Find the value of X given that the triangles are similar

There are approximately 3263 total albums and CDs are in the collection.

Percentage is defined as part of a whole expressed in hundredths or out of 100. It is usually written with the symbol "%".

let 'x' be the total albums and CDs in the collection

If the music fan has 2000 CDs, which comprise 61.3% of the total collection, then 61.3% of x is equal to 2000.

2000 albums and CDs = 61.3% of the total albums and CDs in the collection

2000 = 61.3% of x

2000 = 0.613x

Solving for x,

x = 3262.6

the total albums and CDs in the collection ≅ 3263

Therefore, the the total albums and CDs in the collection is approximately 3263.

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The inequalities that represent Chocolate and Saffron in a gift bag are

x + 2y<7 and x + y <5.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given, To'ak Chocolate is the rarest chocolate in the world with a cost of $5 per gram. Saffron is a spice used for flavoring and coloring foods and costs $10 per gram.

Let x be the number of grams of chocolate and y be the number of grams of saffron

Hence,

Cost of chocolate = 5x

Cost of spices = 10y

Also given She has to keep the cost to less than $35

Thus, the Linear equation

5x + 10y < 35

Divide by 5 into both sides

x = 2y < 7

Also given, A party planner for a celebrity event wants to include no more than 5 grams (g) of To'ak Chocolate and Saffron in a gift bag.

Thus, x + y < 5

therefore, The inequalities x + 2y < 7 and x + y < 5 depict the combination of chocolate and saffron in a gift bag.

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Complete question:

To'ak Chocolate is the rarest chocolate in the world with a cost of $5 per gram. Saffron is a spice used for flavoring and coloring foods and costs $10 per gram. A party planner for a celebrity event wants to include no more than 5 grams (g) of To'ak Chocolate and Saffron in a gift bag. She has to keep the cost to less than $35. Write a system of inequalities where x is the number of grams of To’ak Chocolate and y is the number of grams of Saffron in each gift bag.

Area = 12√3

An equilateral triangle is a triangle that has all its sides equal in length. Since the three sides are equal therefore the three angles, opposite to the equal sides, are equal in measure. Therefore, it is also called an equiangular triangle, where each angle measure 60 degrees.

Given,

Length of apothem of equilateral triangle  = 2

It is an equilateral triangle made up of six 30°-60°-90°  right triangles with the short leg of 2 units.

2 is the altitude of small triangles

tan 30° = altitude/base

1/√3 = 2/base

base = 2√3

Area of the equilateral triangle

= 6 × area of the small triangles

= 6 ×1/2 × altitude × base

= 3 × 2 × 2√3

= 12√3

Hence the area of equilateral triangle becomes = 12√3

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Answer: B. 128a⁶b¹³

Step-by-step explanation:

The area of the rectangle with the dimensions shown below represents :

[tex](2a^2b)^3*(4b^5)^2=\\\\2^3a^{2*3}b^3*4^2b^{5*2}=\\\\8a^6b^3*16b^{10}=\\\\(8*16)a^6b^{3+10}=\\\\128a^6b^{13}[/tex]

The total number that can be formed by the numbers 1,2,3,4,5 (without repeating digits) is 120.

Now, half of the unit's digit will be bigger than the ten's digit and in half of them it will be smaller.

Example: Let's say we have three digits 1,2,3. Total number of numbers without repeating digits = 3*2*1=6

Numbers with the Unit's digit greater than the ten's digit

123, 213, 312

Numbers with Ten's digits greater than the unit's digit

321, 132, 231

So total Number of cases = 120/2 = 60

Thus, the Total Number which can be formed by numbers 1,2,3,4,5 (without repeating digits) = 5*4*3*2*! = 5! = 120.

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As per the combination method, the number for formation from the digits 12345 is 120 without repetition.

The term combination method in math is defined as  a way of selecting items from a collection where the order of selection does not matter.

Here we have given the digits as 12345.

Here we have calculated the total Number of Numbers which can be formed by numbers 1,2,3,4,5 without repeating digits is written as

=> 5 x 4 x 3 x 2 x 1

Which is also equal to,

=> 5! = 120.

While we looking into the set we have identified that in half them unit's digit will be bigger than the ten's digit and in half of them it will be smaller.

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Answer:

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by 2 gives the next term.

Step-by-step explanation:

Answer:

  x = -1

Step-by-step explanation:

You want the solution to the equation -4(3x+2) = 4.

First of all, we can divide by -4.

  3x +2 = -1

Subtracting 2 gives ...

  3x = -3

Finally, dividing by 3, we have the solution:

  x = -1

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The speed of yellow car has a higher speed. Then the yellow car has more momentum.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The equation of the momentum is written as,

P = mv

Where 'm' is the mass and 'v' be the velocity.

On the motorway, two similar vehicles of various colors may be seen. The yellow automobile is traveling at 70 mph while the green vehicle is moving at 50 mph.

Let the mass of the bodies be the same.

The speed of yellow car has a higher speed. Then the yellow car has more momentum.

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Answer:

Below

Step-by-step explanation:

x = third part

5/9 x    + 5/9 x  + x   = 114    <=======given

19/9  x = 114

x = 114 * 9/19 = 54 cm      then the other two are 30 cm each

Answer:

The two equal parts are 30 cm, the third part is 54 cm

Step-by-step explanation:

x =  third part

(5/9)x + (5/9)x + x = 114

10/9(x) + x = 114

(19/9)x = 114

x = 114(9/19) = 54

(5/9)54 = 30

The precentile for a student in the class who studies 8 hours a week is 5.74%.

To find the percentile for a student who studies 8 hours a week, we need to first standardize the student's study time by subtracting the mean study time and dividing it by the standard deviation of study time. This will give us the student's z-score. We can then look up the student's z-score in a standard normal table to find the percentile.

The student's z-score is (8 - 9.92) / 4.54 = -1.67.

Looking up -1.67 in a standard normal table, we find that the percentile is about 5.74%. This means that about 5.74% of the students in the class studied for less than 8 hours per week.

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As per the given standard deviation, the percentile for a student in the class who studies 8 hours a week is 50.80%

The term standard deviation in math is known as a measure which shows how much variation from the mean exists.

Here we have given that in one statistics course students reported studying an average of 9.92 hours a week with a standard deviation of 4.54.

Through this details, we have identified that the value of the following are given that,

=> weekly study time = 10 hours

=> average study time = 9.92 hours

=> standard deviation = 4.54 hours

Then the formula to calculate the Test statistic is written as

=> z = (weekly study time - average study time)/standard deviation

Apply the values on it, then we get

=> z = (10 - 9.92)/4.54

=> z = 0.08/4.54 = 0.02

While we take the value of z table, then we get the Cumulative area of the test statistic is 0.5080.

And the percentile is calculated by multiply the value by 100 as,

=> 0.5080 × 100 = 50.80

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Answer:

Step-by-step explanation:

(-5,7)

The number of solutions the system have is 2. They will meet in 5 hours.

For that , we will try solving it first using the method of substitution in which we express one variable in other variable's form and then you can substitute this value in other equation to get linear equation in one variable.

If there comes a = a situation for any a, then there are infinite solutions.

If there comes wrong equality, say for example, 3=2, then there are no solutions, else there is one unique solution to the given system of equations.

Matt drives at a rate of 40 miles per hour. Matt drives 50 miles before Kylie begins traveling.

So the total distance for Matt is given by;

M(t)= 40t+50

Kylie drives at a rate of 50 miles per hour.

When he starts(at position 0), Matt will be already at 50. So Kylie's equation is given by:

K(t)= 50t

To find out how many hours until they meet?

K(t)= M(t)

So, 50t= 40t+50

10t= 50

t=5

Therefore the answer of the equation will be 2.

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By using the bubble sort algorithm, a total of 9 passes/scans will be there.

When an array or list of items has to be rearranged, a sorting algorithm is used to compare the elements and sort the elements in the array or list. In each data structure, the new order of the items is determined using the comparison operator.

The simplest sorting method is called Bubble Sort, and it involves periodically exchanging nearby components if they are arranged incorrectly. Since the average and worst-case time complexity of this approach is relatively high, it is not appropriate for huge data sets.

According to the question, we have

Total number of elements we are having, i.e., n = 10

The total number of passes = n-1 = 10 - 1 = 9

(Number of passes required by bubble sort of n elements will be n-1)

therefore, the total number of passes/scans will be 9

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The claim might be considered to be inaccurate because Joseph's actual average quiz grade for math is 85

When given a set of numbers of variables, the average variable can be found by dividing the sum of the variables by the number of variables in the set.

For Joseph therefore, the average of the quiz grades that he has from his math quizzes would be :
= ( 81 + 89 + 80 + 84 + 89 + 85 ) / 6

= 508 / 6

= 84. 6

= 85

This shows that Joseph's claim of an average of 89 in his math quizzes is therefore inaccurate.

Most likely, what Joseph thought he meant was that the mode of his math quizzes was 89 as the mode refers to the variable that appears the most in a set.

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On solving the provided question, we can say that the value of the ellipse from give data will be = 4/9 + 9/36 = OD. (-2,4±3√3)

In mathematics, an ellipse is a planar curve that encompasses two focus points and ensures that the sum of the two distances from any point on the curve to the focal points is constant. In doing so, the circle—a particular variety of ellipse with two equal focus points—is generalized. The ellipse, whose eccentricity is less than 1, indicates the area containing the points whose distances from its two foci add up to a certain amount. Running tracks in sporting arenas and 2D egg forms are two straightforward examples of ellipses in daily life.

[tex](x+2)^2/9 + (y-4)^2/ 36 = 1[/tex]

x = 0 and y = 1

4/9 + 9/36

OD. (-2,4±3√3)

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Answer:

Step-by-step explanation:

the answer is 162 I now this because I took the quiz and got a 100% just for that answer so I hope this is helpful

Answer:

You can do it by dividing 18 by 9 and you would get 2.

ANSWER: 2

C is the most accurate one i guess

Assuming no denominator equals zero, b^4/a expression is equivalent to the given expression a^3b^5/ a^4b

Definition of Expression in Math? An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

The applicable rules of exponents are ...

 (a^b)/(a^c) = a^(b-c)

 a^-b = 1/a^b

The expression can be rewritten as ...

a^3b^5/ a^4b

The expression can be rewritten as ...

b^4/a

complete question

Assuming no denominator equals zero, which expression is equivalent to the given expression?.

a^3b^5/ a^4b

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Answer:

6.45 kg

Step-by-step explanation:

250 g is equal to 0.25 kg, so the pumpkin weighs [tex]2+0.25=2.25[/tex] kg.

Thus, the combined weight is [tex]2.25+4.2=6.45[/tex] kg.

Answer:

[tex]P(x)=x^5+10x^4+75x^3+10x^2+74x[/tex]

Step-by-step explanation:

Given information:

For any complex number  [tex]z=a+bi[/tex], the complex conjugate of the number is defined as  [tex]z^*=a-bi[/tex].  

If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.

Therefore, if P(x) is a polynomial, and i is a root of f(x)=0, then its complex conjugate -i is also a root of P(x)=0.

Similarly, if P(x) is a polynomial, and -5+7i is a root of f(x)=0, then its complex conjugate -5-7i is also a root of P(x)=0.

Therefore, the polynomial in factored form is:

[tex]P(x)=x(x-i)(x-(-i))(x-(-5+7i))(x-(-5-7i))[/tex]

[tex]P(x)=x(x-i)(x+i)(x+5-7i)(x+5+7i)[/tex]

Expand the polynomial:

[tex]P(x)=x(x^2-i^2)(x^2+10x+25-49i^2)[/tex]

[tex]P(x)=x(x^2-(-1))(x^2+10x+25-49(-1))[/tex]

[tex]P(x)=x(x^2+1)(x^2+10x+74)[/tex]

[tex]P(x)=x(x^4+10x^3+75x^2+10x+74)[/tex]

[tex]P(x)=x^5+10x^4+75x^3+10x^2+74x[/tex]

Answer:

$29.88

Step-by-step explanation:

We first would need to figure out what 20% of $37.35 is.

0.2 (or 0.20) × 37.35 = 7.47

This means that the discount price is $7.47

Now subtract that from the total.

37.35 - 7.47 = 29.88

Therefore, his total in dollars and cents after the discount and before tax is twenty-nine dollars and eighty-eight cents.

The probability that the sweet is yellow will be;

⇒ 9 / 25

The term probability refers to the likelihood of an event occurring.

Given that;

There are 25 sweets in a jar.

And, 9 of the sweets are yellow.

Now,

Since, Jamie takes at random a sweet from the jar.

Hence, The probability that the sweet is yellow = 9/25

                                                                          = 0.36

Thus, The probability that the sweet is yellow = 0.36

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Answer:

sinθ = -3/5, Quadrant IV (Option B)

Step-by-step explanation:

Let's first find the sine

cosθ = adj./hyp.

Pythagorean theorem (in terms of right triangle trig) = (opp)^2 + (adj)^2 = (hyp)^2

Plug in the adjacent and hypotenuse

(opp.)^2 + 16 = 25

solve for the opposite side

opp. = 3

To find the quadrant, recall the sin <0, so the sin has to be negative.

So, your sine value is -3/5.

Sine is negative at Quadrants III and IV, so eliminate C and D.

Since your cosine value is positive, it is at Quadrant IV (Cosine is positive at the first and fourth quadrants.)

Therefore, Option B is correct.

The distance between the ball and pole is divided by the time taken to travel that distance to calculate the rate of shadow travel, which is 80 fps.

The shadow of the ball is moving at a rate of 80 feet per second (fps). This can be calculated as follows:

Distance Fallen = 16t^2

Distance Fallen in 0.5 Seconds

= 16(0.5)^2

= 4 feet

Distance Between Ball and Pole

= 50 feet - 4 feet

= 46 feet

Time Taken To Travel Distance

= 0.5 Seconds

Rate of Travel = 46/0.5

= 80 fps

The shadow of the ball is moving at a rate of 80 fps. This is calculated by taking the distance between the ball and pole (50 feet-4 feet=46 feet) and dividing it by the time taken to travel that distance (0.5 seconds). This results in 80 fps.

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Answer:

y + 4 = - [tex]\frac{5}{6}[/tex] (x - 8)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = - [tex]\frac{5}{6}[/tex] and (a, b ) = (8, - 4 ), that is a = 8, b = - 4 , then

y - (- 4) = - [tex]\frac{5}{6}[/tex] (x - 8) , that is

y + 4 = - [tex]\frac{5}{6}[/tex] (x - 8)

Answer:

The numbers are: 3, 4, 5, 6, 7, 8, 9

Step-by-step explanation:

Natural Numbers are whole number from 0 to infinty. If you were to find all blow 10 but greater than 2 you would have 3, 4, 5, 6, 7, 8, 9

Hope This Helped!

[tex]\sqrt{x^5}\cdot \sqrt{x^{10}}\implies \sqrt{x^5\cdot x^{10}}\implies \sqrt{x^{5+10}}\implies \sqrt{x^{15}}\implies \sqrt{x^{14+1}} \\\\\\ \sqrt{x^{14}\cdot x^1}\implies \sqrt{x^{7\cdot 2} x}\implies \sqrt{(x^7)^2 x}\implies x^7\sqrt{x}[/tex]

The popular vote, which determines the winner of a presidential election, is simply the total number of voters from all 50 states. The popular vote is deemed to have been won by the candidate with the most votes cast nationally.

Every four years on the first Tuesday in November, the US holds its presidential election. The candidate must have at least 35 years of age, have been born in the US, and have resided in the US for the previous 14 years in order to be eligible.

Traditionally, candidates announce their intention to run for president one year prior to the election. Since there is no national body that organises elections, local authorities organise them with the aid of tens of thousands of administrators.

On January 20, the United States Capitol in Washington, D.C., will host Inauguration Day. The Vice President is sworn in first, then the President.

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