Select each equation which is equivalent to 60% of 25.
0.6 • 25 = x
x • 1.6 = 25
610=x25
60100=25x
x25=60100
6.0 • 25 = x

By using arithmetic progression, it can be calculated that

The common difference is 12

Third option is correct

A series of numbers is called an arithmetic progression if the difference between each term in the sequence is the same.

If there is always the same difference between any two consecutive terms in a series of integers, then progression is known as an arithmetic progression. Simply put, it means that the previous number in the series is added to determine the next number in the series. A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms. One arithmetic progression with a common difference of 2 is the sequence 5, 7, 9, 11, 13, 15,...

This is a problem on arithmetic progression

[tex]a _1 = 5[/tex]

[tex]a_n = a_{n-1} + 12[/tex]

[tex]a_2 = a_1 + 12[/tex]

[tex]a_2 = 5 + 12 = 17[/tex]

[tex]a_3 = a_2 + 12 = 17 + 12 = 29[/tex]

[tex]a_4 = a_3 + 12 = 29 + 12 = 41[/tex]

[tex]a_2 -a_1 = 17 - 5 = 12\\a_3 - a_2 = 29 - 17 =12\\a_4 - a_3 = 41 - 29 =12[/tex]

So the common difference is 12

Third option is correct

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By using arithmetic progression, it can be calculated that, the common difference is 12.

Third option is correct

If the common difference between each term in the sequence is the same, a group of numbers is referred to as an arithmetic progression.

A progression is referred to as an arithmetic progression if there is consistently the common difference between any two successive terms in a series of integers. To put it simply, it indicates that the series' next number is produced by adding the previous one.

An arithmetic progression or arithmetic sequence, also known as AP, is a set of numbers where the terms are always different from one another. The numbers 5, 7, 9, 11, 13, and 15 make up one mathematical progression with a common difference of 2.

We know that the arithmetic progression, this is based on the same

[tex]\begin{aligned}& a_1=5 \\& a_n=a_{n-1}+12 \\& a_2=a_1+12 \\& a_2=5+12=17 \\& a_3=a_2+12=17+12=29 \\& a_4=a_3+12=29+12=41 \\& a_2-a_1=17-5=12 \\& a_3-a_2=29-17=12 \\& a_4-a_3=41-29=12\end{aligned}[/tex]

So the common difference is 12

Third option is correct

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Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

sin x= 12/ 13

So, B = √13² - 12² = √169 - 144 = √25 = 5

cos x= 5/ 13

So, sin 2x= 2 sin x cos x =2 (12/13)(5/13) = 120/169

and, cos 2x= 1- 2 sin²x

                  = 1- 2( 144 / 169)

                  = -119/ 169

and, tan 2x = sin 2x/ cos 2x = 120/ 169 / (- 119/ 169)= 120/ 119

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A table of values that models this situation is as follows;

Distance (miles)               Time (hour)

120                                          0

150                                          1

180                                          2

210                                          3

240                                          4

An equation for D in terms of t representing Elizabeth's distance from city A, t hours after leaving her house is d = 30t + 120.

Mathematically, a constant of proportionality (time) for Elizabeth's journey (distance) with respect to time can be represented with the following mathematical expression:

d = kt

Where:

Therefore, the required function that relates the distance (d) and speed (s) at t hours is given by;

d = 30t + 120

Next, we would develop a table of value;

At time (t) = 1 hour, we have;

Distance, d = 30(1) + 120

Distance, d = 150 miles.

At time (t) = 2 hours, we have;

Distance, d = 30(2) + 120

Distance, d = 180 miles.

At time (t) = 3 hours, we have;

Distance, d = 30(3) + 120

Distance, d = 210 miles.

At time (t) = 4 hours, we have;

Distance, d = 30(4) + 120

Distance, d = 240 miles.

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Olivia's quiz average must be 24.4 to achieve a 90 average in algebra.

To get the average for the quiz, we first evaluate for the sum of the test average and the homework average, and the subtract the result from 90 average in algebra.

the test average = (92/100) × 55

test average = 50.6

100% homework average implies Olivia got a homework average of 15

Let x be the quiz average, so that

x = 90 - (50.6 + 15)

x = 90 - 65.6

x = 24.4

Therefore, the quiz average of 24.4 is what Olivia needs to achieve a 99 average in algebra.

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It is Syllogism. It is an example of a type of reasoning where a conclusion is reached from two given or assumed propositions, each of which shares a term with the conclusion.

The Greek term "syllogismos," which means "conclusion, inference," is the source of the English word "syllogism." A logical argument employing assertions and deductive reasoning is known as a syllogism. The most important contribution to the topic of syllogisms is attributed to Aristotle. A major premise, a minor premise, and a conclusion make up a syllogism. One phrase from each of the premises and the conclusion are shared.

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(a) After 25 years 47.37g of the initial sample left in the sample. (b) 12.83 years takes  the initial sample to decay half of its original amount.

Given:

[tex]A(t) = 200 e^{-0.054t}[/tex]

Substituting 25 for t in the expression, we get:

A(25) = 200e⁰.⁰⁵⁴ × 25

         = 47.37 g

Thus, after 25 years, there will be 47.37g of the initial sample left in the sample.

(b.) 12.83 years takes the initial sample to decay half of its original amount.

We want to find t such that

[tex]A(t) = 200e^{0.054} \times t[/tex]

where, t = 100.

Solving for t, we get:

[tex]200e^{0.054} \times t = 100[/tex]

Dividing both sides by 200 and applying the natural logarithm to both sides, we get:

0.054 × t = ln(0.5)

Therefore,

[tex]t = \frac{\ln(0.5)}{0.054}[/tex]

  = 12.83 years.

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The total years taken to double the money according to Compounding will be 13.75 years.

What is compound interest?

Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.

Main body:

Given :

rate = 2%

amount = $1700

Total amount = $2200

Compounded monthly,

so formula becomes,

Total amount = amount (1+r/400)^4t

T = A([tex](1+r/400)^{4t[/tex]

2200 = 1700(1 +2/400)^4t

22/17 = (1 +1/200)^4t

22/17 = (1.005)^4t

1.29 = (1.005)^4t

taking log on both sides

0.11/0.002 = 4t

t = 13.75 years.

Hence the time taken to double the money is 13.75 years.

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Answer:

17 and 18 because they are equal

Answer: 4. -1/6, 5. 2/5

Step-by-step explanation:

1. The formula for slope is rise/run. To find the slope, you subtract the y coordinates (it doesnt matter the order, and you divide it by the difference of the x coordinates.

2. The y coordinates for 3 are 10 and 6, and the x coordinates are 0 and 24.

10-6/0-24 is 4/-24 which is -1/6.

3. you do the same thing for #4. The y coordinates are 6 and 14, and the x coordinates are 0 and 20. 14-6/20-0=slope. 8/20 is the slope, and that is equal to 2/5.

4. the slope for 3 is -1/6 and the slope for 4 is 2/5.

Using the formula of combination and the provided condition that any child can get any number of books, The answer is 637.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. We use permutation to determine how many possible ways we have to arrange items from a collection system.

The required formula is:

[tex]C(n,r) = \frac{n!}{r!(n-r)!}[/tex]

where, n= total number of objects in the set.

r= number of choosing objects from the set.

from the given data, total number of books = n= 5

number of children we need to distribute, r= 10

total possible ways of distribution= C(10,1)+C(10,2)+C(10,3)+C(10,4)+C(10,5)

=10+45+120+210+252

=637

hence, we have total 637 possible ways to distribute.

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To find out how far the seagull flew while the sailor was watching, you can use the following steps:

Calculate the total distance the seagull flew in 28 seconds. You can do this by multiplying the seagull's speed (11 meters per second) by the time it flew (28 seconds):

Distance = Speed * Time

= 11 meters/second * 28 seconds

= 308 meters

Calculate the time the sailor watched the seagull fly. You can do this by dividing the total time the seagull flew (28 seconds) by 4:

Time = 28 seconds / 4

= 7 seconds

Calculate the distance the seagull flew while the sailor was watching. You can do this by multiplying the seagull's speed (11 meters per second) by the time the sailor watched the seagull fly (7 seconds):

Distance = Speed * Time

= 11 meters/second * 7 seconds

= 77 meters

Therefore, the seagull flew 77 meters while the sailor was watching.

What are conditional problems?

Conditional problems are problems that involve determining the likelihood or probability of an event occurring under certain conditions. They often involve the use of probability and statistics to evaluate the likelihood of different outcomes or to make predictions about future events.

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Answer:

$345 (PLEASE GIVE BRAINLYEST )

Step-by-step explanation:

1/3x=115

x=345

y-intercept of given function is y = 1

How to graph the function?

The collection of ordered pairings with the (x,y). (x,y) sign is known as the graph of a function in mathematics, where  f(x)=y. x and  f(x) are Cartesian coordinates of points in two-dimensional space, and in the typical scenario where they are real numbers, they constitute a subset of this plane.

Given function , f(x) = 2· [tex]3^{x}[/tex]

Graph of the function is given below:

As the given graph is intersecting the y-axis at y=1 So, y-intercept of given function is y = 1

Therefore, y-intercept is y = 1

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Answer: 11

Step-by-step explanation:

we know that : ax² + bx + c = 0

then,

a = −1

b = −22

c = −121

putting the values in the following equation:

x=−b±√b²−4ac ⁄ 2a

=−(−22)±√(−22)²−4⌈(−1)(−121)⌉  ⁄  2(−1)

=22±√484−484  ⁄ −2

=22±√0  ⁄ −2

=22 ⁄ −2

=11 ⁄ −1

=11

Hence the answer for this equation will be 11.

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The perimeter of the rectangle can be expressed as 12x+2

The perimeter of a rectangle is the total distance covered by its boundaries or the sides. Since there are four sides of a rectangle, thus, the perimeter of the rectangle will be the sum of all four sides.

The perimeter of a rectangle is given as 2(l+w)

where l is the length and w is the width.

If the length is represented by 4x and width by 2x+1, therefore the perimeter of the rectangle = 2(4x+2x+1)

= 2( 6x+1)

= 12x+2

the perimeter can also be found by adding all the four sides, this means that

perimeter = 4x+4x+2x+1+2x+1=8x+4x+2= 12x+2

therefore the perimeter of the rectangle is 12x+2.

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Answer:

20π cubic units

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cylinder}\\\\$V=\pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]

Given:

Substitute the given values into the formula for the volume of a cylinder and solve for V:

[tex]\implies V=\pi \cdot 2^2 \cdot 5[/tex]

[tex]\implies V=\pi \cdot 4 \cdot 5[/tex]

[tex]\implies V=\pi \cdot 20[/tex]

[tex]\implies V=20\pi\;\; \sf cubic \;units[/tex]

Answer:

1. The denominator of a fraction represents the number of equal parts the whole is divided into.

2. The numerator of a fraction represents the number of parts being considered.

3. A fraction is in simplest form when the numerator and denominator have no common factors other than 1.

4. The denominator of a fraction must be greater than zero.

5. The numerator of a fraction must be greater than or equal to zero.

6. When two fractions have the same denominator, the fraction with the larger numerator is greater.

7. When two fractions have the same numerator, the fraction with the smaller denominator is greater.

8. To add and subtract fractions, the denominators must be the same.

9. To multiply fractions, multiply the numerators and denominators separately.

10. To divide fractions, invert the second fraction (flip the numerator and denominator) and then multiply.

Step-by-step explanation:

Answer:

For fractions to be added or subtracted, their denominators must match (the bottom value). It just requires adding or subtracting the numerators if the denominators are already equal (the top value). A common denominator must be determined if the denominators are dissimilar.

Step-by-step explanation:

I disagree with the student because y = x/9 represents a proportional relationship

Proportional relationships are relationships between two variables where their ratios are equivalent

A proportional relationship can we written as follows:-

y = mx

Where 'y' is dependent variable, 'x' is independent variable, and 'm' is the slope or we can say 'm' is constant of proportionality.

'm' can take any value whether negative or positive, decimal or whole number. 'm' is a real number.

The given problem is y = x/9 and student says we can only multiply constant, and not divide. We disagree with this comment because m= 1/9 is correct.

So y = 1/9 x makes sense.

Hence, y = x/9 represents a proportional relationship.

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After solving, the value of f^(-1)(g(7)) is 6.

In the given question, we have to find the f^(-1)(g(7)).

The given table of functions f and g is:

x          f(x)                   y          g(x)  

-3          1                     -2          -5

0          4                     1            -4

1           5                     5            2

6         -6                     7           -6

To find the value of f^(-1)(g(7)) we put the value of g(7) from the table. As we can see in the table that at the value of g(x) at point 7 is -6.

Then we find the value of from the table of f(x).

f^(-1)(g(7)) = f^(-1)(-6)

The value of f^(-1)(-6) from the table f(x) is

f^(-1)(g(7)) = 6

Hence, the value of f^(-1)(g(7)) is 6.

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The number of ways the 6 books can be arranged on the 4 shelves by Amanda is 360 ways

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

Total number of books, n = 6

Total number of shelves, r = 4

The number of ways the books could be arranged on the shelves is calculated using the following permutation formula

Total = ⁿPᵣ

Where

n = 6 and r = 4

Substitute the known values in the above equation, so, we have the following representation

Total = ⁶P₄

Apply the permutation formula

ⁿPᵣ = n!/(n - r)!

So, we have the following representation

Total = 6!/2!

Evaluate the quotient

Total = 360

Hence, the number of ways is 360

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Answer:

-3

Step-by-step explanation:

Combining like terms, [tex]x-3x=-2x[/tex]. Since this means the variable terms on both sides combine to have the same coefficient, this means there are no solutions (since the constant terms differ).

Answer:

C.) -3

Step-by-step explanation:

We're looking for an equation with NO SOLUTION.

A.) 5

-2x + 11 = x + 21 + 5x

x = -1.25.

A.)  is INCORRECT

B.) -2

-2x + 11 = x + 21 + (-2)x

x = -10

B.) is INCORRECT

C.) -3

-2x + 11 = x + 21 + (-3)x

No solution

C.) is CORRECT

D.) 2

-2x + 11 = x + 21 + 2x

x = (-2)

D.) is INCORRECT

The mean amount won based on the expectation formula of probability will be - 2/13.

The probability of an event occurring is defined by probability.

Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.

Probability of winning = 4/52 = 1/13

Probability of lossing = 1 - 1/13 = 12/13

The mean amount or expectation is given as,

E(X) = 10 × (1/13) + - 1(12/13)

E(X) = 10/13 - 12/13

E(X) = - 2/13

Hence "The mean amount won based on the expectation formula of probability will be - 2/13".

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The simplification of the given expression on the basis of identity is given as  144 - 24y +  y².

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given expression is (12 - y)².

It can be expanded on the basis of the algebraic identity (a - b)² = a² - 2ab + b² as follows,

(12 - y)²

= 12²- 2×12y + y²

= 144 - 24y +  y²

Hence, the given expression can be simplified as 144 - 24y +  y².

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Relationship to the line y=3/4x and its equation is line B.

What is an equation ?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

y = mx+c

y = 3/4x [which shows that the line B as the points]

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The slope of the line given in the graph will be [m] is  - 0.78.

The general equation of a straight line is -

y = mx + c

Where -

[m] is the slope of the line.

[c] is the y - intercept.

Given is the graph of a straight line.

The line passes through the coordinates as follows -

(- 1.8, 0)        [lying on x-axis]

(0, - 1.4)        [lying on y-axis]

The slope of the line can be calculated using the formula -

m = (y₂ - y₁)/(x₂ - x₁)

m = (- 1.4 - 0)/(0 + 1.8)

m = - 1.4/1.8

m = - 0.78

Slope of the line will be -0.78.

Therefore, the slope of the line given in the graph will be [m] = - 0.78.

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Answer:

To solve this problem, we can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side of a right triangle. Since the angle formed by the ladder and the ground is 72 degrees, we can consider the horizontal distance between the base of the ladder and the wall to be the adjacent side of the right triangle, and the height of the ladder to be the opposite side.

We can set up the following equation to represent this relationship:

tan(72^{\circ}) = opposite/adjacent

Substituting the values given in the problem, we get:

tan(72^{\circ}) = 26 feet / adjacent

To find the value of the adjacent side, we can solve for "adjacent" in the equation above. We can do this by dividing both sides of the equation by 26 feet and then taking the inverse tangent (tan^(-1)) of both sides:

adjacent = 26 feet / tan(72^{\circ})

Using a calculator or a table of tangent values, we can find that the value of tan(72^{\circ}) is approximately 3.73. Substituting this value into the equation above, we get:

adjacent = 26 feet / 3.73

Solving this equation, we find that the horizontal distance between the base of the ladder and the wall is approximately 6.99 feet. Rounding this value to the nearest hundredth of a foot, we get an answer of approximately 6.99 feet.

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Answer: 8.03

Step-by-step explanation:

The resulting expression after the expressions are subtracted is 9x - 6y

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

(-x-3y)(−x−3y) is subtracted from (8x-9y)(8x−9y)

Rewrite these expressions properly

So, we have the following representations

(−x−3y) is subtracted from (8x-9y)

When the first equation is subtracted from the second, we have the following representation

8x - 9y - (-x - 3y)

Open the brackets

So, we have

8x - 9y + x + 3y

Evaluate the like terms

9x - 6y

Hence. the solution is 9x - 6y

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The area of the rectangle training field is 4264 m².

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

We know the area of a rectangle is (length×width).

So, The area of the rectangle 82m long and 52m wide is,

= (82×52) m².

= 4264 m².

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Answer:

Step-by-step explanation: