A right-angled triangle is shown below.
By first writing an equation involving tan 63°, calculate the length r.
Give your answer in metres to 2 d.p..
13.85 m
63°

The odd one out from the three given ratios 3:6, 3:9 and 6:12 is 3:9 as 3x2 = 6 and 6x2 = 12 but 3x3 = 9.

A ratio is a means to compare two numbers that are similar or to demonstrate a relationship.

In the previous illustration, B and G are terminology. G is referred to as the consequent term, and B as the antecedent word.

Ratios are used to compare items with the exact same type. To analyze the proportion of boys to girls in your class, for instance, we might use a ratio. Another illustration would be to assess the ratio of peanuts to all other nuts in a container of mixed nuts.

The given ratios are;

3:6,3:9 and 6:12

Here the pattern follows:

3x 2 = 6

3x 3 = 9

6x 2 = 12

Thus, odd one out will be the ratio 3:9.

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Assuming the triangles in the pair above are similar, the value of x is equal to 11.

In Mathematics, the basic proportionality theorem states that when any of the two (2) sides of a triangle is intersected by a straight line which is parallel to the third (3rd) side of the triangle, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.

By applying the basic proportionality theorem to the given triangle, we have the following:

UV/VW = SU/ST

(5x + 11)/88 = 18/24

By cross-multiplying, we have the following:

24(5x + 11) = 18(88)

120x + 264 = 1,584

By rearranging and collecting like-terms, the value of x is given by:

120x = 1,584 - 264

120x = 1,320

x = 1,320/120

x = 11.

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Given the ratio of CD:DE:EF as 1:6:3 and CF as 20, we can use the sum of segment lengths equation to find the length of EF to be 12 units.

We're given that points C, D, E, and F lie on the same line segment in that order, with the ratio CD:DE:EF equal to 1:6:3. This means that the length of segment CD is 1x, the length of segment DE is 6x, and the length of segment EF is 3x, for some common factor x.

We're also given that CF (the total length of the segment from C to F) is equal to 20. So that we can set an equation:

CD + DE + EF = CF

Substituting the values we know from the ratio and CF:

1x + 6x + 3x = 20

Combining like terms:

10x = 20

Solving for x:

x = 2

Now we can use this value of x to find the lengths of each segment:

CD = 1x = 1(2) = 2

DE = 6x = 6(2) = 12

EF = 3x = 3(2) = 6

So the length of segment EF is 12 units.

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Answer:The most accurate inference from this boxplot is that: The visiting team had more variability in the number of shots taken.

Step-by-step explanation:

The box and whiskers plot is a way of presenting data that gives 5 major information about the distributionFrom the whiskers of the plot, one can read- The minimum value - The maximum value Then, from the boxplot, one can read- The Median, represented by the middle line of the boxplot.- The first Quartile or 25th percentile, represented by the lower end of the boxplot.- The third quartile or 75th percentile, represented by the upper end of the boxplot.Other variables that can be obtained from these five data points include- The range of the distribution (maximum value minus minimum value)- The interquartile range (a measure of variation, which is the difference between the third and first quartile of the distribution)For the two boxplots that the coach madeHome teamWhiskers range from 16 to 32Minimum value = 16maximum value = 32the box ranges from 20 to 23. A line divides the box at 22.First quartile = 20Third quartile = 23Median = 22IQR = 23 - 20 = 3For the visiting teamWhiskers range from 14 to 32Minimum value = 14maximum value = 32the box ranges from 16 to 24. A line divides the box at 18.First quartile = 16Third quartile = 24Median = 18IQR = 24 - 16 = 8Since the median only represents the midpoint of the distribution, one cannot conclude with certainty that home team took more shots than the visiting team, information on the mean would confirm that. A less controversial and evident inference is that the visiting team had more variability in their shots as their distribution has a higher Interquartile Range (IQR of 8 > 3) which is a direct measure of variation for distributions.

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A toy shop purchases 125 identical stuffed animals for a total cost of $321.50 and sells them for $7 each. The percent markup is 171.9%.

The total cost of purchasing 125 identical stuffed animals is $321.50.

To find the cost per stuffed animal, we divide the total cost by the number of stuffed animals:

Cost per stuffed animal = Total cost / Number of stuffed animals

Cost per stuffed animal = $321.50 / 125

Cost per stuffed animal = $2.572

The toy shop sells each stuffed animal for $7.

To find the markup, we need to calculate the difference between the selling price and the cost price, and then express that difference as a percentage of the cost price:

[tex]Markup = (Selling price - Cost price) / Cost price * 100%[/tex]

Markup = ($7 - $2.572) / $2.572 x 100%

Markup = $4.428 / $2.572 x 100%

Markup = 1.719 x 100%

Markup = 171.9%

Therefore, the percent markup is 171.9%.

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Barbara can make six different compound machines if order matters.

There are three different simple machines that Barbara can use. Let's call them A, B, and C.

If order matters, then for the first machine, Barbara can choose any of the three simple machines. For the second machine, she can choose any of the remaining two simple machines. And for the third machine, she can choose the last remaining simple machine.

Therefore, the total number of different compound machines that Barbara can make is:

3 x 2 x 1 = 6

So Barbara can make six different compound machines.

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With the help of probability we can solve our question-

The idea of probability describes the possibility of an event happening.

We frequently have to make forecasts about the future in real life.

We may or may not be aware of the outcome of an event.

When this happens, we declare that there is a chance the event will take place.

In summary, probability has a wide range of fantastic applications in entertainment, business, and this recently expanding branch of artificial intelligence.

The probability formula can be used to determine the likelihood of an event by only dividing the favorable number of possibilities by the entire number of possible outcomes.

s=d/t

75 minutes

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Answer:

30cm²

Step-by-step explanation:

If yu remove the triangle FED and replace it in place ABC, you will recive a rectangle of side a=AC=6cm and b=DC=5cm. And the area of rectangle is a*b.

Area=a*b=6cm*5cm=30cm²

We can conclude by answering the provided question that As a result, Figure B has a capacity of approximately 226.19 cubic centimetres and a surface area of approximately 94.25 square centimetres.

The surface area of an object indicates the total volume filled by its surface. The surface area of a three-dimensional shape is the entire quantity of space that surrounds it. The surface area of a three-dimensional object refers to its total surface area. By adding the areas of each face, the surface area of a cuboid with six rectangular sides can be determined. As an alternative, you can use the following algorithm to identify the box's dimensions: 2lh + 2lw + 2hw = surface (SA). Surface area is a measurement of the total quantity of room occupied by the surface of a three-dimensional shape (a three-dimensional shape is a shape that has height, width, and depth).

For each figure, we will compute the volume and surface area individually.

Diagram A:

Figure A is a rectangle pyramid in form. It measures 10 centimetres long, 6 cm wide, and 4 cm tall.

Diagram B:

Figure B is a cylindrical in form. It has a radius of 3 centimetres and a height of 8 cm.

Image B volume = x radius2 x height = x 32 x 8 cm3 = 226.19 cubic centimetres

Figure B surface area = 2 x radius x height + 2 x radius2 = 2 x 3 cm x 8 cm + 2 x 32 cm2 = 94.25 square centimetres

As a result, Figure B has a capacity of approximately 226.19 cubic centimetres and a surface area of approximately 94.25 square centimetres.

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Answer:

To find the perimeter of the shaded shape, we need to determine the length of the sides of the shaded shape.

First, we need to find the area of the two small rectangles that were removed from the large rectangle:

Area of small rectangle 1: length x width = 4 cm x 3 cm = 12 cm²

Area of small rectangle 2: length x width = 4 cm x 2 cm = 8 cm²

The total area of small rectangles: 12 cm² + 8 cm² = 20 cm²

Now we can find the area of the shaded shape by subtracting the area of the small rectangles from the area of the large rectangle:

Area of large rectangle: length x width = 10 cm x 8 cm = 80 cm²

Area of shaded shape: 80 cm² - 20 cm² = 60 cm²

Since the shaded shape is rectangular, we can find the length and width by dividing the area by a factor pair:

60 cm² ÷ 6 cm = 10 cm

60 cm² ÷ 10 cm = 6 cm

So the shaded shape has sides of 6 cm and 10 cm.

Finally, we can find the perimeter of the shaded shape by adding up the lengths of all four sides:

Perimeter = 6 cm + 10 cm + 6 cm + 10 cm = 32 cm

Therefore, the perimeter of the shaded shape is 32 cm.

Step-by-step explanation:

Answer: (-4,5)

Step-by-step explanation:

The number of observation taken to obtain confidence interval of 50% is equal to 484.

Confidence interval for p = 50%

Use the formula for the confidence interval of a proportion to find the sample size n,

p ± z√(p×(1-p)/n) = (0.57, 0.63)

where z is the z-score corresponding to a 50% confidence interval, which is 0.674.

Midpoint of the interval is,

(p1 + p2) / 2

= (0.57 + 0.63) / 2

= 0.60

Rewrite the equation as,

0.60 ± 0.674√(0.60(1-0.60)/n) = (0.57, 0.63)

Simplifying this equation, we get,

⇒ 0.674√(0.60(1-0.60)/n) = 0.03/2

⇒ 0.674√(0.60(1-0.60)/n) = 0.015

Squaring both sides and solving for n, we get,

⇒n = 0.60×(1-0.60)×(0.674/0.015)^2

⇒n = 483.84

Rounding up to the nearest integer, the sample size is n = 484.

Therefore, n k equals 484 k, and 484 observations were taken to obtain the 50% confidence interval of (0.57, 0.63) for p.

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Answer:

Let's assume the width of the door is x inches. Then, according to the problem, the length of the door is 48 inches longer than the width, which means the length is x+48 inches.

The area of the door is given as 3024 square inches, so we can set up an equation:

Area = width x length

3024 = x(x+48)

Simplifying the equation, we get:

x^2 + 48x - 3024 = 0

Now we can solve for x using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

where a = 1, b = 48, and c = -3024

x = (-48 ± √(48^2 - 4(1)(-3024))) / 2(1)

x = (-48 ± √(2304 + 12096)) / 2

x = (-48 ± √14400) / 2

We take the positive root since the width of a door cannot be negative:

x = (-48 + 120) / 2

x = 36

Therefore, the width of the door is 36 inches.

Step-by-step explanation:

4x2/9

Both will result to 8/9

If all else remains constant and the values of two variables move in the same direction, it indicates a positive correlation.

  Correlation is a statistical measure that expresses the relationship between two variables. The correlation coefficient, which ranges from -1 to +1, is used to quantify the correlation.

 A positive correlation is when the values of the variables move in the same direction. A correlation of +1 indicates that the variables are perfectly positively correlated, implying that as one variable increases, the other also increases.

 A correlation of -1 indicates that the variables are perfectly negatively correlated, implying that as one variable increases, the other decreases. A correlation of zero indicates that there is no correlation between the variables.

   Hence a positive correlation exists when the values of two variables move in the same direction while all other factors remain constant.

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Answer: 9x4=36

Step-by-step explanation:

The wall is 9 meters long and 9 meters wide.The area of a square is equal to the length multiplied by the width.

The area of a square is equal to the length multiplied by the width. Therefore, in order to determine the dimensions of the wall, we must solve the equation 81 = l x w, where l and w represent the length and width of the wall, respectively. By dividing both sides of the equation by 9, we get that l = w = 9, meaning that the wall is 9 meters long and 9 meters wide.

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Answer: (4 x 3) - (2 + 9)

The correct numerical expression is:

(4 x 3) - (2 + 9)

Number of different page that numbers contain the digit 1 is 20

We can approach this problem by counting the number of pages that do not contain the digit 1 and subtracting that from the total number of pages, which is 200.

Let's count the number of pages that do not contain the digit 1. We can do this by considering each digit in turn. There are 9 choices for the first digit (it cannot be 1), and 10 choices for each of the remaining digits (since 1 is now allowed). So, there are 9 × 10 × 10 = 900 page numbers that do not contain the digit 1.

Therefore, the number of page numbers that do contain the digit 1 is 200 - 900 = -700.

However, this answer does not make sense since we cannot have negative page numbers. Therefore, there must be a mistake in our calculation. The mistake occurs when we consider the case where the first digit is 1. In this case, there are only 2 digits left to choose from (0 and 2-9), not 10. So, the correct number of page numbers that do not contain the digit 1 is 9 × 2 × 10 = 180.

Therefore, the number of page numbers that do contain the digit 1 is 200 - 180 = 20.

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Whatn the 5 highest is removed then standard deviation will decrease. (C)

The standard deviation is a measure of how spread out numbers are from the mean. Removing the 5 highest scores from the distribution of 20 scores will cause the numbers to become more concentrated around the mean, thus decreasing the standard deviation.

This is because the 5 highest scores are further away from the mean than the other numbers and by removing them, the average distance between the numbers and the mean decreases.

Mathematically, the formula for standard deviation is the square root of the sum of squared deviations from the mean divided by the number of scores minus 1.

When the 5 highest scores are removed, this means the sum of squared deviations from the mean is reduced, and since the number of scores is also reduced, the overall standard deviation value decreases.(C)

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Check the picture below.

So, the total cost including sales tax is 1.07 times the cost before tax.

Percent is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%". It is commonly used to represent proportions, rates, and changes in quantity. For example, if 50 out of 100 students in a class passed an exam, the pass rate is 50%, which means that 50% of the students in the class passed the exam.

Here,

Let's say the cost of the fishing gear before tax was $X. Then, the sales tax would be 0.07*X. To get the total cost, we add the cost before tax and the sales tax:

Total cost = cost before tax + sales tax

Total cost = X + 0.07X

Total cost = 1.07X

So, the total cost including sales tax is 1.07 times the cost before tax. If you know the cost before tax, you can calculate the total cost by multiplying it by 1.07.

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The new variance is  0.35.

The variance of a random variable measures how spread out the values are from the mean.

The formula for the variance is Var(X) = E[(X - E[X])²], where E[X] is the expected value (or mean) of X.

If the price of a box of Cheerios Oat Crunch increases by 25 cents, the new mean cost would be $4.25. To find the new variance, we can use the formula Var(aX + b) = a²Var(X), where a is a constant and b is a constant. In this case, a = 1 (because we are not changing the units of measurement) and b = 0.25 (because we are adding 25 cents to the price).

Therefore, the new variance is Var(X + 0.25) = Var(X) = Var(X) x 1² = Var(X) = 0.35.

This means that the variance remains the same even though the price has increased. This is because the variance is a measure of how spread out the values are from the mean, and the mean has shifted by the same amount as the price increase. Therefore, the distance between the values and the new mean is the same as the distance between the values and the old mean, so the spread is unchanged.

The variance is a measure of how spread out a set of data is from its mean. It is calculated as the average of the squared differences between each value and the mean. The formula for variance is Var(X) = E[(X - E(X))²], where E is the expected value or mean of X.

In this case, we are given that the mean cost of a box of Cheerios Oat Crunch is $4.00 and the variance is 0.35. This means that the average squared difference between each box's cost and the mean cost is 0.35.

Now, if the price of each box increases by 25 cents, this means that the new mean cost will be $4.25. However, this does not affect the variance directly. This is because the variance only measures how spread out the data is from the mean, and the mean has shifted by the same amount as the price increase.

To see this more clearly, imagine a set of data that has a mean of 4 and a variance of 0.35. If we add 0.25 to each value, we get a new set of data that has a mean of 4.25. However, the spread of the data is still the same; that is, the distance between each value and the new mean is the same as the distance between each value and the old mean. Therefore, the variance remains the same even though the price has increased.

In summary, the variance measures how spread out a set of data is from its mean, and a shift in the mean does not affect the variance directly.

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Answer: d

≥

3/4

Step-by-step explanation:

2d+7.5d≥ 5.5d +3

9.5d≥ 5.5d +3

9.5d-5.5d ≥ 3

4d ≥ 3

***Divide 4 on both sides

d

≥

3/4

After answering the prοvided questiοn, we can cοnclude that Therefοre, equatiοn the cοst οf οne apple pie is $8, and the cοst οf οne lemοn meringue pie is $20.

In mathematics, an equatiοn is a statement that implies the unity οf twο traits. An equatiοn cοnsists οf twο sides separated because οf an analytical sοlutiοn (=). Fοr instance, the debate "2x + 3 = 9" asserts that the remark "2x + 3" equals the valuatiοn "9". The gοal οf sοlving equatiοns is tο determine the amοunt οr values οf the variable in the mοdel) that wοuld allοw the equatiοn tο really be true.

Fοrmulae can be simple οr cοmplex, regular οr nοnlinear, and cοntain οne οr mοre variables. Fοr example, in the equatiοn "x² + 2x - 3 = 0," the variable x is elevated tο the secοnd pοwer. Lines are used extensively in mathematics, including algebra, equatiοns, and geοmetry.

Let x be the cοst οf οne apple pie, and y be the cοst οf οne lemοn meringue pie.

[tex]6x+8y=208[/tex]

[tex]6x+ 2y= 88[/tex]

[tex]-24x - 8y = - 352[/tex]

[tex]6x + 8y = 208[/tex]

[tex]-18x =-144[/tex]

[tex]X = 8[/tex]

[tex]6(8) +8y =208[/tex]

[tex]48+8y=208[/tex]

[tex]8y =160[/tex]

[tex]Y= 20[/tex]

Therefοre, the cοst οf οne apple pie is $8, and the cοst οf οne lemοn meringue pie is $20.

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Answer:

120,000

Step-by-step explanation:

1.2 x 10^5 in standard form is 120,000.

To convert a number from scientific notation (with a power of 10) to standard form, you simply move the decimal point to the right or left depending on the sign of the exponent.

In this case, the exponent is positive, so we move the decimal point to the right by 5 places, filling in any empty spaces with zeros. This gives us the final answer of 120,000 in standard form.

The new mean cost of a box of Cheerios Out Crunch is $4.40. This means that, on average, customers can expect to pay $0.40 more for a box of cereal after the price increase.

The new mean cost of a box of Cheerios Out Crunch after a 10% increase in price would be $4.40.

To see why, we can start with the original mean cost of $4.00 per box. To calculate a 10% increase, we can multiply the original mean cost by 1.10 (or 110% as a decimal), which gives:

$4.00 x 1.10 = $4.40

The mean cost is the proportion of the cost of the multitude of items to the absolute number of items. In Maths, we likewise have the term called "normal". The normal of some random arrangement of information is known as the mean of information.

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As a result, the icicle has a volume of about 4.19 cubic inches.

. The formula V = (1/3)r2h, where r is the radius of the base and h is the height of the cone, determines the volume of a cone.

The distance between a circle's center to any other point on the circle is known as the radius. It is frequently represented by the letter "r."

The radius of a sphere, in this example, is the separation between any two points on its surface from the sphere's centre.

In this instance, the icicle is shaped like a cone with a 1 in. radius and a 12 in. height.

As a result, the icicle's volume is:

V = (1/3)π(1 in.)²(12 in.)

V ≈ 4.19 cubic inches

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