Which set of measurements would prove that ΔABC and ΔDEF are similar?

A. DE = 15, EF = 20 and m∠D = 35
B. DE = 16, DF = 21 and m∠D = 35
C. DE = 12, DF = 16 and m∠D = 35
D. DE = 18, EF = 24 and m∠D = 70

On solving the provided question, we can say that  percentage terms is 41.93%

A percentage in mathematics is a figure or ratiο that is stated as a fraction of 100. The abbreviatiοns "pct.," "pct," and "pc" are also occasionally used. It is frequently denοted using the percent symbol "%," though. The amount of percentages has nο dimensions. With a denominator of 100, percentages are basically fractiοns.

To show that a number is a percentage, place a percent symbol (%) next tο it. For instance, if yοu correctly answer 75 out of 100 questions on a test (75/100), yοu receive a 75%. To cοmpute percentages, divide the amount by the tοtal and multiply the result by 100. The percentage is calculated using the fοrmula (value/total) x 100%.

total no. of students = 31

no. of students play sports = 13

percentage terms = 13/31 × 100= 41.93%

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Answer:

The quotient is 3x^3 + 2x and the remainder is 0.

Step-by-step explanation:

Quotient: 3x³ + 2x

Remainder: -5

Answer:

3x^3 - 3x^2 + x - 1

x + 1 | 3x^4 + 2x^2 - 6x + 1

- (3x^4 + 3x^3)

---------------

-x^3 - 6x + 1

- (-x^3 - x^2)

-------------

-5x^2 - 6x + 1

-(-5x^2 - 5x)

------------

-x + 1

Therefore, the quotient is 3x^3 - 3x^2 + x - 1, and the remainder is -x + 1.

Answer:

  $20M

Step-by-step explanation:

You want the "natural breakpoint" for a lease that specifies rent is the maximum of $5 per square foot for 120,000 square feet, or 3% of sales.

The minimum rent is ($5/ft²)×(120000 ft²) = $600,000.

The amount of sales that makes $600,000 equal to 3% of sales is ...

  $600000 = 0.03s

  s = $600000/0.03 = $20,000,000

The "natural breakpoint" is $20M in sales.

__

Additional comment

When sales exceeds $20M, 3% of sales is more than $5/ft², so the rent will be based on sales.

Answer:

LCD → 468

Step-by-step explanation:

[tex]\frac{5}{18} = \frac{5}{18} * \frac{26}{26} = \frac{130}{468}[/tex]

[tex]\frac{11}{12} = \frac{11}{12} * \frac{39}{39} = \frac{429}{468}[/tex]

[tex]\frac{6}{13} = \frac{6}{13} * \frac{36}{36} = \frac{219}{468}[/tex]

Hence, the least common denominator for these three fractions would be 468.

The equation to represent the function is y = 6x + 10 where y is the height of the drone in meters and x is the time in seconds. so the drone rises 6 meters per second.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

Let us  find the rate of change, we can divide the total change in the height of the drone by the time taken for the change.

rate of change = (change in height) / (time taken)

(40 m - 10 m/ (5 s - 0 s)= 30 m/5 s=6m/s

The drone rises 18 m every 3 s

rise per second = 18 m / 3 s = 6 m/s

This means that the initial height of the drone is 10 meters, since it takes 3 seconds for the drone to rise to a height of 28 meters

Therefore, the equation to represent the function is:

y = 6x + 10

where y is the height of the drone in meters and x is the time in seconds.

Therefore, the drone rises 6 meters per second.

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the measure of the angle will be 70°.

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.An isosceles triangle in geometry is one with at least two sides that are of equal length. Both having exactly two sides of equal length and having at least two sides of equal length are acceptable specifications, with the latter version containing the equilateral triangle as an exception.

The sum of all angle of triangle = 180

The given triangle two angles are given 44° and 68°

The other angle is 180° - (44+68) = 180 - 110 = 70°

Hence the measure of the angle will be 70°.

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Another way to find 4x2x5 is to multiply two of the digits and multiply the last digit with the product of two.

Multiplication is when you take one number and add it together a number of times. Example: 5 multiplied by 4 = 5 + 5 + 5 + 5 = 20. We took the number 5 and added it together 4 times. This is why multiplication is sometimes called "times".

Given are three numbers multiplied, 4x2x5, we need to find the another way to solve it,

So,

4x2x5 = 40

So, in another method,

Multiply 4 and 2, we get, 8 as product, now multiply the product 8 to the last number 5,

8x5 = 40

Hence, the another way to find 4x2x5 is to multiply two of the digits and multiply the last digit with the product of two.

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The question is incomplete solved for:

Find the another method to solve 4x2x5

The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.

What is meant by continuous compounding?

If compound interest is calculated and reinvested into the balance of an account across an essentially unlimited number of periods, continuous compounding is the mathematical limit that compound interest can reach. Continuous compounding determines interest by assuming constant compounding across an infinite number of periods, as opposed to computing interest on a finite number of periods, such as annually or monthly.

Given,

rate per period  = 3%

Principal amount = $1000

Compounding is done after 1,5 and 20 years.

But we are asked to find the amount after continuous compounding after 1 year.

The formula of the amount after continuous compounding is:

[tex]A = Pe^{rt}[/tex]

where A = amount after continuous compounding

        r = rate of period

     t = time period

    P  = principal amount

[tex]A = Pe^{rt} = 1000e^{0.03*1}[/tex] = $1030.45

Annual yield formula (AYP) = [tex](1+\frac{r}{n} )^n-1[/tex]

n = times it compounds per year = 365

r = 0.03

AYP = [tex](1+\frac{0.03}{365} )^{365}-1 = 0.0304[/tex]

                                  = 3.04%

Therefore The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.

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For the given triangle, the value of 'a' would be 41.41 degrees.

What is cosine angle?

In mathematics, the cosine of an angle is a trigonometric function that relates the ratio of the adjacent side of a right triangle to the hypotenuse.

More formally, the cosine of an angle is defined as the ratio of the length of the adjacent side of a right triangle to the length of the hypotenuse. It is denoted by the symbol cos and is calculated using the following formula:

cos(theta) = adjacent side / hypotenuse

where theta is the measure of the angle in radians or degrees.

By using the cosine definition,

cosθ = adjacent side/Hypotenuse

cos(a) = 45/50

[tex]a = cos^{-1}(\frac{45}{60})[/tex]

a = 41.41°

Hence, for the given triangle, the value of 'a' would be 41.41 degrees.

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On solving the provided question, we can say that Area of Rhombus is 24 cm²

A rhombus is an equal-sided quadrilateral in Euclidean plane geοmetry. The term "equilateral triangle" alsο refers to a quadrilateral whose sides are of the same length. A parallelοgram has a unique variation knοwn as a rhombus. In a rhombus, the οpposite sides and angles are parallel and equal.

A rhombus's diagοnal is split in half by a right angle, and each of its sides is the same length. Rhombic diamοnds and diamonds are other names for rhοmbuses. The length οf every side is the same. Diagοnals are equal in a rhοmbus. At a 90° angle, parallel lines split in half, 180 degrees is the sum of adjacent angles.

By distance formula

BD = [tex]\sqrt{(-2-4)^2 + (-1-5)^2}[/tex]

BD = [tex]\sqrt{36 + 36}[/tex]

BD = 6√2

similarly,

AC = 4√2

and, Area = 1/2 × (product of diagonals)

Area of Rhombus = 1/2 × 6√2 × 4√2 = 24 cm²

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The measure that changes the most is the mean and the new value is 74.33°

If a value of 71° is changed to 93°, we have:

58, 61, 93, 77, 91, 100, 105, 102, 95, 82, 66, 57

Mean = (58+ 61+ 93+77+ 91+ 100+ 105+ 102 + 95 + 82+ 66+ 57)/12 = 74.33°

To find the median, arrange the data in order of size and pick the middle number. That is:

57, 58, 61, 66, 77, 82, 91, 93, 95, 100, 102, 105

Median = (82+91)/2 = 86.5°

Range = 105 - 57 = 48°

IQR = 97.5 - 63.5 = 34°

Therefore, the measure that changes the most is the mean and the new value is 74.33°

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Answer: it is 86.5 i got the answer correct on test trust me i want to help you guys out.

Step-by-step explanation:

If a poll is to be conducted in an elementary school by interviewing 50 students, the following samples have been described as either representative or not representative as follows:

a. The first 50 students leaving the cafeteria. Not representative

b. Fifty randomly chosen names from a computer-generated list of names of all students at the school. Representative

c. Ten students randomly chosen from each of the 5 areas of campus. Representative

d. Five students from 10 teachers' classes. Representative

A representative sample is a small collection from a larger group from which any information obtained will be as good as the larger group. While choosing a representative sample, the researcher should take care not to zone the participants from a given section of the population. This will cause the information to be skewed and not objective.

Selecting 50 students leaving a cafeteria will not be representative because this might only represent a section of the school that will be giving their response based on a certain mood.

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A) The homeownership rate in the United States calculated by the U.S. Census Bureau for the second quarter of 2019 as 64.1 percent means that about 64% of the U.S. homes are owner-occupied instead of renting.

B) The homeownership rate is the quotient of the number of owner-occupied homes and the total number of U.S. homes.

The homeownership rate describes the percentage or proportion of U.S. homes occupied by owners instead of renters.

The rate refers to the ratio, which is the relative size of one quantity compared to another.

To compute the homeownership rate, the number of owner-occupied homes is divided by the total number of U.S. homes and multiplied by 100.

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Answer:

The expansion of (3x² - k/x)^9 can be found using the binomial theorem. The binomial theorem states that for any real numbers a and b and any positive integer n, the expansion of (a + b)^n is given by:

(a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^(n-1)b^1 + C(n, 2)a^(n-2)b^2 + ... + C(n, n-1)a^1b^(n-1) + C(n, n)a^0b^n

where C(n, k) = n! / (k! (n-k)!).

Using this formula, we can find the coefficient of the term in x^6 in the expansion of (3x² - k/x)^9. The term in x^6 will be of the form C(9, 3) (3x²)^3 (-k/x)^6. We can find the value of C(9, 3) as follows:

C(9, 3) = 9! / (3! (9 - 3)!) = 84.

So, the coefficient of the term in x^6 is 84 * (3^3) * (-k/x)^6 = 84 * 27 * (-k)^6.

Since we are told that this coefficient is 6048, we can set these two expressions equal to each other:

6048 = 84 * 27 * (-k)^6

Dividing both sides by 84 * 27, we get:

k^6 = -6048 / (84 * 27) = -1.

Taking the sixth root of both sides, we find:

k = -1^(1/6).

So the value of k is approximately -1.122462048309372981433.

Answer:

Step-by-step explanation:

Martina has been given 5 bands and asked to place a vote for her favorite and second favorite bands. The number of different votes possible can be calculated using combinations.

A combination is a way of selecting items from a set, where order does not matter and repetition is not allowed. To find the number of combinations, we can use the formula:

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

where:

n is the number of items

k is the number of items being selected

! denotes factorial, which is the product of all positive integers up to that number

Step-by-step, the calculation is as follows:

Determine the number of items and the number of items being selected:

n = 5 (the number of bands)

k = 2 (the number of bands Martina is voting for)

Calculate the number of combinations using the formula:

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

C(5, 2) = 5! / (2! * (5 - 2)!)

C(5, 2) = 120 / (2 * 3!)

C(5, 2) = 120 / (2 * 6)

C(5, 2) = 120 / 12

C(5, 2) = 10

So, there are 10 different votes possible for Martina's favorite and second favorite bands from the list of 5 bands.

The following is deduced from the equation f(x)=(x - 1)^3 + 5

Horizontal shift: 1 left

Vertical shift: 5 down

Vertical stretch factor: 1

Vertical compression factor: 1

Axis of reflection: -x + 6

Domain: all real numbers

Range: all real numbers

Inflection Point: (1, 5)

The vertical stretch factor is a term used in mathematics to describe the transformation that changes the height of a graph while leaving the horizontal axis unchanged. In other words, it's a factor by which the y-values of a function are multiplied to produce a new, stretched or compressed version of the original graph.

The stretch factor is usually represented by the symbol "k". For example, if the equation of a function is y = f(x), then the equation of its vertically stretched image would be y = k * f(x). A positive value of k stretches the graph upward, while a negative value of k compresses the graph downward. If k > 1, the graph is stretched vertically; if 0 < k < 1, the graph is compressed vertically; if k = 1, the graph remains unchanged.

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The original markup price that will lead to a markup on cost of 25 % would be $ 1. 68 per pound

To find the marked up price, first, find the amount that is a 25 % markup on cost to be :

= ( 100 pounds x 79 cents per pound ) x ( 1 + 25 %)

= 79 x 1. 25

= $ 98. 75

The 40 % sold would bring in:

= 40 % x 100 x 0. 79

= $ 31. 60

The amount left to be raised is:

= 98. 75 - 31. 60

= $ 67. 15

The markup price on the rest of the mushrooms is:

= 67.15 / ( 100 - 40 % - 20 %)

= $ 1. 68 per pound

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Based on the information provided, the passage that explains the citation is "The outcome...is situational irony..." (option A).

When you cite information from other sources or authors, there are three elements that should be included:

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The 5th , 6th and 7th term of the arithmetic sequence is 1 , 13/16 and 10/16 respectively

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Given data ,

Let the first term of the AP be a₁ = 1 3/4

Let the second term of the AP be a₂ = 1 9/16

So , the common difference of AP d = a₂ - a₁

On simplifying the equation , we get

The common difference d = 1 9/16 - 1 3/4 = ( 25/16 - 7/4 )

The common difference d = - ( 3/16 )

And , the nth term of the AP is a + (n - 1) d

So , the 5th term of the AP = ( 1 3/4 ) + ( 4 ) ( -3/16 )

On simplifying the equation , we get

The 5th term of the AP = ( 7/4 ) + ( -3/4 )

The 5th term of the AP = 4/4 = 1

Therefore , the value of A = 1

And , the 6th term of the AP = ( 1 3/4 ) + ( 5 ) ( -3/16 )

On simplifying the equation , we get

The 6th term of the AP = ( 7/4 ) + ( -15/16 )

The 6th term of the AP = 13/16

Therefore , the value of B = 13/16

And , the 7th term of the AP = ( 1 3/4 ) + ( 6 ) ( -3/16 )

On simplifying the equation , we get

The 7th term of the AP = ( 7/4 ) + ( -18/16 )

The 7th term of the AP = 10/16

Therefore , the value of C = 10/16

Hence , the arithmetic progression is solved

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Answer: To solve this expression, we first need to simplify the terms in the denominator:

5 1/3 - 4 2/3 + 1 1/6 x 2

We can convert each fraction to a mixed number:

5 1/3 = 5 + 1/3

4 2/3 = 4 + 2/3

1 1/6 x 2 = 2 x 1/6 + 2 = 2 + 1/3

Now we can perform the subtraction:

(5 + 1/3) - (4 + 2/3) + (2 + 1/3)

= 5 + 1/3 - 4 - 2/3 + 2 + 1/3

= 5 + 1/3 - 4 + 2 + 1/3 + 1/3

= 7

So the denominator simplifies to 7.

Next, we simplify the numerator:

8 - (2/3)^2

We can first square the fraction:

(2/3)^2 = 4/9

Now we can perform the subtraction:

8 - 4/9

= 8 - 4/9

= 8 x 9/9 - 4/9

= 72/9 - 4/9

= 68/9

So the numerator simplifies to 68/9.

Finally, we divide the numerator by the denominator:

68/9 ÷ 7 = 9.71

So, the expression simplifies to 9.71.

Step-by-step explanation:

P(B A)=P(B)

Step-by-step explanation:Given situation that two events occurred event A and event B event A has already occurredtherefore, there is no relationship between them event A and event B since, the probability of B does not depend on any activity of A therefore, P(B A)=P(B)

The probability that event B occurs, given that event A has already occurred is P(A) = P(A ∩ B) / P(B | A).

An event is the outcome of a chance experiment or a collection of similar outcomes.

As the sample space is a collection of all potential outcomes of a random experiment, it might be defined as every subset of that space.

When the event B is dependent on event A,

P(A ∩ B) ≠ P(A) x P(B)

When the event A comes before event B. So, the probability of B given A:

P(B | A) = P(A ∩ B) / P(A)

P(A) = P(A ∩ B) / P(B | A)

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Answer:

This is not math...

Step-by-step explanation:

Answer:

Step-by-step explanation:Angles 1 and 2 form a linear pair and are supplementary. So to find m∠2, subtract m∠1 from 180o. m∠2 = 180o - 135o = 45o.

...

Solution

m∠1 + 32 = 90 Substitute 32 for m∠2.

m∠1 = 58 Subtract 32 from each side.

m∠1 + m∠ 2 = 90 Definition of complementary angles.

In the trigonometry relation the value of θ is 45 degrees and the coterminal angle between 0° < θ < 360° is 315 degrees

Coterminal angles are angles that have the same terminal side in a given circle. They are angles that differ by a multiple of 360 degrees.

In other words, if two angles are coterminal, they have the same trigonometric functions, despite having different degrees.

If sec θ = √2

θ = arc sec (√2)

θ = arc cos (1/√2))

θ = 45 degrees

coterminal of angle 45 degrees between 0° < θ < 360°

360 - 45 = 315.

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The number of dots will be in each pattern in 4th step:

1. In pattern A: 16 dost

2. In pattern B: 18 dots

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

two patterns,

Pattern A:

number of dots,

step 0:  0

step 1: 4

step 2:  8

step 3:  12

So here it can be seen that,

4 dots are more in each step in compare with previous step,

So generalized expression can be written as:

Number of dots in nth step =  0 + 4n

In 4th step, there will be- 16 dots

Similarly, in Pattern B:

Number of dots in nth step = 2 + n²

In 4th step, there will be- 18 dots

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Answer:

As a fraction, the probability that a person picked at random from the group is a male or is fit to climb Mount Shasta is 12/100.

Step-by-step explanation:

Let the number of fit men is x.

Now,

we know

x = 12% of 200 men

x =  [tex]\frac{12}{100}[/tex]   ×200

x = 0.12 × 200

   = 24 men.

Given,

The 60 people are fit to climb the Mount Shasta ,24 of them are men,

so there must be

60 - 24 = 36 women who are fit to climb the mountain.

The probability of a person picked at random from the group is a male or is fit to climb Mount Shasta is the sum total of the probability of picking a fit male and the probability of picking a fit female is,

P(male or fit) = P(male and fit) + P(female and fit)

P(male or fit) = P(male) × P(fit | male) + P(female) × P(fit | female)

P(male or fit) = ([tex]\frac{200}{500}[/tex]) ×([tex]\frac{24}{200}[/tex]) + ([tex]\frac{300}{500}[/tex]) × ([tex]\frac{36}{300}[/tex])

                     =.4 × .12 + .6 × .12

                     = 0.048 + 0.072

                     =.12

So,

P(male or fit) ≈ 0.12

As a fraction, the probability that a person picked at random from the group is a male or is fit to climb Mount Shasta is 12/100.

The length of f to the nearest 10th of an inch is 308.8 inches.

A trigonometric rule known as the Law of Sines connects any triangle's sides and angles. It claims that for all three sides of a triangle, the ratio of the length of one side to the sine of the angle opposite that side is the same. To put it another way, we may write: If we have a triangle with sides a, b, and c, and opposing angles A, B, and C:

Sin(A) / a = b / a sin(B) / c / sin (C)

Using the Law of Sines we have:

f / sin(89°) = e / sin(27°)

f = sin(89°) * 310 / sin(27°)

f ≈ 308.8 inches

Hence, the length of f to the nearest 10th of an inch is 308.8 inches.

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Answer:

  613.7 in

Step-by-step explanation:

You want the length of side f in ∆EFG with e = 310 in, E = 27°, G = 89°.

The law of sines tells you ...

  f/sin(F) = e/sin(E)

Angle F is the third angle in the triangle, so its measure is ...

  F = 180° - 89° -27° = 64°

Then the length of f is ...

  f = e·sin(F)/sin(E) = (310 in)·sin(64°)/sin(27°) ≈ 613.7 in

The length of f is about 613.7 inches.

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if seven less than three times a number is negative one then the number is 2.

Two or more expressions with an Equal sign is called as Equation.

Let the number be x.

Seven less than three times a number is negative one.

We need to find the unknown number x from the given statement.

Less than we use when we use subtraction, times we use for multiplication.

seven less than three times a number is negative one.

3x-7=-1

Add 7 on both sides

3x=6

Divide both sides by 3

x=2

Hence, if seven less than three times a number is negative one then the number is 2.

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Answer:

Prepaid expenses are payments made in advance for goods or services that will be received or used in the future. These expenses are considered assets on a company's balance sheet because they provide future economic benefits. Examples of prepaid expenses include rent payments made in advance, insurance premiums, and prepaid service contracts. They are recorded as an asset on the company's balance sheet until the expense is incurred, at which point it is recognized as an expense on the income statement.

Step-by-step explanation: