what is a necessary step for consturcting perpendicular lines through a point off the line?

The expected value for each roll is [tex](1+2+3+4+5+6)/6 = 3.5.[/tex]

The average of Brandon's rolls, we simply add up all the results and divide by the number of rolls:
[tex](1+2+2+3+4+6+2+1+5+6+1+6+2+6+4+6+2+6+4+6)/20 = 3.6[/tex]
So the average of Brandon's rolls is 3.6.
Now we need to count how many times he rolled above the average. To do this, we simply count how many rolls were greater than 3.6:
4, 6, 5, 6, 6, 4, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 4, 6, 4, 6
There were 18 rolls that were greater than 3.6, so Brandon rolled above the average 18 times.
In summary, Brandon rolled a six-sided die 20 times and recorded the results in a table. To find out how many times he rolled above the average, we first calculated the average roll to be 3.6. We then counted how many times he rolled above this value and found that he did so 18 times.

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Choose the correct measurement of the paper clip to the nearest 1/8 inch

1 1/2 inch

7/8 inch

1 2/8 inch

1 4/8 inch

1 3/8 inch

None of the given options (A, B, C, or D) is a solution to sin x − cos 2x = 0 on the interval [0, 2π).

The solution of any trigonometric equation represents the value of the parameter which satisfies the given equation. The solution should lie within a given range and it should have the same value as ±π .

To find the solutions to sin x − cos 2x = 0 on the interval [0, 2π), we can start by using the identity cos 2x = 1 - 2sin² x, which gives:

sin x - (1 - 2sin² x) = 0

Simplifying this equation, we get:

2sin² x - sin x + 1 = 0

We can solve this quadratic equation using the quadratic formula:

sin x = [1 ± √(1 - 8)] / 4

sin x = [1 ± √(-7)] / 4

Since the square root of a negative number is not a real number, this equation has no real solutions. Therefore, none of the given options (A, B, C, or D) is a solution to sin x − cos 2x = 0 on the interval [0, 2π).

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The distance between P(3, 3) and Q(6.5, 11.75) is approximately 9.42 units.

We can use the distance formula to find the distance between two points in a coordinate plane. The distance formula is

where (x1, y1) and (x2, y2) are the coordinates of the two points, and d is the distance between them.

Using the given coordinates of points P and Q, we can find the distance between them as follows:

[tex]d = sqrt((6.5 - 3)^2 + (11.75 - 3)^2)[/tex]

= [tex]sqrt(3.5^2 + 8.75^2)[/tex]

= [tex]sqrt(12.25 + 76.5625)[/tex]

= [tex]sqrt(88.8125)[/tex]

≈[tex]9.42[/tex]

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Answer:

False

Step-by-step explanation:

Because it is convex, that is, it has bulges

The missing angle m∠U of the quadrilateral is calculated as:  117°

From the given quadrilateral, we see that the angle m∠R is given as 117°.

We also see that the sides TU and RS are congruent to each other. No, we know that the sum of angles of a quadrilateral is 360 degrees.

However, we see that since TU and RS are congruent, this can be likened to an isosceles trapezium and as such the angle m∠U must be equal to the angle m∠R.

Thus:

m∠R = m∠U  = 117°

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Answer: The mode in this data set would be 10.

Step-by-step explanation: Mode is the most frequent number—that is, the number that occurs the highest number of times. Example: The mode of {4 , 2, 4, 3, 2, 2} is 2 because it occurs three times, which is more than any other number.

Answer: The mode is 10.

Step-by-step explanation: To find the mode of a data set, you need to determine which number appears most frequently. In your case, the number 10 occurs three times, but all other numbers appear only once or twice. So, the mode is 10.

The area of the trapezoid by decomposing it into other shapes is 55 sq. cm.

A quadrilateral with at least one set of parallel sides is known as a trapezium. The trapezoid's other two sides are referred to as its legs, and its parallel sides are known as its bases. The distance between the bases of a trapezium measured perpendicularly is its height. By multiplying the average of the bases (the total of the bases divided by 2) by the height, one may get the area of a trapezium. A = (b1 + b2)h/2, where b1 and b2 are the lengths of the bases and h is the height, is the formula for a trapezoid's surface area.

The trapezoid can be divided into one right angles triangle and a trapezium.

The area of the triangle is given as:

A1 = 1/2 bh

A1 = 1/2(5)(4)

A1 = 10 sq. cm.

Now, the area of trapezium is given as:

A2 = 1/2 h (a + b)

Here, a = 12, b = 15 - 5 = 10, and h = 4.

A2 = 1/2 (4) (12 + 10)

A2 = 2(22) = 44 sq. cm

The total area of the trapezoid is:

A = A1 + A2

A = 10 + 44

A = 55 sq. cm.

Hence, the area of the trapezoid by decomposing it into other shapes is 55 sq. cm.

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Answer: 282.6 [tex]cm^{2}[/tex]

Step-by-step explanation:

as the TSA of Cylinder is [tex]2\pi r[r+h][/tex] so here r = 3cm & h = 12cm so by putting values in the above formula we get the answer

The probability of the ball falling into red slots 12 or fewer times in 23 rolls is approximately 0.3486.

A. Using the binomial probability formula, we can determine the likelihood that the ball will land in the green slots two or more times out of 23 rolls:

[tex]P(X > = 2) = 0 - 1 - P(X = 0)[/tex]

where P(X): likelihood that X will occur and X is the number of times the ball has fallen into the green slots.

The chances of the ball landing in a green slot on one roll are 2/38, whereas the chances of it not landing there are 36/38. This allows us to compute:

[tex]P(X = 0) = (36/38)^(23) = 0.288359853[/tex]

[tex]P(X = 1) = 23 * (2/38) * (36/38)^(22) = 0.357973143[/tex]

With the binomial probability formula substituted, we obtain:

[tex]P(X > = 2) = 1 - 0.288359853 - 0.357973143 = 0.353666004[/tex]

As a result, there is a roughly 0.3537 percent chance that the ball will land in the green slots two or more times during the course of 23 rolls.

B. The likelihood that the ball will not land in any green slots after 23 rolls is:

[tex]P(not green) = (36/38)23, or 0.288359853[/tex]

Hence, there is a roughly 0.2884 percent chance that the ball won't land in any green slots after 23 rolls.

B. Using the binomial probability formula, we can determine the likelihood that the ball will land in the black slots 14 or more times:

[tex]P(X > = 14) = 1 - P(X < = 13)[/tex]

where P(X): likelihood that X will occur and X is the number of times the ball has fallen into the black slots.

The odds of the ball not falling into a black slot in one roll are 20/38, while the odds of the ball going into a black slot are 18/38. This allows us to compute:

[tex]P(X = 13) = sum of (23 pick I (18/38)*i* (20/38)*(23-i) from i=0 to 13 = 0.829288657[/tex]

With the binomial probability formula substituted, we will get:

[tex]P(X > = 14) = 1 - 0.829288657 = 0.170711343[/tex]

The likelihood of the ball landing in the black slots 14 or more times during the course of 23 rolls is therefore roughly 0.1707.

D. Using the binomial probability formula once more, we can determine the likelihood of the ball landing in the red slots 12 or fewer times:

[tex]P(X = 12) = sum of (23 pick I from i=0 to 12 * (18/38) * I * (20/38) * (23-i) = 0.348609995[/tex]

The likelihood that the ball will land in a red slot 12 or fewer times in 23 rolls is therefore roughly 0.3486.

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The list with the smallest standard deviation is the following: 16, 12, 13, 16, 14, 15, 16, 14, 14, 13.

What is standard deviation?

Standard deviation is a statistical measure of the variability of a set of data values. It's a step-by-step process for determining how far each value is from the mean. It is important since it may reveal the amount of variability in a set of data. The formula for calculating standard deviation is as follows:

σ=√∑(x−μ)²nσ=√∑(x−μ)²n

In this equation, x represents the values in the data set, μ represents the mean of the data set, and n represents the number of values in the data set. Let us now compute the standard deviation of each of the given data sets, starting with the first one. We can utilize the formula given above to do so:

6, 19, 9, 18, 19, 9, 17, 18, 17, 15                        μ = 15.8,σ = 4.83 (rounded to two decimal places)

31, 30, 26, 28, 18, 28, 18, 21, 23, 32                μ = 25.5,σ = 5.93 (rounded to two decimal places)

20, 21, 20, 19, 25, 24, 19, 14, 21, 15                μ = 19.8,σ = 3.98 (rounded to two decimal places)

14, 20, 16, 14, 28, 13, 17, 21, 12, 22                μ = 17.7,σ = 4.96 (rounded to two decimal places)

16, 12, 13, 16, 14, 15, 16, 14, 14, 13                  μ = 14.3,σ = 1.96 (rounded to two decimal places)

The list with the smallest standard deviation is the following: 16, 12, 13, 16, 14, 15, 16, 14, 14, 13.

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9. Expression matches with option C: log3 12.
10. Expression matches with option D: log3 36.
11. Expression matches with option A: log3 64.
12. Expression matches with option C: log3 12.

To match the expression with the logarithm that has the same value, we need to simplify each expression and rewrite it

in the form of log3 x.

9. log3 6 + log3 2 = log3 (6 × 2) = log3 12.

Therefore, the expression matches with option C: log3 12.

10. [tex]2 log36 = log36^2 = log3 (6^2)^2 = log3 36.[/tex]

Therefore, the expression matches with option D: log3 36.

11. [tex]6 log32 = log32^6 = log3 (2^5)^6 = log3 2^30.[/tex]

Therefore, the expression matches with option A: log3 64.

12. log3 6 + log3 2 = log3 (6 × 2) = log3 12.

Therefore, the expression matches with option C: log3 12.
In summary:
9. Expression matches with option C: log3 12.

10. Expression matches with option D: log3 36.

11. Expression matches with option A: log3 64.

12. Expression matches with option C: log3 12.

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The order of operations that should be completed first to find the value of given expression 12+30÷(6-3)+1 is (6-3) which is option-B

What is the correct order of operations?

To solve any given expression the rule applied is PEMDAS or the BODMAS . PEMDAS acronym for-

P indicates the parentheses that are the brackets to be solved first in an expression.

E which indicates exponents or powers to be solved.

M refers to Multiplication

D refers to divide

A refers to add

S indicates subraction

BODMAS is similar to PEMDAS whose sequence of solving stands for

B- brackets

O-Order/Of

D-Divide

M-Multiply

A-Add

S-Subtract

Here in the given expression: 12+30÷(6-3)+1 , the order would be

=12+30÷(6-3)+1

=12 + 30 ÷ (3) + 1 { brackets/parentheses}

= 12 + 30 ÷ 3 + 1

=12 + 10 + 1  {divide}

=23

∴ the first operation was to solve brackets/parentheses (6-3)

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Refer to the attachment below for complete question.

The domain and range of this square root function y = 5/2√(-5x + 1) - 87 are as follows;

Domain = {x|x ≤ 1/5}.

Range = {y|y ≥ -87}.

The domain and range of this square root function y = -315√(11x - 3) - 15/88 are as follows;

Domain = {x|x ≥ 3/11}.

Range = {y|y ≤ -15/88}.

In Mathematics and Geometry, a domain refers to the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached below for the given square root function y = 5/2√(-5x + 1) - 87 and y = -315√(11x - 3) - 15/88, we can reasonably and logically deduce the following domain and range:

Domain = {-∞, 1/5} or {x|x ≤ 1/5}.

Range = {-87, ∞} or {y|y ≥ -87}.

Domain = {3/11, ∞} or {x|x ≥ 3/11}.

Range = {-∞, -15/88} or {y|y ≤ -15/88}.

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There were 7 number of pieces that were in the puzzle that took the child 30 seconds to complete,that can be found using the data given & the coordinates on the graph (7,30) which indicates the number of pieces as 7 and time as 30 sec.

What is data?

Data is the collected information that can be arranged and used for analysing or interpretation. The collected data is also called as raw data, which further needs to be arranged. The data can be represented visually, in tabular form , grouped or ungrouped form. Pictographs, bargraphs, box-whisker plot, line plot, histogram, pie chart are the visual representations.

Here given that the data is arranged in the form of graph containing x-axis & y-axis. Data collected/arranged represents the number of pieces contained in the puzzle & the time taken to solve it.

X-axis represents the number of pieces in the puzzle & Y-axis represents the time taken to complete that.

The points plotted on graph are:

(4,15): Number of pieces=4

         Time taken to complete=15 seconds

(5,15):Number of pieces=5

         Time taken to complete=15 seconds

(7,30): Number of pieces=7

         Time taken to complete=30 seconds

(8,25): Number of pieces=8

         Time taken to complete=25 seconds

(12,40): Number of pieces=12

         Time taken to complete=40 seconds

∴The puzzle that was completed by child in 30 seconds contained 7 pieces.

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Refer to the attachment for the graph.

The required Perimeter and area of the shape is 27.42 units and 64.26 sq units.

The circumference of a shape is its perimeter. How is a perimeter calculated? The border can be found by including the lengths of each side of a shape.

We have given a shape which made up of two circle and rectangle

diameter of circle = 12 - 6 = 6

then radius = 3 units

Perimeter = 3+3+3+3+3+3+π(3)

= 18 + 3.14(3)

= 18 + 9.42

= 27.42 units

and

Area = area of rectangle + area of two half circles

= 12(3) + π(3)²

= 36 + 28.26

= 64.26 sq units.

Thus, required Perimeter and area of the shape is 27.42 units and 64.26 sq units.

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The true statements about the inequality are

n > -24.

The circle is open.

The arrow points right.

To solve for n in the inequality -2/3n < 16, we need to isolate the variable n on one side of the inequality.

First, we can multiply both sides by -3/2 to get rid of the fraction:

(-3/2) * (-2/3n) > (-3/2) * 16

n > -24

Therefore, the solution for n in the inequality -2/3n < 16 is n > -24.

The circle is open means that the inequality sign is either less than or greater than

Having greater that means it points to the right

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The solution set for x + 10 ≥ 14 is x ≥ 4, and it can be represented as graph as a shaded region to the right of x = 4 on a number line.

The inequality [tex]x + 10 \geq 14[/tex] can be solved algebraically as follows:

[tex]x + 10 \geq 14[/tex]

Subtracting 10 from both sides, we get:

[tex]x \geq 4[/tex]

This means that any value of x that is greater than or equal to 4 will satisfy the inequality. To graph the solution, we can draw a number line and shade in all the values of x that satisfy the inequality. Since x is greater than or equal to 4, we can represent the solution set as follows:

────●────●────●────●────●───> x

0 1 2 3 4

The dot at x = 4 indicates that 4 is included in the solution set (since the inequality is "greater than or equal to"), and the shaded region to the right of the dot represents all values of x that are greater than 4 and satisfy the inequality.

Therefore, the solution set for [tex]x + 10 > = 14[/tex] is[tex]x \geq 4[/tex], and it can be represented as graph as a shaded region to the right of x = 4 on a number line.

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Answer:

[tex]14. \: \: \: m {}^{4} - 16 \\ = (m {}^{2} -4)(m {}^{2} + 4) \\ = (m - 2)(m + 2)(m {}^{2} + 4) \\15. \: \: \: x {}^{2} + 4xy + 4y {}^{2} - 4z {}^{2} \\ (x + 2y) {}^{2} - 4z {}^{2} \\ (x + 2y - 2z)(x + 2y + 2z) \\ 16. \: \: m {}^{4} + m {}^{2} - 12 \\ (m {}^{4} + 4m {}^{2} )( - 3m {}^{2} - 12) \\ m {}^{2} (m {}^{2} + 4) - 3(m {}^{2} + 4) \\ (m {}^{2} + 4)(m {}^{2} - 3) \\ [/tex]

The expression that would best fit the situation is: "Andy descended five flights of stairs, and then ascended three floors."

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.

Andy walked down five flights of stairs, and then he walked back up three floors.

The expression that would best fit the situation would be:

Andy descended five flights of stairs, and then ascended three floors.

Therefore, the expression that would best fit the situation is: "Andy descended five flights of stairs, and then ascended three floors."

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The accumulated interest the investor should expect at the end of 6 years is $1,755.00.

Total 6-digit numbers that can be made from 1 to 9 will be 60480 and without repetition will be 84. The numbers that have at least one digit repeated will be 60396.

There are 9 digits from 1 to 9. If the digits are not repeated, the combination is called simple combination and is calculated using the formula

 C(n, r) = n!/ r!(n-r)!

Here n= 9 and r = 6

 C(9, 6) = 9!/6!(9-6)! = 9!/ (6! × 3!) = 84

So without repeating the digits there are 84  six digit numbers using 1 to 9.

Total numbers that can be made with or without repetition of digits is calculated by using permutations. The formula is

P( n, r) = n!/(n-r)!

           = 9!/(9-6)! = 60480

So total number without repetition = 84

Number with or without repetition = 60480

So the total numbers that have at least one digit repeated will be = 60480 - 84 = 60396

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To solve the problem, we can use the following steps:

Determine the difference in mass between the two bags with different numbers of guavas:

Mass of bag with 68 guavas = 7.55 kg Mass of bag with 62 guavas = 6.95 kg Difference in mass = 7.55 kg - 6.95 kg = 0.6 kg

Determine the mass of the 6 extra guavas:

Mass of 6 guavas = ? We can assume that the mass of each guava is roughly the same, so the mass of 6 guavas is proportional to the difference in mass between the two bags:

Difference in mass = 0.6 kg Mass of 6 guavas / 6 = 0.6 kg / 6 Mass of 6 guavas = 0.1 kg

Subtract the mass of the 6 extra guavas from the mass difference to get the mass of the bag:

Mass of bag with no guavas = ? Mass of bag with 68 guavas - mass of bag with 62 guavas = Mass of 6 extra guavas + Mass of bag with no guavas 0.6 kg - 0.1 kg = Mass of bag with no guavas Mass of bag with no guavas = 0.5 kg

Convert the mass of the bag from kilograms to grams:

Mass of bag with no guavas = 0.5 kg = 500 g

Therefore, the mass of the bag when it is empty is 500 grams.

Answer:

1,200

Step-by-step explanation:

The formula for Simple Interest is I=prt p=principal r=rate expressed as decimal t=time in years

I=1,000*0.05*4

0.05 because 5% in decimal form it’s 0.05

4 because 48months dived by 12= 4 years

200=1,000*0.05*4 The interest is 200 but they are asking for the total value so then you add the amount you initiated with 1,000+200=1,200

The drive-thru that  is able to estimate their wait time more consistently and why is: A. Burger Quick, because it has a smaller IQR.

The IQR is a measure of the spread of the middle 50% of the data, and is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). A smaller IQR indicates that the data is less spread out around the median, and therefore more consistent.

In this case, the IQR for Super Fast Food is 15.5 - 12 = 3.5, while the IQR for Burger Quick is 24 - 15.5 = 8.5. Therefore, Burger Quick has a larger range (24 - 2 = 22) than Super Fast Food (27 - 3 = 24), but a smaller IQR, indicating that their wait time estimates are more consistent.

Therefore Quick is able to estimate their wait time more consistently because it has a smaller interquartile range (IQR).

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The volume of the cone is approximately 12π cubic feet

What is the volume of a cone?

[tex]V = \frac{1}{3} \pi {r}^{2}h[/tex] where r is the radius of the base and h is the height of the cone.

In this case, the base of the cone is a square with a side length of b = 4 ft. The radius of the base is half the length of a side of the square, so:

[tex]r = \frac{b}{2} = \frac{4}{2} = 2 \: ft[/tex]

The height of the cone is h = 9 ft.

Now we can substitute these values into the formula for the volume of a cone:

[tex]V = \frac{1}{3} \times \pi {r}^{2} h \\V = \frac{1}{3} \pi {2}^{2} \times 9 \\ V = \frac{1}{3}\pi \times 4 \times 9 \\ V = \frac{1}{3} \times \pi \times 36 \\ V = 12\pi[/tex]

So the volume of the cone is approximately 12π cubic feet.

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Answer:

Option D

Step-by-step explanation:

'Height h’ is plotted on the y-axis, which has units of ft. 'Years after planning’ is plotted on the x-axis, which has units of yr.

Rate of change is denoted by the slope or gradient m  of the graph

m = [tex]\frac{Rise}{Run}[/tex]

Rise = Δy

       = Change along the y-axis

       = Difference in values along the y-axis

Run = Δx

       = Change along the x-axis

       = Difference in values along the x-axis

∴Rate of Change for this graph will have units of [tex]\frac{ft}{yr}[/tex]

The actual value can be calculated using coordinates of any two points along this graph

I used [tex](2, 7)[/tex] as [tex](x_{1} , y_{1})[/tex] and [tex](3, 9.5)[/tex] as [tex](x_{2} , y_{2})[/tex]:

m = [tex]\frac{y_{2} - y_{1}}{x_{2} -x_{1}}[/tex]

   = [tex]\frac{(9.5 - 7) ft}{(3 -2) yr}[/tex]

   = [tex]\frac{2.5ft}{1yr}[/tex]

∴ Rate of Change in tree’s height = 2.5 [tex]\frac{ft}{yr}[/tex]

∴ Option D

According to the given information, any value of y greater than 1/35 would make the product 5xy7 greater than 5 when x = 1.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

The expression 5xy7 can be interpreted as 5 times x times y times 7. To make the product greater than 5, we need to find a value of y such that:

5xy7 > 5

Dividing both sides by 5 and 7, we get:

xy > 1/7

So, we need to find a value of y such that the product xy is greater than 1/7. The value of x is not given, so we can assume that it is a positive number.

For example, if we choose x = 1, then we need to find a value of y such that:

y > 1/35

Therefore, any value of y greater than 1/35 would make the product 5xy7 greater than 5 when x = 1.

If we choose a different value of x, we would get a different inequality, but the general idea is the same: we need to find a value of y such that the product xy is greater than a certain value (in this case, 1/7 divided by 5 times 7).

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