What is the range of this data set?
Length in Roses length in cm 22cm 23cm 24cm 25cm 26cm Number of roses 2 4 5 3 1

The answer is: There were about 169 principals in attendance.

what is proportion?

In mathematics, a proportion is an equation that states that two ratios or fractions are equal. A proportion can be written in the form of a/b = c/d, where a, b, c, and d are numbers or variables.

Proportions are used to compare two or more quantities or to find an unknown value. For example, if we know that the ratio of the length of a rectangle to its width is 2:1, and we also know that the length is 6 feet, we can use a proportion to find the width. We set up the proportion as 2/1 = 6/w, where w is the width of the rectangle, and then solve for w by cross-multiplying and simplifying the equation.

Proportions are also used in many real-world applications, such as cooking, finance, and science.

To make a prediction about the number of principals in attendance at the conference, we need to use the given information and make some assumptions.

We know that in one exhibit room of 80 people, there were 15 principals. Let's assume that this exhibit room is representative of the entire conference, and that the proportion of principals to attendees in this room is the same as the proportion of principals to attendees in the entire conference.

Using this assumption, we can set up a proportion:

15 principals / 80 attendees = x principals / 900 attendees

To solve for x, we can cross-multiply and simplify:

15 * 900 = 80 * x

x = (15 * 900) / 80 = 168.75

So our prediction is that there were about 169 principals in attendance at the conference.

Therefore, the answer is: There were about 169 principals in attendance.

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Answer: tan(R) = m/p

Step-by-step explanation: In the right triangle shown in the diagram, we know that the tangent of angle R is equal to the length of the opposite side (m) divided by the length of the adjacent side (p).

Therefore, an expression in terms of m and p that represents tan(R) would be tan(R) = m/p

The probability that the sample mean would be less than 100.9 months is approximately 0.9600.

We can use the central limit theorem to approximate the sampling distribution of the sample mean as a normal distribution with a mean of 97 months (the population mean) and a standard deviation of σ/√n, where σ is the population standard deviation and n is the sample size.

The standard deviation of the sampling distribution can be calculated as follows

σ/√n = √(169)/√59 = 2.065

Therefore, the z-score corresponding to a sample mean of 100.9 months is

z = (100.9 - 97) / 2.065 = 1.75

Using a standard normal distribution table or calculator, we can find that the probability of obtaining a z-score less than 1.75 is approximately 0.9599.

Therefore, the probability that the sample mean would be less than 100.9 months is approximately 0.9599.

Rounding this to four decimal places, we get

P(x < 100.9) ≈ 0.9600

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keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]7x-5y=-6\implies -5y=-7x-6\implies y=\cfrac{-7x-6}{-5} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{7}{5}}x+\cfrac{6}{5}\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so we're really looking for the equation of a line whose slope is 7/5 and it passes through (-4 , -5)

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-5})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{7}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{ \cfrac{7}{5}}(x-\stackrel{x_1}{(-4)}) \implies y +5 = \cfrac{7}{5} ( x +4) \\\\\\ y+5=\cfrac{7}{5}x+\cfrac{28}{5}\implies y=\cfrac{7}{5}x+\cfrac{28}{5}-5\implies {\Large \begin{array}{llll} y=\cfrac{7}{5}x+\cfrac{3}{5} \end{array}}[/tex]

The 5th term in the expansion of (a+b)⁴ in simplest form is 4a³b.

The binomial theorem is a mathematical formula that provides a way to expand the power of a binomial expression, which is an expression that consists of two terms.

The 5th term in the expansion of (a+b)⁴ can be found using the binomial theorem formula:

(a + b)ⁿ = C(n,0)aⁿ + C(n,1)[tex]a^(n-1)[/tex]b + C(n,2)[tex]a^(n-2)[/tex]b² + ... + C(n,n-1)a[tex]b^(n-1)[/tex] + C(n,n)bⁿ

where C(n,r) is the binomial coefficient, given by:

C(n,r) = n! / (r! * (n-r)!)

In this case, n = 4 and we want to find the 5th term, which means we want the coefficient for the term with a³b. Using the formula, we can see that the coefficient for this term is:

C(4,3) = 4! / (3! * (4-3)!) = 4

So the 5th term in the expansion of (a+b)⁴ is:

4a³b

In simplest form, we cannot simplify this expression any further. Therefore, the 5th term in the expansion of (a+b)⁴ in simplest form is:

[tex]4a^3b[/tex].

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Answer:

3 & 4

Step-by-step explanation:

Since you have 3 choice, you want to pick the options that can represent 3 options.

1. False, since a coin only has 2 sides.

2. False, black and red is two halves of a deck, meaning you only have 2 options.

3. True, 6 is divisible by three, so it can be used. Assuming each choice is represented by two number.

4. True, 3 choices is evenly represented by 3 sections

Answer:

So after dividing 8 by 20 your answer will come out to be 1 by 3. So the time is 1/3.

8 hours and 20 minutes is equivalent to 8.3333... hours, or approximately 8 hours and 20 minutes, or 0.35 of a day.

The exact value of cos a as required to be determined in the task content is; √57 / 8.

It follows from the task content that sin a = 3 / 8 and the exact value of cos a is to be determined in the task content.

Recall from trigonometric identities that;

cos ² a + sin² a = 1

Therefore, cos² a + (3 / 8)² = 1 since sin a = (3 / 8).

cos²a = 1 - (9 / 64)

cos²a = (64 - 9) / 64

cos²a = 57 / 64

cos a = √57 / 8.

Ultimately, the value of cos a as required to be determined in the task content is; √57 / 8.

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If the house value of $89,548 and two points, attorney's fees $324, title fees $105, then closing cost is option (b) $2,219.96

Closing costs are fees associated with the purchase or refinance of a property that are paid at the closing of the transaction.

To calculate the closing cost, we need to add up all the fees associated with the purchase of the house.

First, we need to calculate the cost of the points. Two points on a house value of $89,548 would be

2 x $89,548 x 0.01 = $1,790.96

Next, we need to add the attorney's fees and title fees

$1,790.96 + $324 + $105 = $2,219.96

Therefore, the correct option is (b) $2,219.96

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Here is the tree diagram to represent the sample space of spinning the spinner twice:

sp1 - Possible outcomes of the first spin:

Red, Blue, Green

sp1 - Red

sp2 - Red Red, Red

sp2 - Blue Red, Blue

sp2 - Green Red, Green

sp1 - Blue

sp2 - Red Blue, Red

sp2 - Blue Blue, Blue

sp2 - Green Blue, Green

sp1 - Green

sp2 - Red Green, Red

sp2 - Blue Green, Blue

sp2 - Green Green, Green

So the full sample space would be:

{(Red, Red), (Red, Blue), (Red, Green),

(Blue, Red), (Blue, Blue), (Blue, Green),

(Green, Red), (Green, Blue), (Green, Green)}

Does this capture the correct sample space for spinning the spinner twice? Let me know if you need any clarification.

Answer: To find the point on the line 3x + y = 8 that is closest to the point (-3,2), we need to minimize the distance between the line and the point.

Let (x, y) be the point on the line that is closest to (-3, 2). Then the vector from the point (-3, 2) to (x, y) is orthogonal (perpendicular) to the line. The direction vector of the line is <3, 1>, so the direction vector of the orthogonal vector is <-1/3, 1>.

Now we can write an equation for the line passing through (-3, 2) with the direction vector <-1/3, 1>:

(x - (-3))/(-1/3) = (y - 2)/1

Simplifying, we get:

3x + y = 11

This is the line passing through (-3, 2) that is orthogonal to the original line 3x + y = 8.

To find the intersection of these two lines, we can solve the system of equations:

3x + y = 8

3x + y = 11

Subtracting the first equation from the second, we get:

0 = 3

This is a contradiction, which means the two lines do not intersect. Therefore, the point on the line 3x + y = 8 that is closest to (-3, 2) does not exist.

However, we can still find the closest point to (-3, 2) on the line 3x + y = 8. This point will be the intersection of the line passing through (-3, 2) with the direction vector <-1/3, 1> and the line 3x + y = 8.

The equation of the line passing through (-3, 2) with the direction vector <-1/3, 1> is:

(x - (-3))/(-1/3) = (y - 2)/1

Simplifying, we get:

3x + y = 11

To find the intersection point with the line 3x + y = 8, we can solve the system of equations:

3x + y = 8

3x + y = 11

Subtracting the first equation from the second, we get:

0 = 3

This is a contradiction, which means the two lines do not intersect. Therefore, the point on the line 3x + y = 8 that is closest to (-3, 2) does not exist.

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Since it is an equilateral triangle AB=AC=5

If I sum up all sides u will get 18. How this helps.

Answer:

The answer is 6

Step-by-step explanation:

y=3

-3+y²

-3+(3)²

-3+6=6

The longest segment that would fit inside the cylinder is approximately 9.06 centimeters.

The longest segment that would fit inside the cylinder would be the diagonal of the cylinder's base, which is equal to the diameter of the base. The diameter of the base is equal to twice the radius, so it is 6 cm. Using the Pythagorean theorem, we can find the length of the diagonal:

[tex]diagonal^2 = radius^2 + height^2 \\diagonal^2 = 3^2 + 8^2 \\diagonal^2 = 9 + 64 \\diagonal^2 = 73 \\diagonal = sqrt(73)[/tex]

Therefore, the longest segment that would fit inside the cylinder is approximately 8.54 cm (rounded to the nearest hundredth).
To find the longest segment that would fit inside the cylinder, we need to calculate the length of the space diagonal of the cylinder. This is the distance between two opposite corners of the cylinder, passing through the center. We can use the Pythagorean theorem in 3D for this calculation.

The terms we'll use are:
- Radius (r): 3 cm
- Height (h): 8 cm

To find the space diagonal (d), we can use the following formula:

[tex]d = \sqrt{r^2 + r^2 + h^2}[/tex]
Plug in the values:

[tex]d = \sqrt{((3 cm)^2 + (3 cm)^2 + (8 cm)^2)} d = \sqrt{(9 cm^2 + 9 cm^2 + 64 cm^2)} d = \sqrt{(82 cm^2)}[/tex]
d ≈ 9.06 cm

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The longest segment that can fit inside the cylinder is. [tex]$\sqrt{73}$ cm[/tex].

The longest segment that can fit inside a cylinder is a diagonal that connects two opposite vertices of the cylinder.

The length of this diagonal by using the Pythagorean theorem.

Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.

It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

This theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, often called the Pythagorean equation:[1]

[tex]{\displaystyle a^{2}+b^{2}=c^{2}.}[/tex]

The theorem is named for the Greek philosopher Pythagoras, born around 570 BC.

The theorem has been proven numerous times by many different methods – possibly the most for any mathematical theorem.

The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years.

Consider a right triangle with legs equal to the radius.

[tex]$r$[/tex] and the height [tex]$h$[/tex] of the cylinder, and with the diagonal as the hypotenuse.

Then, by the Pythagorean theorem, the length of the diagonal is:

[tex]$\sqrt{r^2 + h^2} = \sqrt{3^2 + 8^2} = \sqrt{73}$[/tex]

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Answer:

a)

jenny - $160 + $50X = total

hong - $90X = total

b)

$160 + $50X = $90X

Step-by-step explanation:

a)

b)

The approximate volume of the small truck is 577.5 cubic feet.

A truck that would be best for them to rent is the 3-Bedroom Moving Truck.

The volume of the Mega Moving Truck is about 641.25 cubic feet greater than the 2-bedroom moving truck.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

For the approximate volume of the small truck, we have;

Volume of small truck = 11 1/3 × 7 5/12 × 7

Volume of small truck = 577.5 cubic feet.

The approximate volume of each moving truck can be calculated as follows;

2-Bedroom Moving Truck = 14.5 × 7.5 × 7 = 761.25 cubic feet.

3-Bedroom Moving Truck = 21 × 7.5 × 8 = 1,260 cubic feet.

Mega Moving Truck = 22 × 7.5 × 8.5 = 1,402.5 cubic feet.

Difference = 1,402.5 cubic feet - 761.25 cubic feet

Difference = 641.25 cubic feet.

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The expressions when matched with their equivalents would be:

The given expressions involve basic arithmetic operations such as addition, subtraction, and division of numbers. To find their equivalent expressions, we need to apply these operations in the correct order and simplify the result as much as possible.

For example, in the expression 3/5 - 0.60, we first convert the decimal number 0.60 to a fraction with a denominator of 5 so that we can subtract it from the fraction 3/5.

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The trigonometric ratios with respect to the angle C are:

sin(C) = 15/17, cos(C) = 8/17, tan(C) = 15/8, cosec(C) = 17/15, sec(C) = 17/8, cot(C) = 8/15

Trigonometric ratios are ratios of the sides of a right triangle used to calculate angles and side lengths.

The three main ratios are sine, cosine, and tangent, which are defined as the ratios of the opposite, adjacent, and hypotenuse sides.

Using the right triangle ABC, we can find the trigonometric ratios with respect to angle C:

sin(C) = opposite/hypotenuse = AB/AC = 15/17

cos(C) = adjacent/hypotenuse = BC/AC = 8/17

tan(C) = opposite/adjacent = AB/BC = 15/8

cosec(C) = 1/sin(C) = AC/AB = 17/15

sec(C) = 1/cos(C) = AC/BC = 17/8

cot(C) = 1/tan(C) = BC/AB = 8/15

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The function f(x) is x³ - 8x² - 12x + 29.  

The division algorithm is a fundamental concept in arithmetic and algebra that describes how to divide one number (the dividend) by another number (the divisor) to obtain a quotient and a remainder.

The algorithm can be expressed as follows:

Dividend = Divisor × Quotient + Remainder

where the dividend, divisor, quotient, and remainder are all integers.

Here we have

The function f(x) is divided by x - 9, the quotient is x² + x - 3 and the remainder is 2.

Hence,

Divisor = x - 9, quotient = x² −x+3 and remainder = 2

As we know,

dividend = divisor × quotient + remainder

f(x) = (x - 9) × (x² + x - 3) + 2

f(x) = x³ + x² - 3x - 9x² - 9x + 27 + 2

f(x) = x³ - 8x² - 12x + 29  

Therefore,

The function f(x) is x³ - 8x² - 12x + 29.  

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Note that according to the histogram, the number of customer s that spent less than $20 are 14 in number.

To derive the above amount, you simple add the frequency of the bars which rank from 0-9 and 10-19, since the other bars are $20 and above.

Thus, we have:

8 + 6 = 14 Customers.

Thus, it is correct to state that  that according to the histogram, the number of customer s that spent less than $20 are 14 in number.

Recall that a  histogram is a graphical representation of the distribution of a dataset. It displays the frequency of occurrence of data values in different intervals or bins along the x-axis, with the height of each bar representing the frequency.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

The histogram shows the amount, to the nearest dollar, that customers spent at a museum gift shop. How many customers spent less than $20?
See the attached image.

Answer:r= -5

Step-by-step explanation:

Answer:

r=-5

Step-by-step explanation:

2r-22=4(r-3)

first expand brackets

2r-22=4r-12

then take away the least amount of r's from one side

-22=2r-12

add 12 to each side

-10=2r

divide by 2 to get r by itself

-5=r

The required original  number that Peter was thinking about is 18.25.

Let us assume that the original number be x that Peter is thinking about.

Peter adds 6 to the number, therefore the number becomes = (6 + x )

Then doubles the new number therefore it becomes = 2(6 + x) = 12 + 2x

According to question by applying rule of forming equations ( from the information given ) we get,

12 + 2x = 48.5

⇒ 2x = 48.5 - 12

⇒ 2x = 36.5

⇒ x = 36.5/2

⇒ x = 18.25

Hence the original number is 18.25.

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Answer:

9. You don't need to take action because the denominator is the same. You only operate on the numerator.

10. Use equivalent fractions that do have a shared denominator if the denominators are not the same. To accomplish this, you must identify the two denominators' least common multiples (LCM). Rename the fractions having a common denominator before adding those with different denominators.

Step-by-step explanation:

9. You don't need to take action because the denominator is the same. You only operate on the numerator.

10. Use equivalent fractions that do have a shared denominator if the denominators are not the same. To accomplish this, you must identify the two denominators' least common multiples (LCM). Rename the fractions having a common denominator before adding those with different denominators.

Note that the function that is graphed below is y = x + 7.

The equation y = x + 7 represents a linear function, where x is the independent variable and y is the dependent variable.

It has a slope of 1, which means that for every unit increase in x, y increases by 1. The y-intercept is 7, which is the value of y when x is zero. This equation can be graphed as a straight line on a coordinate plane, with a positive slope and y-intercept of (0, 7).

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Answer:

Cosine, sine, and tangent are trigonometric functions used in mathematics and geometry to calculate angles and sides in right triangles.

Here is a brief explanation of each:

Cosine (cos): The cosine of an angle in a right triangle is defined as the adjacent side length divided by the hypotenuse length. In other words, it represents the ratio of the length of the adjacent side to the angle to the length of the hypotenuse. It is usually abbreviated as cos.

Sine (sin): The sine of an angle in a right triangle is defined as the opposite side length divided by the hypotenuse length. In other words, it represents the ratio of the length of the opposite side to the angle to the length of the hypotenuse. It is usually abbreviated as sin.

Tangent (tan): The tangent of an angle in a right triangle is defined as the opposite side length divided by the adjacent side length. In other words, it represents the ratio of the length of the opposite side to the angle to the length of the adjacent side. It is usually abbreviated as tan.

To solve questions that involve these functions, you need to know at least two values of a right triangle, such as the lengths of two sides or one side and an angle. Then you can use the trigonometric function and the given values to calculate the missing side or angle.

For example, if you know the length of the hypotenuse and one acute angle of a right triangle, you can use the sine or cosine function to calculate the length of one of the other sides. If you know the length of one side and one acute angle, you can use the tangent function to calculate the length of the other side.

There are also trigonometric identities and equations that can be used to simplify or solve more complex problems involving these functions.

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to know if the fractions (2 1/2)/(6.5) and (5/8)/(1 5/8) are in a proportional relationship, and the simplest form of each.

Equivalent fractions can be found by multiplying numerator and denominator by the same number.

  (2 1/2)/(6.5) = 2·(2 1/2)/(2·6.5) = 5/13

  (5/8)/(1 5/8) = 8(5/8)/(8·(1 5/8)) = 5/(8+5) = 5/13

Both fractions are equivalent to 5/13, so their relationship is proportional.

Thus, the Area of shaded region for the given sector of circle is found as:

1.14 sq. cm.

Two radii that meet at the centre to form a sector define a circle. The sector is the portion of the circle created by these two radii. Knowing a circle's central angle measurement and radius measurement are both crucial for solving circle-related difficulties.

Given:

Area of shaded region = area of sector - area of triangle

Area of shaded region = Ф/360° * (πr²) - 1/2*base*height

Area of shaded region = 90/360° * (3.14*2²) - 1/2*2*2

Area of shaded region = 1/4*3.14*4 - 2

Area of shaded region = 3.14 - 2

Area of shaded region = 1.14 sq. cm

Thus, the Area of shaded region for the given sector of circle is found as:

1.14 sq. cm.

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