understand the definitions of each of the terms:
- True or False: this is a type of question that requires the student to choose between two possible answers, True or False.
- Normal Distribution: this is a type of data distribution in which the data is symmetrically distributed around the mean, and the probability of occurrence is equal for all values.
- Standard Deviation: this is a measure of how spread out a set of data is from the mean. It is calculated by taking the square root of the variance of the data set.
- Median: this is the middle value in a data set when the values are arranged in ascending or descending order.
- Quartile: this is a type of quartile division in which a data set is divided into four equal parts, each containing 25% of the data.
- Mode: this is the most frequently occurring value in a data set.
- Population Standard Deviation: this is a measure of the spread of the population, and it is calculated by taking the square root of the variance of the population.

Therefore, the correct answer to the given question is:
a. False
b. True
c. False
d. False

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Step-by-step explanation:

Let L and W be the length and width of the rectangle, respectively.

We know that the perimeter, P, of a rectangle is given by:

P = 2L + 2W

In this case, P = 16 cm, so we have:

16 = 2L + 2W

Simplifying, we get:

8 = L + W

To find the greatest area of the rectangle, we need to maximize the product of L and W, which is the formula for the area, A:

A = L * W

We can solve for one variable in terms of the other using the equation we found earlier:

L = 8 - W

Substituting this into the formula for the area, we get:

A = (8 - W) * W

Expanding and simplifying, we get:

A = 8W - W^2

To find the maximum value of A, we can use calculus or complete the square. Completing the square, we get:

A = -(W - 4)^2 + 16

Since the square of a real number is always nonnegative, the maximum value of A occurs when (W - 4)^2 = 0, which is when W = 4.

Substituting this value back into the equation for the perimeter, we get:

8 = L + 4

L = 4

Therefore, the rectangle with a perimeter of 16 cm and the greatest area is a square with sides of length 4 cm, and its area is:

A = L * W = 4 * 4 = 16 square centimeters.

The asymptotes of the rational function f(x)=(5)/(3x+6) are x=-2 .

To find the asymptotes of a rational function, we need to analyze the degree of the numerator and denominator, and find the values of x that make the denominator equal to zero.

First, let's find the vertical asymptotes. Vertical asymptotes occur when the denominator of a rational function is equal to zero. In this case, the denominator is 3x+6. Setting this equal to zero, we get:

3x+6=0
3x=-6
x=-2

So, the vertical asymptote is x=-2.

Next, let's find the horizontal asymptotes. Horizontal asymptotes occur when the degree of the numerator is less than or equal to the degree of the denominator. In this case, the degree of the numerator is 0 and the degree of the denominator is 1, so there is a horizontal asymptote. To find the horizontal asymptote, we need to look at the leading coefficients of the numerator and denominator. The leading coefficient of the numerator is 5 and the leading coefficient of the denominator is 3. So, the horizontal asymptote is y=5/3.

Therefore, the asymptotes of the rational function f(x)=(5)/(3x+6) are x=-2 (vertical asymptote) and y=5/3 (horizontal asymptote).

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The mass of the solid copper cuboid with dimensions length = 10cm, breadth = 5cm, and height = 3cm, is 1.479 kg.

A cuboid is a three-dimensional geometric shape that has six rectangular faces. It is also known as a rectangular parallelepiped. A cuboid has six rectangular faces, where opposite faces are congruent and parallel. The cuboid has eight vertices, twelve edges, and six rectangular faces.

To calculate the mass of a cuboid, you need to know its volume and density. The volume of a cuboid is the product of its length, width, and height. The density of a material is its mass per unit volume. Once you have these values, you can use the following formula to calculate the mass of the cuboid:

Mass = Density x Volume

where Mass is the mass of the cuboid, Density is the density of the material of which the cuboid is made, and Volume is the volume of the cuboid.

In the given question,

Using the given values, we can now calculate the mass of the solid copper cuboid in kg.

The volume of the copper cuboid is:

Volume = Length × Breadth × Height = 10 cm × 5 cm × 3 cm = 150 cm³

The mass of the copper cuboid can be calculated by multiplying its volume with its density. We are given that the density of copper is 9.86 g/cm³. Therefore, we have:

Mass = Volume × Density = 150 cm³ × 9.86 g/cm³ = 1479 g

To convert the mass in grams (g) to kilograms (kg), we need to divide the mass by 1000. Therefore:

Mass in kg = Mass in g / 1000 = 1479 g / 1000 = 1.479 kg

Therefore, the mass of the solid copper cuboid with dimensions length = 10cm, breadth = 5cm, and height = 3cm, is 1.479 kg.

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The zeros of the polynomial are -5i, √5i, -√5i.

The given polynomial is: f(x)=x⁴+16x²-225.

Zeros of a polynomial are the values of x that make the polynomial equal to zero. These will be the x-intercepts of the polynomial's graph. To find the zeros of a polynomial, use the factored form of the polynomial and set each factor equal to zero. The solutions of this equation are the zeros of the polynomial.

The given zero is: -5i

To find the remaining zeros of the polynomial, we need to factor the polynomial.

We can factorize the polynomial as:

f(x) = (x² + 5i)(x² - 5i)

Finding Zeros:

Therefore, the remaining zeros of the polynomial are:

x = ±√5i

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NO, the ordered pair (9,2) is not the solution to the system 8x-4y=64 3y=6x-47.

The given ordered pair is (9,2) and the system of equations is:

8x-4y=64
3y=6x-47

To determine whether the given ordered pair is a solution to the system, we can substitute the values of x and y into the equations and see if they are true.

For the first equation:

8(9)-4(2)=64
72-8=64
64=64

For the second equation:

3(2)=6(9)-47
6=54-47
6=7

The first equation is true, but the second equation is not true. Therefore, the given ordered pair is not a solution to the system.

The final answer is: No, the given ordered pair is not a solution to the system.

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Answer:

20000

Step-by-step explanation:

1.4 divided by 0.007%

1.4 - 0.0007%

x - 100%

0.0007x = 1.4

x = 2000

∴ 1.4 is 0.0007% of 2000.

The two variables that vary the most across these countries are "Animal Protein" and "Vegetable Protein."

The variable that varies the least is "Total Protein." The profile plot tells us that Denmark has the highest amount of animal protein, followed by Norway and then Sweden. However, Sweden has the highest amount of vegetable protein, followed by Denmark and then Norway. Overall, Denmark has the highest total protein, followed by Norway and then Sweden.

This suggests that Denmark relies more heavily on animal protein sources, while Sweden relies more heavily on vegetable protein sources. Norway falls somewhere in the middle, with a more balanced mix of animal and vegetable protein sources.

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The number of students who voted for each mascot is given as follows:

Then the difference is given as follows:

nT - nC.

The difference between the two amounts is obtained applying the proportions in the context of the problem.

The circle graph gives the percentage of each type of vote.

Hence the amounts relative to each type of vote are given as follows:

In which:

The problem is incomplete, hence the general procedure is given to solve the problem.

More can be learned about proportions at https://brainly.com/question/24372153

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