Two polygons are similar. The perimeter of the larger polygon is 120 yards and the ratio of the corresponding side lengths is $\frac{1}{6}$. Find the perimeter of the other polygon

Note that the angles above are marked to  be similar hence, one half of the base has a length of 16 units.

To solve this problem, we can use the fact that the line bisecting the angle at the top of a triangle also bisects the base. This means that the two halves of the base are equal in length.

Let's call the length of one half of the base "z". Then, the length of the other half of the base is also "z". The total length of the base is 32 units, so we can set up an equation:

z + z = 32

Simplifying this equation, we get:

2z = 32

Dividing both sides by 2, we get:

z = 16

So one half of the base has a length of 16 units.

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The factorised form of the given expression would be = (3x+2)(2x+y). That is option D.

Factorisation is when a number is written as a product of several other numbers.

The given expression is as follows:

6x² + 3xy + 4x + 2y

Insert bracket to simplify the above expression;

(6x² + 3xy) (4x + 2y)

Factorise the expressions one after the other;

3x(2x+y) +2( 2x+ y)

The factorised form = (3x+2)(2x+y). This is soo because when multiplied will give the same expression such as 6x² + 3xy + 4x + 2y .

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Answer:

D. (2x + y)(3x + 2)

Step-by-step explanation:

i took the test :)

When Trevor graduated high school, he put his pirating CDs behind him and got a job at a clothing store to save money for college. Saving money is an essential part of financing college.

A student can achieve their dream of attending college by following the steps below.

Step 1: Create a budget. Creating a budget is the first step in saving for college. The budget should include all expenses, such as tuition, room and board, books, and other fees.

Step 2: Find ways to save money. Save money by finding ways to reduce spending on non-essentials such as entertainment, dining out, and shopping. Every little bit counts, and the savings can be put toward college.

Step 3: Explore scholarships and financial aid. Apply for financial aid and scholarships to help pay for college. Grants, loans, and scholarships are available from federal, state, and private sources.

Step 4: Consider community college or online education. Consider community college or online education as an affordable way to earn college credit and save money.

Step 5: Work and save Continue working and saving money during college. A part-time job or paid internship can help cover expenses and reduce student loan debt.

These are the essential steps for saving money for college. A student can explore these options and make smart financial decisions to achieve their dream of attending college.

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Answer:33

Step-by-step explanation:45-12=33

Answer: two right-angled triangle, equilateral triangle

Step-by-step explanation:

It is a combination of two right-angled triangle or it is an equilateral triangle.

Explanation:

You want to prove a point P on the perpendicular bisector of segment YZ is equidistant from Y and Z.

1. PX is the perpendicular bisector of YZ . . . . given

2. angles at X are right angles . . . . definition of perpendicular

3. YX = XZ . . . . definition of bisector

4. PX = PX . . . . reflexive property of congruence

5. ∆PXY ≅ ∆PXZ . . . . LL congruence theorem

6. YP ≅ ZP . . . . CPCTC

Answer: -2g^7h^8

Step-by-step explanation:

Answer:

Step-by-step explanation:

4. The cοrrect οptiοn is A) David had a higher variability because his IQR is 8 mοre than Gabrielle

6. The cοrrect οptiοn is D) The IQR For both sets is 8.

Descriptive statistics is a branch οf statistics that invοlves the cοllectiοn, presentatiοn, and characterizatiοn οf a set οf data.

4) Given

1. Number οf text messages frοm David 10, 2, 5, 22, 19, 11, 8

2. Number οf text messages frοm Gabrielle 19, 15, 25, 24, 20, 29, 21

Find the median fοr the data οf David

10, 2, 5, 22, 19, 11, 8

Arrange in ascending οrder

2, 5, 8, 10, 11, 19, 22

Median οf the data is (n + 1)/2

= (7 + 2)/2

= 4

= 4th term =  10

Nοw Find Q1 and Q3

Q1 = 5 and Q3= 19

IQRD=Q3−Q1

IQRD=19−5

IQRD=14 Equatiοn (1)

Find the median fοr the data οf Gabrielle

19, 15, 25, 24, 20, 29, 21

Arrange in ascending οrder

15, 19, 20, 21, 24, 25, 29

Median οf the data is 4th term 21

Nοw Find Q1 and Q3

Q1=19 and Q3=25

IQRG=Q3−Q1

IQRG=25−19

IQRG=6 Equatiοn (2)

Frοm equatiοn 1 and 2 we can say that

David had a higher variability because his IQR is 8 mοre than Gabrielle.

Hence, The cοrrect οptiοn is A) David had a higher variability because his IQR is 8 mοre than Gabrielle.

5) Seventh grade = 6 10 14 18 22 26

Median = 4th value = (18 + 14)/2 = 16

Q1=10 and Q3=22

IQR = 22 - 14 = 8

Eighth grade =  22 26 30 34 38

Median (n + 1)/2 = 3rd value = 30

Q1=22 and Q3=38

IQR = 34 - 26 = 8

Thus, The IQR For both sets is 8.

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The length of the long diagonal of the cube is 3sqrt(3) inches.

Let's denote the length of one side of the cube as "a". Then the cube has a volume of a^3, a surface area of 6a^2 (since a cube has 6 faces with side length a), and a total edge length of 12a (since each face has 4 edges of length a).

Using the given equation, we can write

a^3 + 3(12a) = 2(6a^2)

Simplifying this equation, we get

a^3 + 36a = 12a^2

a^3 - 12a^2 + 36a = 0

a(a^2 - 12a + 36) = 0

a(a - 6)^2 = 0

The only positive solution for "a" is a = 6 (since a cannot be zero or negative). Therefore, the cube has a side length of 6 inches.

To find the length of the long diagonal of the cube, we can use the Pythagorean theorem. The long diagonal passes through the center of the cube and connects two opposite corners. The distance from the center to a corner is half the length of the long diagonal. Let's call this distance "d".

Using the Pythagorean theorem, we can write

d^2 = (6/2)^2 + (6/2)^2 + (6/2)^2

d^2 = 3(6^2)/4

d = (sqrt(3)×6)/2

d = 3sqrt(3) inches

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The equation for calculating the number of pairwise comparisons in a pairwise ranking matrix is: (n*(n-1))/2 where n is the number of items being compared in the matrix.

A pairwise ranking matrix is a tool that is used to rank items on the basis of pair-wise comparisons of the items. In order to find out the number of pairwise comparisons in such a matrix, one needs to use the following formula:(n*(n-1))/2where n is the number of items being compared in the matrix.

The formula works on the principle that every item in the matrix needs to be compared with every other item, but each comparison needs to be done only once. This is why the formula divides the total number of comparisons by two.

Therefore, the equation is: (n*(n-1))/2


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Answer:

45.6%

Step-by-step explanation:

166.50 minus 45.6% equals 90 dollars

The given function [tex]y=x^2 - 6x - 7[/tex] describes the graph A.

What is function?

In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the codomain) with the property that each input is related to exactly one output.

We can solve this Function by substituting the 0 for Y.

To find the value of x when y is equal to 0, we can substitute 0 for y in the equation and solve for x:

[tex]0 = x^2 - 6x - 7[/tex]

To solve for x, we can use the quadratic formula:

x = (-b ± [tex]\sqrt{(b^2 - 4ac)}[/tex]) / 2a

In this case, a = 1, b = -6, and c = -7. Substituting these values into the formula, we get:

x = (-(-6) ± [tex]\sqrt {((-6)^2 - 4(1)(-7)}[/tex])) / 2(1)

Simplifying:

x = (6 ± [tex]\sqrt{64}[/tex]) / 2

x = (6 ± 8) / 2

x = 7 or x = -1

Therefore, when y is equal to 0, x can be either 7 or -1.

Therefore the given function describes the graph A.

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As per the concept of parallelogram, the area of the hexagons is 1237.9 cm², one isosceles trapezoid is 130 cm², one triangle is 60 cm², one circle is 78.5 cm².

Since we know the apothem is 10 cm, we can use the tangent function to find the length of the side:

tan(72) = side length / 10

Solving for the side length, we get:

side length = 10 * tan(72) ≈ 21.2 cm

Now that we know the side length, we can use the formula for the area of a regular polygon:

area of the hexagon = (5 x side length² x √(3)) / 2 ≈ 1237.9 cm²

Next, let's find the area of the isosceles trapezoid.

To find the area, we can use the formula:

area of the trapezoid = ((base1 + base2) / 2) x height

Substituting the given values, we get:

area of the trapezoid = ((12 + 14) / 2) x 10 = 130 cm²

Now, let's move on to the triangle. We are given the base (12 cm) and the height (10 cm). To find the area of a triangle, we can use the formula:

area of the triangle = (base x height) / 2

Substituting the given values, we get:

area of the triangle = (12 x 10) / 2 = 60 cm²

Next, let's find the area of the circle. We know that the diameter of the circle is equal to the height of the isosceles trapezoid (10 cm), so the radius is half of that:

radius = 10 / 2 = 5 cm

Using the formula for the area of a circle, we get:

area of the circle = π x radius² = π x 5² ≈ 78.5 cm²

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Complete Question:

There are 3 regular hecagons, one isocrles trapezoid, one triangle, one circle and one parallelogram. Use the provded measurements to find the area. You will need to use trigonometry to find some measurements

base is 12 cm, length is 14 cm and height is 10 cm

Answer:  Therefore, the maximum distance you can ride for $20 is 6 kilometers.

Step-by-step explanation:   The inequality to determine the distance in kilometers, d, you can ride for $20 is:

$5 + $2.50d ≤ $20

Simplifying the above inequality, we get:

$2.50d ≤ $15

Dividing both sides by $2.50, we get:

d ≤ 6

Answer:

First figure:

Faces--5

Edges--8

Vertices--5

Type--pyramid

Second figure:

Faces--6

Edges--12

Vertices--8

Type--rectangular prism

The sum elements for the expected hidden state of a Kalman filter at time t1 given data at time t1 and a hidden state distribution at time t are the prior state distribution and the posterior state distribution.

The weights are the posterior probability, which is determined by the Kalman filter's prediction and measurement likelihood.

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Hence, there's a 36.41 percent chance that a voicemail will be between 10 and 20 or 30 and 40 seconds in length.

It is based on the possibility that something will actually happen. The basis for theoretical probability is the justification for probability. For example, the theoretical probability of getting a head when flipping a coin is ½.

Calculating the area underneath the normal curve of distribution between the two iterations will allow us to determine the likelihood that a specific voicemail will last between 10 and 20 or 30 and 40 seconds.

The intervals must first be standardized by transforming it into z-scores using following formula:

z = (x - μ) / σ

Where x is the value, we want to convert, μ is the mean of the distribution, and σ is the standard deviation.

For the period of 10 to 20 seconds:

z1 = (10 - 40) / 10 = -3

z2 = (20 - 40) / 10 = -2

For the interval 30 to 40 seconds:

z3 = (30 - 40) / 10 = -1

z4 = (40 - 40) / 10 = 0

The region of the curve between such z-scores can now be calculated or found using a calculator and a standard normally distributed table. As an alternative, we can employ the normal distribution's CDF, or cumulative distribution function.

P(10 ≤ x ≤ 20 or 30 ≤ x ≤ 40) = P(10 ≤ x ≤ 20) + P(30 ≤ x ≤ 40)

P(10 ≤ x ≤ 20) = P(-3 ≤ z ≤ -2) ≈ 0.0228

P(30 ≤ x ≤ 40) = P(-1 ≤ z ≤ 0) ≈ 0.3413

As a result, the likelihood that a voicemail will be between 10 and 20 or 30 and 40 seconds is:

P(10 ≤ x ≤ 20 or 30 ≤ x ≤ 40) ≈ 0.0228 + 0.3413 ≈ 0.3641

A voicemail that is between 10 and 20 or 30 to 40 seconds in length has a 36.41% chance of being left.

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Answer:

There are many options, like:

14/1 or 28/2...

Step-by-step explanation:

First write the system:

(21 x 8) / 12

Then simplify the brackets:

(168) / 12

= 14

Then you can put 14 over 1 as an example of proportionality:

14/1 : (21 x 8) / 12

Or multiply it by 2, 3 etc.:

42/3 : (21 x 8) / 12.

The accurate solution is that the probability of the proportion of nearsightedness of at least 0.09 is approximately 0.0324 or 3.24%.

There are a few steps to answer this question about probability with the proportion of nearsightedness:

1. Define the variable: Let p be the true proportion of children with nearsightedness.

2. Check the conditions for using the normal approximation to the binomial distribution: np = 356 × 0.09 = 32.04 and n(1 - p) = 356 × 0.91 = 323.96, both greater than or equal to 10.

3. Calculate the z-score using the formula: z = (x - np) / √(np(1 - p)), where x = 0.09 × 356 = 32.04.

4. Find the probability using a calculator.

The probability that 356 randomly selected children will have a proportion of nearsightedness of at least 9% is approximately 0.0324, or 3.24%.

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The closest value to the standard deviation of the 100 times is (C) 20 seconds.

To determine the closest value to the standard deviation of the 100 times, we would need the actual histogram or the data points themselves.

In general, the standard deviation measures the spread or dispersion of a set of values. A higher standard deviation indicates a greater dispersion, while a lower standard deviation indicates a smaller dispersion.

Looking at the given options, (A) 2.5 seconds and (B) 10 seconds are relatively small values, which suggests a low dispersion among the times. On the other hand, options (D) 50 seconds and (E) 90 seconds are larger values, indicating a higher dispersion.

Option (C) 20 seconds falls in between the smaller and larger values. While it is difficult to determine the exact standard deviation without the data, option (C) of 20 seconds seems like a reasonable choice as it represents a moderate spread among the 100 times.

Therefore, the closest value to the standard deviation of the 100 times is (C) 20 seconds.

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Answer: 2.

Step-by-step explanation:

Mean = Population / Number of Integers.

Mean = 7.

Subtract the integers from the mean.

5 - 7 = -2

6 - 7 = -1

10 - 7 = 3.

Put differences in absolute value.

|-2| = 2

|-1| = 1

|3| = 3.

add the differences then divide by the population number.

2 + 1 + 3 = 6

6 / 3

2

The geometric sequence is 9 + 2 + 20 = 29.

The smallest number the third term in the geometric sequence can be is 29.

This is because when you add 2 to the second term and 20 to the third term of the three-term arithmetic sequence with a first term of 9,

the third term of the geometric sequence is 9 + 2 + 20 = 29.

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The probability that the 15 cards contain exactly one queen given that they contain exactly two aces is approximately 0.060 or 6.0%.

We can use conditional probability. Let A be the event that the 15 cards contain exactly two aces, and B be the event that they contain exactly one queen. Then we want to find the conditional probability P(B|A).

First, let's find the probability of A. There are C(4,2) ways to choose the two aces out of four, and C(48,13) ways to choose the other 13 cards out of the remaining 48 cards. So the total number of ways to choose 15 cards with exactly two aces is:

C(4,2) × C(48,13) ≈ 4.57 × 10^12

Next, let's find the probability of both A and B. There are C(4,2) ways to choose the two aces out of four, C(4,1) ways to choose one queen out of four, and C(47,12) ways to choose the other 12 cards out of the remaining 47 cards. So the total number of ways to choose 15 cards with exactly one queen and exactly two aces is:

C(4,2) × C(4,1) × C(47,12) ≈ 2.76 × 10^11

Finally, we can use the formula for conditional probability:

P(B|A) = P(A and B) / P(A)

P(B|A) = (C(4,2) × C(4,1) × C(47,12)) / (C(4,2) × C(48,13))

P(B|A) ≈ 0.060

Therefore, the probability is approximately 0.060 or 6.0%.

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There is a 68.26% chance of a value falling between 3 and 7 in the given normal distribution.

This indicates a normal distribution, which is a type of continuous probability distribution. It is characterized by a bell-shaped curve that is symmetric about the mean, with a specific formula given by f(x) = [tex]1/(σ√2π)e^(-(x-μ)^2/2σ^2)[/tex]where μ is the mean, σ is the standard deviation, and x is the random variable.

In terms of calculation, we can use the formula to calculate the probability of a certain event occurring. For example, if we know the mean and standard deviation of a normal distribution, we can calculate the probability of a value between two given points. For example, if the mean is 5 and the standard deviation is 2, then the probability of a value between 3 and 7 is given by the integral of f(x) from 3 to 7, which is equal to 0.6826. This means that there is a 68.26% chance of a value falling between 3 and 7 in the given normal distribution.

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15 divided by 289 is approximately equal to 0.0519 or 519/10000. Fifteen divided by two hundred and eighty nine is a division problem that involves dividing 15 by 289. To solve this problem, we can use long division or a calculator.

Using long division, we start by dividing the first digit of the dividend (2) by the divisor (15). Since 2 is less than 15, we add a decimal point and a zero to the dividend and continue the process. We bring down the next digit (8) and divide 28 by 15, which gives us a quotient of 1 with a remainder of 13. We add a decimal point after the quotient and bring down the next digit (9) to get 139 as the new dividend. We divide 139 by 15, which gives us a quotient of 9 with a remainder of 4. We add a decimal point after the quotient and bring down the last digit (0) to get 40 as the new dividend. We divide 40 by 15, which gives us a quotient of 2 with a remainder of 10. Finally, we add a decimal point after the last quotient and write the remainder as a fraction over the divisor to get the final answer:

15 divided by 289 is approximately equal to 0.0519 or 519/10000.

In summary, fifteen divided by two hundred and eighty nine is a division problem that can be solved using long division or a calculator. The answer is a decimal or a fraction, depending on how the division is carried out.

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The total number of hours is 30 hours as the sum of 7/8 and 3/8 comes out to be 30 hours.

1) We know that there is a total of 24 hours in a day.

therefore, 7/8 hours of Wednesday =

number of hours in a day = 24

number of hours every Wednesday = 7/8

= 7/8 x 24 hours

= 7 x 3 hours

= 21 hours

7/8 hours every Wednesday means 21 hours every Wednesday.  

2) We know that there are a total of 24 hours in a day;

therefore, 3/8 hours of Friday =

number of hours in a day = 24

number of hours every Friday = 3/8

= 3/8 x 24 hours

= 3 x 3 hours

= 9 hours

3/8 hours every Friday means 9 hours every Friday.

therefore, the total number of hours = 21 + 9 = 30

The total number of hours is 30 hours as the sum of 7/8 and 3/8 comes out to be 30 hours.

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The number of hours Cora's friend paint in total is found to be - twenty-one fifths.

The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top on the line.

Three-fifths of an hour was spent by Cora painting.

= 3/5 of hour

Her companion spent seven times as long painting.

= 7 * 3/5 of hour

= 21 /5  of hour

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Answer:

Step-by-step explanation:

The area of a circle is pi times the radius squared (A = π r²).

In a rectangle where the length is 3 times the width, and the perimeter is 3 times the width. The perimeter is 96 cm, the length is 36 cm and the width is 12 cm.

Given,

Length of a rectangle is 3 times the width.

Perimeter is 3 times the width.

Perimeter is 96 cm.

Let w be the width of the rectangle.

The length of the rectangle is 3 times the width, so the length l is 3w.

The perimeter of the rectangle is equal to the sum of all its sides, so:

2w + 2(3w) = 96

2w + 6w = 96

8w = 96

w = 12

Therefore, the length is 36 cm and the width is 12 cm.

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Answer:Your answer is 67.

Step-by-step explanation:Your very welcome! :D

hope im right. Good luck acing your quiz!

the interest earned on 250000 at a 7.5% interest rate for half a year is 4687.50. This means that after half a year, the total amount that you would have is the sum of the principal and the interest, which is 254687.50.

To calculate the interest on 250000 at a 7.5% interest rate for half a year, we first need to determine the annual interest rate, as most interest rates are quoted on an annual basis. To do this, we can divide the annual interest rate of 7.5% by 2 to get the half-yearly interest rate, which is 3.75%.

Next, we can use the formula for simple interest to calculate the interest earned over half a year. Simple interest is calculated by multiplying the principal amount (in this case, 250000) by the interest rate (3.75%) and the time period (0.5 years).

So, the interest earned would be:

Interest = Principal x Rate x Time

= 250000 x 0.0375 x 0.5

= 4687.50

Therefore, the interest earned on 250000 at a 7.5% interest rate for half a year is 4687.50. This means that after half a year, the total amount that you would have is the sum of the principal and the interest, which is 254687.50.

It's worth noting that this calculation assumes that the interest is simple interest, which means that the interest earned is not reinvested. If the interest is compounded (i.e., the interest earned is reinvested), then the interest earned would be higher.

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