4) Students in Ms. Udon
science class planted 13
conifers in different places
around the school yard. They
measured the heights (in inches)
of the conifers one month after
planting them. How many
conifers are greater than 6 1/4
inches tall but less than 8 1/2
inches tall?

When Y is increased by 44%, X increases by 20%.

If X is proportional to the square root of Y, then we can express this relationship as X = k√Y, where k is the constant of proportionality. Now, let's consider the scenario where Y is increased by 44%.

Let's denote the initial value of Y as Y₀. When Y is increased by 44%, the new value of Y becomes Y₁ = Y₀ + 0.44Y₀ = 1.44Y₀.

Since X is proportional to the square root of Y, we can write the initial value of X as X₀ = k√Y₀, and the new value of X as X₁ = k√(1.44Y₀).

To find the percentage increase in X, we can calculate the difference between the new and initial values of X and express it as a percentage of the initial value:

Percentage increase in X = ((X₁ - X₀) / X₀) * 100

Substituting the values, we get:

Percentage increase in X = ((k√(1.44Y₀) - k√Y₀) / k√Y₀) * 100

Simplifying the expression, we find:

Percentage increase in X = ((√1.44 - √1) / √1) * 100

Percentage increase in X = (1.2 - 1) x 100

Percentage increase in X = 0.2 x 100

Percentage increase in X = 20%

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The probability that 7 or 8 machines will produce all bolts within specification is approximately 0.9841.

Using the binomial distribution formula, we get:

P(X = 7) = (8 choose 7) * (0.002)⁷ * (0.998)¹ ≈ 0.0081

P(X = 8) = (8 choose 8) * (0.002)⁸ * (0.998)⁰ ≈ 0.000003

Therefore, P(X = 7) + P(X = 8) ≈ 0.0081 + 0.000003 ≈ 0.9841.

Probability is a branch of mathematics that deals with the study of the likelihood of occurrence of events or outcomes in situations where there is uncertainty or randomness. It is a measure of the degree of uncertainty of an event, typically expressed as a number between 0 and 1. Probability is used to make predictions and decisions in various fields, including science, engineering, economics, finance, and social sciences.

It is based on the analysis of past events or observations, and it enables us to estimate the likelihood of future events or outcomes. Probability theory provides a mathematical framework for modeling and analyzing random phenomena and helps us understand the laws of chance that govern various natural and artificial systems.

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Based on the application of the complementary angles, the measures of the angles are: m<DEG = 54 degrees;   mm<GEF = 36 degrees

When two angles make up a right angle, they are referred to as complementary angles because they add up to 90 degrees when summed.

6x and 4x make up a right angle, this means their sum will give us 90 degrees when we add them up. Therefore:

6x + 4x = 90

10x = 90

Divide both sides by 10

10x/10= 90/10

x = 9

measure of angle DEG = 6x = 6(9) = 54 degrees.

Measure of angle GEF = 4x = 4(9) = 36 degrees

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Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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Answer:

$17,320 after 12 months.

Step-by-step explanation:

f the Coach chooses the Three-Year Plan, the total amount he will spend after 12 months can be calculated as follows:

First, we need to calculate the total amount of monthly payments made in 12 months:

12 months x $610 per month = $7,320

Then, we need to add the down payment made at the time of purchase:

$7,320 + $10,000 = $17,320

Therefore, if the Coach chooses the Three-Year Plan, he will spend a total of $17,320 after 12 months.

Answer: There are 32,760 color arrangements possible for painting the bedroom, garage, office, and bathroom with different colors chosen from 15 options.

Step-by-step explanation: To determine the number of color arrangements possible for painting the bedroom, garage, office, and bathroom with different colors chosen from 15 options, we need to calculate the number of permutations.

Since each room is assigned a different color, we can arrange the colors in a specific order. The number of ways to arrange 15 colors in 4 distinct positions is given by the permutation formula:

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

where n is the total number of options (15 colors) and r is the number of positions (4 rooms).

Using the formula, the number of color arrangements possible is:

P(15, 4) = 15! / (15 - 4)!

= 15! / 11!

= (15 * 14 * 13 * 12) / (4 * 3 * 2 * 1)

= 32,760

Answer:

In mathematics, a function is a rule that assigns one unique output value for each input value. A linear function is a function that has a constant rate of change between its input and output values. This means that if we plot the function on a graph, it will form a straight line.

For example, the function f(x) = 2x + 1 is a linear function because its graph is a straight line. As x increases by 1, the output of the function increases by 2.

On the other hand, a nonlinear function is a function that does not have a constant rate of change between its input and output values. This means that if we plot the function on a graph, it will not form a straight line.

For example, the function f(x) = x^2 is a nonlinear function because its graph is a curve. As x increases, the output of the function increases at an increasing rate.

In general, nonlinear functions can take many different forms and can have complex behaviors, whereas linear functions have a simple, predictable behavior.

Answer:

the answer is 10.63km/L.

Answer:

-14 = k

Step-by-step explanation:

44 = k+58

Subtract 58 from each side.

44-58 = k+58-58

-14 = k

The letter "V" in the equation XXX × YV=••••+666=799Y is replaced by the number 89.

The equation can be simplified to XXX × YV=1335.

If both sides of the equation are divided by 3, X × YV = 445.

If now all the X's is replaced with 5's, 5 × YV = 445.

This gives the following equation:

5 × YV = 445

Now multiply both sides of the equation by Y, to get 5Y = 445.

This gives us the following equation:

5Y = 445

Finally, divide both sides of the equation by 5, to get Y=89.

Therefore, the letter "V" in the equation XXX × YV=••••+666=799Y is replaced by the number 89.

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From matrix property it can be showed that A=B.

Given,

If A,B and x are matrices with x≠0 and AX=BX

Now.

X must be non-singular matrix because

A[tex]XX^{-1}[/tex]=B[tex]XX^{-1}[/tex]

[tex]XX^{-1}[/tex]  = I( identity matrix )

AI = BI

A = B

Hence Proved, A = B .

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The value of x which could replace the missing value in the table so that y is not a function of x is; 7.

It follows from the task content that the value of x which could make y not a function of is required to be determined.

Recall that a function is a special kind of relation in which case each value of x is assigned one value of y.

On this note, if we assign 7 as the missing value of x, then y is not a function of x as u has now been assigned more than 1 output, y values.

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Step-by-step explanation:

Using the roots given in order given:

y=  ( x+4)(x+2)(x-4)(x-2)     would  fit the bill.....

The probability that a female student chose strawberry ice cream is 7/11 or approximately 0.6364 (rounded to four decimal places).

To calculate the probability that a female student chose strawberry ice cream, we need to consider the total number of female students who made an ice cream choice and the number of female students who chose strawberry ice cream.

From the given information, we have the following breakdown:

         Male    Female   Total

Vanilla 6 4 10

Strawberry 9 14 23

Chocolate 13 4 17

Total 28 22 50

To find the probability, we divide the number of female students who chose strawberry ice cream by the total number of female students:

Probability = (Number of female students who chose strawberry ice cream) / (Total number of female students)

Therefore, the probability of a female student choosing strawberry ice cream is:

Probability = 14 / 22

Simplifying the fraction, we have:

Probability = 7 / 11

Therefore, the probability that a female student chose strawberry ice cream is 7/11 or approximately 0.6364 (rounded to four decimal places).

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Answer:

3:55

Step-by-step explanation:

3:55

Answer:

1/10

Step-by-step explanation:

2/5 * 1/4 = 2/20 = 1/10

2 right answers, 5 possible choices

Select one right choice = 2/5

After selecting one right choice, there are 4 possible choices with one more right choice left.
Select another right choice = 1/4

Answer:

$2174.40

Step-by-step explanation:

2150+1721+829+300=5000

They sold 5000 tickets last month.

300÷5000=0.06

So 6% of the tickets each month are romance.

They expect to sell 8000 next month.

8000x.06=480

They should sell 480 romance tickets next month.

480x4.53=2174.40

Answer:

Option : A

Step-by-step explanation:

To find the x-coordinate of the solution to the system of equations, we need to solve the system by eliminating either x or y. Let's eliminate y by multiplying the first equation by 3 and the second equation by 1:

Equation 1: 2x + y = -4 (multiply by 3)

Equation 2: 5x + 3y = -6 (multiply by 1)

Multiplying equation 1 by 3 gives us:

6x + 3y = -12

Multiplying equation 2 by 1 gives us:

5x + 3y = -6

Now we can subtract equation 2 from equation 1 to eliminate y:

(6x + 3y) - (5x + 3y) = -12 - (-6)

6x + 3y - 5x - 3y = -12 + 6

x = -6

Therefore, the x-coordinate of the solution to the system of equations is x = -6.

The correct option is: Ox=-6.[tex][/tex]

Answer: 0

Step-by-step explanation:8th Place 100*10 1000th Place is 0

The expression O cos(k0 + 0) + i sin(k0 + 0) is commonly used in proofs involving complex numbers and trigonometric functions, representing the complex exponential function [tex]e^(ik0)[/tex].

The expression that will complete the proof depends on the given context and what exactly needs to be proved. However, in general, the expression O cos(k0 + 0) + i sin(k0 + 0) is often used in proofs involving complex numbers and trigonometric functions.

This expression represents the complex exponential function [tex]e^(ik0)[/tex], where k0 is a constant. The cosine term represents the real part of the complex number, while the sine term represents the imaginary part.

The addition of 0 in the arguments of both cosine and sine indicates that the complex number is in polar form, with a magnitude of 1 ([tex]since cos^2 +[/tex] [tex]sin^2 = 1[/tex] for all angles).

Using this expression, we can perform various operations and manipulations to prove different results, such as De Moivre's theorem or Euler's formula.

Ultimately, the choice of expression will depend on the specific problem and what needs to be proved.

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The table can be filled as  Symmetry | Applies to the hexagon Reflective symmetry over AD | Yes Reflective symmetry over CE | No

We are given that;

The hexagon DEFCA

Now,

the hexagon has reflective symmetry over AD, because if we fold it along AD, the vertices B and F will match, as well as the vertices C and E. Therefore, the answer for reflective symmetry over AD is Yes.

However, the hexagon does not have reflective symmetry over CE, because if we fold it along CE, the vertices A and F will not match, nor will the vertices B and D. Therefore, the answer for reflective symmetry over CE is No.

Therefore, Symmetry | Applies to the hexagon Reflective symmetry over AD | Yes Reflective symmetry over CE | No.

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Answer: D: 1/5

Step-by-step explanation:

sinx = 5/13

this ratio is special; it is a 5-12-13 right triangle, (pythagorean triple).

there is also a formula to find tan(x/2); It is tan(x/2) = ±[tex]\sqrt{\frac{1-cosx}{1+cosx} }[/tex]

the + or - sign is decided by the quadrant the half angle is in;

since x is in quad one, it is somewhere between 0 and pi/2. To find the half angles position, simply divide it; x/2 is somewhere between 0/2 and pi/4.

so its also in the first quadrant. Since tangent is positive in the first quadrant, we will take the positive answer:

One more thing. we need the cosx in our formula. cosx will be 12/13, since this is a special right triangle as we said before.

tan(x/2) = [tex]\sqrt{\frac{1-12/13}{1+12/13} }[/tex]

tan(x/2) = [tex]\sqrt{\frac{1/13}{25/13} }[/tex]

tan(x/2)= [tex]\sqrt{1/25}[/tex]

tan(x/2) = 1/5

Option D is the answer :)

The equivalent value of the equation is 18x-9=72 and x=4.5

Given data ,

Let the equation be represented as A

Now , the value of A is

(3/5)(30x-15)=72

On simplifying the equation , we get

3(6x-3)=72

On further simplification , we get

18x-9=72

x=81/18

x=4.5

Hence , the equation is 18x-9=72

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The angle formed by the two hands have a measure less than 1/4 turn

From the question, we have the following parameters that can be used in our computation:

A clock with the hour hand at 12 and the minute hand at 2

The turn represented by the above is represened as

Turn = (2 * 30)/360

When simplified, we have

Turn = 1/6

Next, we have

Angle at the turn = 1/4

1/6 is less than 1/4

This means that the angle formed by the two hands have a measure less than 1/4 turn

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If the coordinates of the intersection of the diagonals of ABCD

with vertices A(0, 2), B(8, 2), C(4, − 4), and D(−4, − 4). The coordinates of the intersection of the diagonals are (4/3, 0).

Using the two point form of the equation of a line to determine the The equation of the line that contains AC

y₋y₁ = (y₂-y₁)/(x₂-x₁) * (x₋x₁)

where:

(x₁, y₁) and (x₂, y₂)= two points on the line

y - 2 = (-4 - 2)/(4 - 0) * (x - 0)

Simplify

y - 2 = -3/2 * x

2y - 4 = -3x

3x + 2y = 4

Equation of the line that has BD

y - 2 = (-4 - 2)/(8 - (-4)) * (x - 8)

Simplify

y - 2 = -3/4 * x + 9/2

4y - 8 = -3x + 36

3x + 4y = 44

Now let find the point of intersection:

3x + 2y = 4

3x + 4y = 44

Multiplying the first equation by -2

-6x - 4y = -8

Eliminate x

0x + 0y = 36

So,

y = 0

3x + 2(0) = 4

3x = 4

x = 4/3

Therefore the coordinates  is (4/3, 0).

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Answer:

C

Step-by-step explanation:

Both equations are the same

The value of x is 45 in the provided assertion, and the Centerior angles do sum up to 180°, indicating that AD and BC are parallel.

We have,

Parallel in mathematics refers to two lines which never cross one another; picture an equal symbol. Three close pals' parallel lives could be depicted in a tale.

(a)

3x + x + 2x + 90 = 360

6x = 360 - 90

6x = 270

x = 45

(b) The answer will be yes, they would be parallel.

We can justify this using co-interior angles, which state that 2 angles subtended by parallel lines add up to 180°

We can check this with both angles 3x & x, or 2x & 90°.

If AD and BC are parallel, then 3x + x = 180, and since you already found the value of x we can substitute this in:

3(45) + (45) = 180

135 + 45 = 180

180 = 180

So the co-interior angles do add up to 180°, which means that AD and BC are parallel.

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