n a coordinate plane, Triangle XYZ is rotated 90 degrees counterclockwise about the origin to form Triangle X'Y'Z'. Which conclusion is always true?

Answer:

W = width

L = length = 2W + 3

P = 36 = 2W + 2L = 2W + 2(2W + 3) =

6W + 6 = 36

6W = 30

W = 5

L = 13

The values needed for the box plot that Adams wants to display are:

Lower quartile = 6.8

Median = 8.4

Upper quartile = 9.5

Given the following data that represents the records of the increase in the height of a plant for 10 weeks, 4.5, 3.2, 8.0, 9.1, 10.2, 6.8, 7.2, 9.5, 10.0, 8.8, in order to draft a box plot, the following steps are what Adams should take to find each of the values needed.

Step 1: Order the data set from least to the greatest.

3.2, 4.5, 6.8, 7.2, 8.0, 8.8, 9.1, 9.5, 10.0, 10.2

Step 2: Find the median.

The median is the middle of the data set = (8.0 + 8.8)/2 = 16.8/2 = 8.4

Step 3: Find the lower quartile which is the center of the first part of the data that is divided by the median.

Lower quartile = 6.8

Step 4: Find the upper quartile which is the center of the second part of the data that is divided by the median.

Upper quartile = 9.5

Therefore, the values that Adam needs for his box plot are:

Lower quartile = 6.8

Median = 8.4

Upper quartile = 9.5

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The sum of the fractions (- 3/5 + 1/5) in simplest form is - 11/20.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, Are two proper fractions - 3/4 and - 1/5, and we are required to take the difference which is,

= - 3/4 - (- 1/5).

Now the negative signs will distribute to positive which is,

= - 3/4 + 1/5.

Now, the LCM of 4 and 5 is 20.

= {(-3×5) + (1×4)}/20.

= (- 15 + 4)/20.

= - 11/20.

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L= 97

Step-by-step explanation:

The perimeter is all of the sides of the rectangular pool added up. We know the both widths are gonna be 54m. So to find both widths together you need to multiply 54 by 2 to give us 108. The we need to find both lengths together, so subtracting 302-108 will get us 194. Both lengths together, 194,  divided by 2 is 97, which is our length.  

flips a fair coin five times, 5/16 is the probability that there are 3 heads in a row somewhere in the sequence of five flips.

The number of positive outcomes to all possible outcomes of an event is the ratio, which is known as probability.

The number of positive outcomes may be expressed by x for an experiment with n number of outcomes.

The following equation can be used to determine an event's probability:

Probability(Event) = Favorable outcomes / Total Outcomes = x/n

Considering a fair coin, after 5 flips, there are [tex]2^5[/tex] = 32 different arrangements of heads and tails.

To get exactly 3 heads,

[tex]^5C_3[/tex] = 5! / (5 - 3)! 3!

     = 5!/ 3! 2!

     = 10 ways

P(exactly 3 heads) = 10/32 = 5/16

Therefore, the probability of exactly 3 heads is 5/16.

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The value of y is 54 when x = -2

The value of y is 18 when x = -1.

The value of y is 6 when x = 0.

The value of y is 2 when x = 1.

The value of y is 2/3 when x = 2.

What is a function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Given function is

y = 6(⅓)^x

To find the value at x = -2, -1, 0, 1, 2, put the value of x in the given equation.

Putting x = -2 in the equation y = 6(⅓)^x

y = 6(⅓)⁻²

Applying index formula (1/a)^(-m) = a^m

y = 6(3)²

y = 6 × 9

y = 54

Putting x = -1 in the equation y = 6(⅓)^x

y = 6(⅓)⁻¹

Applying index formula (1/a)^(-m) = a^m

y = 6(3)¹

y = 6 × 3

y = 18

Putting x = -1 in the equation y = 6(⅓)^x

y = 6(⅓)⁰

Applying a⁰ = 1

y = 6 × 1

y = 6

Putting x = 1 in the equation y = 6(⅓)^x

y = 6(⅓)¹

y = 6 × 1 /3

y = 2

Putting x = 2 in the equation y = 6(⅓)^x

y = 6(⅓)²

y = 6 × (1/9)

y = 6/9

Divide the denominator and numerator by 3:

y = 2/3

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Answer:

infinite

Step-by-step explanation:

the law in most states in the usa states there must be 3 letters and 3 numbers so there could be infinite

                            -hope this helps-

Answer:

x = 2

Step-by-step explanation:

-2x - 48 ≥ 10x - 24

-48 + 24 ≥ 10x + 2x

24 = 12x

x = 2

Answer:

Step-by-step explanation:

The unit rate is 400 square feet per gallon.

What is unitary method ?

Unitary method is a mathematical way of deriving a single unit and then finding the required unit by multiplying.

A graph is shown in the diagram and two points are given x co-ordinate represents paint used per gallon and y co-ordinate represents wall painted in square feet.

Given (1/4,100) implies 1/4th of a gallon paint is needed to pain 100 square feet of wall.

∴ In 1 gallon (100)÷1/4 square feet of wall can be painted which is 400 square feet.

And the unit rate is 400 square feet per gallon.

Answer:

12 notches from both left and right of 0

you want the absolute value of (-12). all that means is how far is the number away from 0. in this case it's just 12

Answer: Total angles on the 4

Step-by-step explanation:

The sum of the marked angles = Total angles on the 4 straight lines – Sum of the interior angles of the quadrilateral. Sum of interior angles of polygon of 4 sides = (4 – 2) *1800 =3600

Hence, sum of the marked angles = 4 * 180° – 360° = 720° – 360° = 360°

From the sampling distribution we know:

a. will become more variable as the sample size increases.

A sampling distribution is the probability distribution of a statistic that was acquired from more samples taken from a certain population. The distribution of frequencies for a variety of potential outcomes that could happen for a population statistic makes up the sampling distribution of a specific population.

When it comes to the spread of all sample proportions, theory predicts behaviour far more accurately than just stating that larger samples have a smaller spread. In actuality, the sample size, n, and the standard deviation of each sample proportion.

Thus, option (a) correctly describe about sampling distribution of the sample proportion.

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Answer:

Step-by-step explanation:

The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is:((x1 + x2)/2, (y1 + y2)/2)Substituting the coordinates of points P and Q into the formula, we get:((2 + (-7))/2, (4 + (-2))/2) = (-2.5, 1)The coordinates of the midpoint of segment PQ are (-2.5, 1).To verify that this point is on the line through P and Q, we can find the slope of the line using the coordinates of points P and Q:slope = (y2 - y1)/(x2 - x1) = (-2 - 4)/(-7 - 2) = -6/-9 = 2/3We can then use the point-slope form of a linear equation to write the equation of the line through points P and Q:y - y1 = m(x - x1)

y - 4 = (2/3)(x - 2)We can substitute the coordinates of the midpoint (-2.5, 1) into this equation to see if it is a solution:1 - 4 = (2/3)(-2.5 - 2)

-3 = -10/3The equation is true, so the midpoint (-2.5, 1) is on the line through points P and Q.To show that this point is just as far from P as it is from Q, we can use the distance formula to find the distance from the midpoint to points P and Q:distance = √((x2 - x1)^2 + (y2 - y1)^2)distance from (-2.5, 1) to (2, 4) = √((2 - (-2.5))^2 + (4 - 1)^2) = √(4.5^2 + 3^2) = √(20.25 + 9) = √(29.25) = 5.4distance from (-2.5, 1) to (-7, -2) = √((-7 - (-2.5))^2 + (-2 - 1)^2) = √(4.5^2 + 3^2) = √(20.25 + 9) = √(29.25) = 5.4. Since the distance from the midpoint to points P and Q is the same, the midpoint is just as far from P as it is from Q.

The equation of the line in slope-intercept form is y = -2x+8

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system

The slope-intercept form of  the equation of a line is y = mx+b,

where m is the slope and b is the y-intercept

Given the table, pick any two points in order to find the slope:

point 1: x₁ = 0, y₁ = 8

point 1: x₂ = -2, y₂ = 12

slope (m) =  (y₂-y₁) / (x₂-x₁)

slope (m) = (12-8)/(-2-0) = 4/(-2) = -2

Using y = mx+b and x₁ = 0, y₁ = 8:

8 = -2(0) + b

b = 8

y = -2x+8

Thus, the equation of the line is y = -2x+8

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Answer:

The amount of water at the Georgia Aquarium is 20 times greater than the aquarium of the Americas hold.

Step-by-step explanation:

What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the tanks at the Georgia Aquarium hold approximately 8.4 × 10⁶ gallons of water. The tanks at the Audubon Aquarium of the Americas hold about 400,000 gallons of water.The number of the time will be calculated as below:-= 8.4 × 10⁶ / 400,000= 20.1

Therefore, the amount of water at the Georgia Aquarium is 20 times greater than the aquarium of the Americas hold.To know more about an expression followbrainly.com/question/15772941#SPJ2

Answer:

Step-by-step explanation:

3

The depth of the dugout is less than 24.

What is inequality?

In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.

Consider, the given inequality

[tex]2\frac{1}{4}d < -54[/tex]

Where d is the depth of the dugout.

We have to find the depth of the dugout.

Now to simplify the inequality.

[tex]2\frac{1}{4}d < -54[/tex]

convert improper fraction into a fraction.

[tex]2\frac{1}{4} = \frac{9}{4}[/tex]

⇒ 9/4d < -54

Multiply both sides by 4/9

⇒  d < -54 x 4/9

    d < -6 x 4

    d < -24

Hence, the depth of the dugout is less than 24.

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Answer: A 2/1

Step-by-step explanation:

Determine the slope of the line by finding 2 points

(2,-1),(4,3)

use slope formula

y2-y1/x2-x1

plug in and solve

3+1/4-2

4/2

2

the slope is 2 or 2/1

The area of land inside the fence is 7600 square feet.

What is the area of the triangle?

If the height of the triangle is 'h' and the base is 'b', then the area of the triangle can be computed by using the formula,

           Area = 1/2 * base * height

To find the area of the land inside the fence, we can use the formula for the area of a right triangle:

Area = (1/2) * a * b

where a is the length of one of the legs of the triangle and b is the length of the hypotenuse.

We are given that the length of fence b is 130 feet and that the measure of angle A is 42°. Since the triangle is right, angle A is complementary to angle 90°, so the measure of angle A is 90° - 42° = 48°. Since the measure of angle A is 48°, the other leg of the triangle (which we will call "a") is the side opposite angle A.

We can use the sine function to find the length of side a:

a = b * sin A

= 130 * sin 48°

= approximately 117.3 feet

Substituting these values into the formula for the area of a right triangle gives:

Area = (1/2) * 117.3 feet * 130 feet

= approximately 7600.5 square feet

Rounded to the nearest square foot, the area of land inside the fence is 7600 square feet.

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Answer: 4^3 * 5^3

Step-by-step explanation: 4 repeats itself 3 times and 5 repeats itself 3 times

4^3 * 5^3

Put the numbers in numerical order

4 comes before 5

Answer:

[tex] { 4}^{3} \times {5}^{3} [/tex]

Step-by-step explanation:

I'd assume your x's stand for multiplication, so using that logic there are three fours and three fives. Each being multiplied by itself, so the simplified/exponential version of the equation is:

[tex] {4}^{3} \times {5}^{3} [/tex]

Make sure you put in numerical order (4 goes before 5).

Ms. Flores using to add these numbers in this order is follow Commutative Property of Addition.

What is Commutative Property of Addition?

No matter what sequence the addends are in when we add two or more integers, the result is always the same. This characteristic may be expressed as A + B Equals B + A. In this case, 2+4=4 + 2 = 6. Due to the fact that the total of both phrases is 6, 2+4 is equivalent to 4+2. The Commutative Property of Addition refers to this.

On the first bus there were 14 students, on the second, 18 students, and on the third bus there were 12 students. The total number of students would then be: 14+18+12=44.

Ms. Flores decides to add 18 and 12 to get 30

18+12= 30

And then adds 14

30+14=44

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The difference in the areas of the signals based on the information given is 549.5km².

The formula to calculate the area of a circle will be:

= πr²

where r = radius

Mast 1 broadcast radio signals that can be heard within a radius of 15km. The area will be:

= πr²

= 3.14 × 15²

= 706.5km²

Mast 2 broadcast radio signals that can be hear within a radius of 20km. The area will be:

= πr²

= 3.14 × 20²

= 1256km²

The difference in the areas will be:

= 1256km² - 706.5km²

= 549.5km²

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Complete question

Mast 1 broadcast radio signals that can be heard within a radius of 15km.

Mast 2 broadcast radio signals that can be hear within a radius of 20km.

Calculate the difference in the areas of the signals.

The Formula for h(x) is 7.5cos(51.4x - 154.3)-1.5.

What is trigonometric function ?

Trigonometric functions are referred to as Circular Functions will be merely outlined because the functions of associate degree angle of a triangle.

The difference in y values from max to min = 15. 15/2 = a
max cosine = 1, min cosine =-1
7.5 x 1 - 1.5 = 6
7.5x -1 -1.5 = -7.5-1.5= -9
h(x) = 7.5cos(bx+c) -1.5
now just get a period or frequency that matches the x coordinates 3 and 6.5 to get b and c
at (3,6) cosine = 1 to get a maximum value. cosine is at a max when cos(bx+c) = 1 and bx+c=0, 360, 720...
if x=3, then 3b +c=0 and c=-3b
for (6.5,-9) to be a minimum h value, then cos(6.5b+c) =-1 that happens when the angle = 180. +n360 for any integer n. 6.5b+c = 180
c= 180-6.5b
c=-3b
180-6.5b =-3b
add 6.5b to both sides to get
180= 3.5b
b = 180/3.5 = 51 1/7
c=-3b = -153 3/7
h(x) = 7.5cos(51.4x - 154.3)-1.5
hence , Formula for h(x) is 7.5cos(51.4x - 154.3)-1.5

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The triangle congruency theorem which can be used to prove

â–³ ≅ â–³onp is  ASA (angle  side angle)

Let the triangles be ONP and GHL

The congruence theorem, which will demonstrate that "GHL" and "ONP ," are congruent is to be discovered.

As can be seen, side lengths GH of GHL and ON of ONP are equal.

Furthermore, we are informed that mONP = mHKJ.

Since line segments GK and JL connect to produce them, we can see that GHL is the vertical opposite angle of ONP . Therefore, using the vertical angles theorem, mONP  congruence mKHJ.

We can see that both triangles contain two congruent angles and one congruent included side; as a result,

GHL ONP by ASA congruence.

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Hypothesis test for µ1 – µ2 can be used to test whether borrowers from this particular bank who receive hamp modifications are more likely to re-default than those who receive non-hamp modifications.

The Independent Samples t Test analyses the means of two separate groups to see if there is statistical support that the population mean values are statistically substantially different. Independent Samples t Test is known as parametric test.

The population means are deemed to be different if the two-sample means are sufficiently dissimilar from one another.

The null and alternative hypothesis for the programs is

H0: μ1 - μ2=0

H1: μ1 - μ2  ≠0        

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Answer:

x=125,2x=250

Step-by-step explanation:

A hexagon sum of angles is 720 degrees.

The sum of the hexagon's angles is 345+3x

345+3x=720

3x=375

x=125

2x=250

Answer:

B) 18 ft

Step-by-step explanation:

The scale is 1 in. model : 6 ft real.

6/1 = 6

To go from model size to real size, multiply the model size by 6 and change from inches to feet.

3 in. model = 3 × 6 ft = 18 ft

In order to increase the likelihood that a blue marble would be drawn at random to 3/4, we must thus add 32 more blue marbles.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to express probabilities.

Here,

Let the number of blue marbles added be x,

Probability=3/4

Total marbles=20

Number of blue marbles=7

(7+x)/(20+x)=3/4

4(7+x)=3(20+x)

28+4x=60+3x

x=60-28

x=32

So, we need to add 32 more blue marbles to make the probability of randomly drawing a blue marble be 3/4.

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Representative fraction is a form of scale that can be used to change the size of an object to form an image. The required length is 32 inches.

A scale is a fraction of numbers that can be used to either increase or decrease the size of a given object. It is majorly referred to as representative fraction in scale drawing.

Representative fraction = [tex]\frac{length on drawing}{original length}[/tex]

In the given question, we have;

12 inches = 1 feet

x inches = 30 feet

So that:

x = 30 x 12 inches

  = 360 inches

representative fraction = [tex]\frac{2 inches}{360 inches}[/tex]

                             = 5.56 x [tex]10^{-3}[/tex]

Thus, given that the length of the Alamo Mission is 480 feet long. Then:

480 feet = 480 x 12 inches

              = 5760 inches

So that,

the required length in inches = 5760 x 5.56 x [tex]10^{-3}[/tex]

                                             = 32 inches

Therefore the expected length of the Alamo Mission is 32 inches.

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Answer:

10L + 21t = 188

t = 4L

Step-by-step explanation:

Let L be the number of hours spent lifeguarding and t be the number of hours spent tutoring. Kayla earned $188 total, so 10L+ 21t = 188(the number of hours spent lifeguarding/tutoring times how much she gets paid every hour). We also know that she spent 4 times longer tutoring than lifeguarding, so t = 4L. These are our systems of equations.