Briefly state, with reasons, the type of chart which would best convey in each of the following:

(i) A country’s total import of cigarettes by source.

(ii) Students in higher education classified by age.

(iii) Number of students registered for secondary school in year 2019, 2020 and 2021 for areas X, Y, and Z of a country.

Answer:

see explanation

Step-by-step explanation:

A translation of 6 units up means adding 6 to the y- coordinate

A translation of 3 units left means subtracting 3 from the x- coordinate

The translation rule is (x, y ) → (x - 3, y + 6 ) , then

A (- 1, 2 ) → A' (- 1 - 3, 2 + 6 ) → A' (- 4, 8 )

B (1, 5 ) → B' (1 - 3, 5 + 6 ) → B' (- 2, 11 )

The distance from each landing point to the boat pulled ashore at point C is given by:-d = sqrt(25^2 (y^2/x^2 + 1))

WHAT IS TRIGONOMETRY ?

Trigonometry is a branch of mathematics that deals with the study of the relationships between the sides and angles of triangles. It is used to solve problems involving distances, heights, angles, and other geometric measurements. Trigonometric functions such as sine, cosine, and tangent are used to relate the angles of a triangle to its sides. Trigonometry has many practical applications in fields such as engineering, physics, and architecture, and is essential for understanding and solving problems involving waves, oscillations, and periodic phenomena. It is also used in navigation, surveying, and astronomy, among other areas.

To solve this problem, we need to use the concept of right triangle trigonometry.

Let's assume that point C is directly opposite the midpoint of AB, and that the distance from point C to the midpoint of AB is x. Then we can draw a right triangle with legs of length x and 25 (half of 50) and a hypotenuse of length d (the distance from point C to each landing point).

Using the Pythagorean theorem, we can write:

d^2 = x^2 + 25^2

We also know that the angles opposite the legs of the right triangle are complementary, so we can use the tangent function to write:

tan(theta) = x/25

where theta is the angle between the hypotenuse and the side of length 25.

We can rearrange this equation to solve for x:

x = 25 tan(theta)

Now we can substitute this expression for x into the equation for d^2:

d^2 = (25 tan(theta))^2 + 25^2

Simplifying this equation, we get:

d^2 = 25^2 (tan^2(theta) + 1)

Finally, we can use the fact that tan(theta) is equal to the height of the opposite bank divided by the distance from point C to the midpoint of AB. Let's call this distance y. Then we have:

tan(theta) = y/x

Substituting this expression for tan(theta) into the equation for d^2, we get:

d^2 = 25^2 (y^2/x^2 + 1)

So the distance from each landing point to the boat pulled ashore at point C is given by:

d = sqrt(25^2 (y^2/x^2 + 1))

where x and y are the distances from point C to the midpoint of AB and the opposite bank, respectively.

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Therefore, the series 4/5 - 4/7 + 4/9 - 4/11 + 4/13 - ... is convergence in nature.

To test the convergence or divergence of the given series: 4/5 - 4/7 + 4/9 - 4/11 + 4/13 - ..., we can use the alternating series test. The alternating series test states that if a series has the form (-1)^n b_n, where b_n is a positive sequence that is decreasing and approaches zero as n approaches infinity, then the series converges.

In the given series, we have b_n = 4/(2n+3), which is a positive sequence that approaches zero as n approaches infinity. To see that b_n is decreasing, we can note that b_{n+1}/b_n = 2(2n+3)/(2n+5) < 1 for all n, since the numerator is always less than the denominator. Therefore, b_n is a positive, decreasing sequence that approaches zero as n approaches infinity.

Furthermore, the series has the form (-1)^n b_n, where the sign alternates between positive and negative. Therefore, we can apply the alternating series test, which tells us that the series converges.

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Solution:

From the given table;

Where, the November values is used as 100 percent;

To find the missing percentages of Elm leaves

For the month of May

To find the missing percentages of Hazel leaves

What is the independent and dependent variable?

An independent variable is a variable that does not depend on any other variable.

For example,

x is an independent variable because for every value of x, there is a different value of y

A dependent variable is a variable whose value depends upon an independent variable.

For example;

From the expression above, the value of y depends on the value of x

Answer:

x = (-39)/11

Step-by-step explanation:

Solve for x:

x - 9 = (3 (5 x + 1))/4

Multiply both sides by 4:

4 (x - 9) = (4×3 (5 x + 1))/4

(4×3 (5 x + 1))/4 = 4/4×3 (5 x + 1) = 3 (5 x + 1):

4 (x - 9) = (3 (5 x + 1))

Expand out terms of the left hand side:

(4 x - 36) = 3 (5 x + 1)

Expand out terms of the right hand side:

4 x - 36 = (15 x + 3)

Subtract 15 x from both sides:

(4 x - 15 x) - 36 = (15 x - 15 x) + 3

4 x - 15 x = -11 x:

-11 x - 36 = (15 x - 15 x) + 3

15 x - 15 x = 0:

-11 x - 36 = 3

Add 36 to both sides:

(36 - 36) - 11 x = 36 + 3

36 - 36 = 0:

-11 x = 3 + 36

3 + 36 = 39:

-11 x = 39

Divide both sides of -11 x = 39 by -11:

(-11 x)/(-11) = 39/(-11)

(-11)/(-11) = 1:

x = 39/(-11)

Multiply numerator and denominator of 39/(-11) by -1:

Answer: x = (-39)/11

Answer: okay so this is what I think is the answer I used a calculate so

Step-by-step explanation:

$12.05

$24.08

$36.12

$48.16

$60.20

Step-by-step explanation:

1 hour        2 hours         3 hours        4 hours          5 hours  

$12.04       $24.08          $36.12         $48.16            $60.20

Answer:

Step-by-step explanation:

2 subtraction symbols equals a plus

so the answer is 9

Answer:`211

123123

Step-by-step explanation:

Each time X increases, there is a perfectly predictable increase in Y  is indicated by a Pearson correlation of r= +1.00 between X and Y

A Pearson correlation coefficient of +1.00 indicates a perfect positive linear relationship between the variables X and Y. It means that as X increases, Y increases in a perfectly predictable manner. The correlation coefficient of +1.00 indicates a strong and direct relationship between the two variables, where the values of Y can be precisely determined based on the values of X.

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ANSWER

3. $185

4. $60,125

EXPLANATION

We are given that a wedding at the Hall Plantation costs $22,200 for 120 people.

3. To calculate how much the wedding costs per guest, we have to divide the total cost for 120 people by the number of people (120).

That is:

22200 / 120 = $185

The cost per guest is $185.

4. To find how much they would charge for 325 guests, we will find the product of the cost per guest ($185) and the number of guests (325).

That is:

$185 * 325 = $60,125

That is the cost for 325 people.

Answer:

A

Step-by-step explanation:

The equation representing a proportional relationship is

y = kx ← k is the constant of proportion

The only equation in this form is

y = 24x ( k = 24 ) → A

Answer:

Length = 49 feet

Step-by-step explanation:

Since 35/5 is equal to 7, that means for every inch on the drawing it represents 7 feet. So you could multiply 7(7) to get the actual length.

Answer:

\(m-n=2\)

Step-by-step explanation:

Instead of using the standard form, we can use the vertex form of a quadratic equation:

\(f(x)=a(x-h)^2+k\)

Where a is the leading coefficient, and (h, k) is our vertex.

Our vertex point is at (2, -4). So, let’s substitute 2 for h and -4 for k:

\(f(x)=a(x-2)^2-4\)

Now, we need to determine a.

We know that it passes through the point (4, 12). So, when x is 4, y must be 12. In other words:

\(12=a((4)-2)^2-4\)

Solve for a. Subtract within the parentheses:

\(12=a(2)^2-4\)

Add 4 to both sides:

\(16=a(2)^2\)

Square:

\(16=4a\)

Solve:

\(a=4\)

Thererfore, the value of a is 4.

So, our function is:

\(f(x)=4(x-2)^2-4\)

Now, let’s find our roots. Set the equation to 0 and solve for x:

\(0=4(x-2)^2-4\)

\(4=4(x-2)^2\\1=(x-2)^2\\x-2=\pm1 \\ x=2\pm1 \\ x=3\text{ or } 1\)

So, our roots are 1 and 3.

The greater root is 3 and the lesser root is 1.

Therefore, m-n, where m>n, is 3-1 or 2.

Our final answer is 2.

Answer:

2

Step-by-step explanation:

Source: AOPS

Answer:

12 cents

Step-by-step explanation:

Approximately 109 grams of protein would be consumed on a 2500 kcal daily diet, with 35% of the calories coming from proteins.

Protein intake is an important aspect of a healthy diet, as it plays a vital role in various bodily functions. To calculate the grams of protein consumed, we start by determining the total calorie intake and then find the proportion of calories that come from proteins. In this case, the daily diet consists of 2500 kcal. To find the protein calories, we multiply this by the percentage of calories from proteins, which is 35%. This gives us 0.35 * 2500 = 875 kcal from proteins.

Next, we need to convert these calories into grams of protein. Each gram of protein provides approximately 4 calories. Therefore, we divide the protein calories (875 kcal) by 4 to get the grams of protein consumed, which is 875 / 4 ≈ 218.75 grams. Rounding this to the nearest gram, the individual would consume approximately 219 grams of protein on a 2500 kcal daily diet with 35% of the calories coming from proteins.

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Answer:

4

Step-by-step explanation:

Evaluate f(3) and g(2)

f(3) = 2(3) - 4 = 6 - 4 = 2

g(2) = - 3(2)² + 5(2) = - 3(4) + 10 = - 12 + 10 = - 2

Then

f(3) - g(2) = 2 - (- 2) = 2 + 2 = 4

Answer: 19.6 feet

Step-by-step explanation:

Using the Pythagorean theorem,

\(x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6\)

Answer:

Ellis needs to buy 21 packages of tiles to build the extension.

Step-by-step explanation:

There are 3 rectangles that are 6.25 m by 1.5 and 2 squares with a side length of 1.5 m  To build the extension, Ellis needs 32.625 m of tile. Each tile is 0.25 wide and 0.25 m long so Elis needs 16 tiles to build 1 m of the extension. Elis buys tiles in packages of 25. Since Ellis cannot buy part of a package, she will need 21 packages to have enough tiles. Ellis needs to buy 21 packages of tiles to build the extension. (*￣▽￣)b

The ordered pair which is the solution to the system of equations is  (3,-1)

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

y=3x-10 and 2x+3y=3    

                   putting y=3x-10 in 2x+3y=3

          ⇒      2x+3(3x-10)=3

          ⇒      2x+9x-30=3

          ⇒      11x=33

          ⇒       x=33/11

          ⇒       x=3

Putting x=3 in y=3x-10 ,we get

                          y=3×3-10

                      ⇒    y=9-10

                      ⇒    y=-1

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The equation which represents line that is parallel to the line y = -4/5x + 6 is; Choice A; 4x + 5y = 20.

The slope-intercept form equation is; y = Mx + c.

Since the given line is; y = -4/5x + 6

By comparison with the line; 4x + 5y = 20.

The slope-intercept form of the line above is;

y = -4/5x + 4

It follows that the slope m of both liens = -4/5.

Ultimately, since parallel lines have equal slopes, the required equation is; Choice A. 4x + 5y = 20.

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At μ = 10.0932 level should the mean be set if it is required that only 1% of the bags weigh less than 9.5 kg.

Given Data:

σ = 0.04 kg

x = 9.5 kg

We want to determine μ such that: P(X ≤ 9.5)= 1% = 0.01

Thus, we know here probability of x is 0.1 which is  less than 9.5

so here Z is -2.326 by the standard table

Determine the z-score in the normal probability table in the appendix that has a probability closest to 0.01:

Then, we have here 1% to left when Z is - 2.326

Now,

The value corresponding to the z-score is then the mean increased by the product of the z-score and the standard deviation:

x = μ+ zσ

= μ− 2.33(0.04) = μ - 0.0932

Since , P(X ≤ 9.5) = 0.95% = 0.095, we know that x also has to be equal to 9.5:

   μ− 0.0932 = 9.5

Add 0.0932 to each side of the previous equation:

μ = 10+ 0.0932

= 10.0932

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Answer:

A. Zero

Step-by-step explanation:

The upside down parabolic graph has no roots because it not linear

Answer: the height of the pole is 16.782 meters

Step-by-step explanation: Let us take the height of the pole as "h".

i) Finding the height of the pole:

distance from the pole is 20m.

The angle of elevation is 40°

\(tan(40°) = h/20\)

Multiply both sides by 20:

\(20 * tan(40°) = h\)

\(h ≈ 20 * 0.8391 ≈ 16.782 meters\)

Therefore, the height of the pole is 16.782 meters.

ii) Finding the angle of depression

The angle of depression is the angle formed between the horizontal ground and the line of sight from the point of observation to the foot of the pole.

angle of depression = angle of elevation = 40°

Therefore, the angle of depression of the foot of the pole from the point of observation is 40°.

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Using trigonometric methods, it is determined that the height of the pole is found by using the formula for tangent, and adding the height of the observer. The angle of depression equals the angle of elevation, so both are 40 degrees.

To solve the problem, we use the properties of a right triangle and trigonometric functions. Since we know the angle of elevation and the length of one side, we can find the length of the other side using the tangent function.

For the height of the pole: we know that tan(θ) = opposite/adjacent, so,
tan(40) = height/20
height = tan(40) * 20

Let's denote the observer's height as h=1.54m, so the total height of the pole is height + h.

For the angle of depression: In a right triangle, the angle of depression and the angle of elevation are equal. Therefore, the angle of depression is also 40 degrees.

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The general solution to the differential equation xy' + 3y = 0 is given by:

y = c/x^3

where c is a constant.

To verify that this is a solution, we can substitute it into the differential equation:

xy' + 3y = 0

\(x(d/dx)(c/x^3) + 3(c/x^3)\)= 0

-c/x^3 + 3(c/x^3) = 0

The last step follows from the fact that the derivative of \(x^(-n)\)is \(-nx^(-n-\)1).

This simplifies to:

\(2c/x^3\) = 0

which is true if and only if c = 0 or x = infinity. Since c can be any constant, this means that y = \(c/x^3\) is a family of solutions to the differential equation.

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The percentage of households in the town with internet access is estimates as 47.8%, give or take 2.2% or so.

According to statement we have given

239 of the 500 households in the sample had internet access.

So, find sample percentage then

Sample percentage= 500/239 =0.478=47.8%

Thus we estimate the percentage as 47.8%.

The box contains 25,000 tickets of which 47.8% are 1's and the remaining 52.2% tickets are 0's. We will draw 500 tickets from the box.

Number of draws=500

Now, find the SD then

\(SD= (Big number - Small number) * \sqrt{Fraction with big number * fraction with small number}\)

Substitute the values then

\(SD= (1 - 0) * \sqrt{0.478 *0.522}\)

\(SD=0.4995\)

Now find the standard error of sum then

The standard error of the sum is the product of the square root of the number of draws and the standard deviation of the box.

\(SE sum =\sqrt{Number of draws} * SD box\)

\(SE sum =\sqrt{500} * 0.4995\)

\(SE sum =11.16\)

Now find the standard error of percentage then

The standard error of the percentage is the standard error for the sum divided by the sample size.

SE percentage= SE for number/Number of draws ×100%

= 50011.1692×100%

≈0.022×100%

=2.2%

​

Thus the percentage of households in the town with internet access is estimates as 47.8%, give or take 2.2% or so.

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Answer:

2n+10q+65

Step-by-step explanation:

3q+9+25+6n+6+25+7q-4n

Reorder so all like terms are by each other.

6n-4n+3q+7q+9+6+25+25

Now combine those like terms.

2n+10q+15+50

2n+10q+65

That's as far as it goes.

-hope it helps

The values of r and s is -1 and -4 respectively.

Given that:-

coordinates of j are (-8,-5)

coordinates of l are (6,-11)

coordinates of k are (r-4,2s)

Also, k is the mid-point of jl.

We have to find the values of r and s.

We know that, for  (x,y) and (z,w), the mid-point is ((x+z)/2, (y+w)/2).

Here,

(x,y) = (-8.-5)

(z,w) = (6,-11)

(r-4,2s) = ((x+z)/2,(y+w)/2)

Hence,

(r-4,2s) = ((-8+6)/2,(-5-11)/2)

(r-4,2s) = (-1,-8)

Comparing the coordinates, we get:-

r - 4 = -1

r = -1+4 =3

2s = -8

s =-8/2 = -4

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The probability of hitting the bull's-eye all three times when throwing darts can be calculated using the multiplication rule of probability as P(3 hits) = p x p x p = \(p^3\),

where p is the probability of hitting the bull's-eye on each throw.

When throwing darts at a dart board, the probability of striking the bull's-eye is affected by many factors, such as the player's skill, the distance from the board, the type of dart used, and so on.

However, assuming that the probability of hitting the bull's-eye is the same for each throw and independent of previous throws;

We can calculate the probability of hitting the bull's-eye all three times using the multiplication rule of probability.

Suppose the probability of hitting the bull's-eye on each throw is p. Then, the probability of missing the bull's-eye on each throw is 1 - p.

The probability of hitting the bull's-eye all three times can be calculated as follows:

P(3 hits) = p x p x p = \(p^3\)

For example, if p = 0.05 (or 5%), then the probability of hitting the bull's-eye all three times would be:

P(3 hits) = 0.05 x 0.05 x 0.05 = 0.000125 or 0.0125%

This means that the chance of hitting the bull's-eye all three times is very low, and it would require a lot of skill and luck to achieve such a feat.

However, the probability of hitting the bull's-eye at least once in three throws would be much higher, and it would depend on the player's skill and consistency.

Overall, the probability of hitting the bull's-eye all three times is quite low, and it is more likely that a player will hit it once or twice or miss it altogether.

Nonetheless, the thrill of the game lies in the challenge and the unpredictability of each throw, making darts a popular game of skill and chance.

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