write each fraction in simplest form. if the fraction is already in simplest form, write simplified


A.
[tex] \ \frac{4}{14} [/tex]
B.
[tex] \frac{15}{20} [/tex]
C.
[tex] \frac{21}{35} [/tex]

Final answer:

The original fraction, based on the provided conditions, is found to be 3/8 by setting up an equation relative to the changes described and solving for the unknown numerator and denominator.

Explanation:

The question involves solving for the numerator and denominator of a fraction based on provided conditions. Let's denote the denominator as x and the numerator as x - 5, since the numerator is 5 less than the denominator. According to the given conditions, when the numerator is multiplied by 2 and the denominator is increased by 16, the fraction becomes smaller by 1/3 of its original value.

Original fraction: [tex]\(\frac{x - 5}{x}\)[/tex]. After the modifications: [tex]\(\frac{2(x - 5)}{x + 16}\)[/tex]. The condition that the fraction becomes smaller by 1/3 of its original value leads to the equation: [tex]\(\frac{x - 5}{x} - \frac{1}{3} \cdot \frac{x - 5}{x} = \frac{2(x - 5)}{x + 16}\)[/tex].

Simplifying this equation, we first express the reduced original fraction as [tex]\(\frac{2(x - 5)}{3x}\)[/tex]. Then, setting it equal to the modified fraction, we get[tex]\(\frac{2(x - 5)}{3x} = \frac{2(x - 5)}{x + 16}\)[/tex]. Canceling out [tex]\(2(x - 5)\)[/tex] from both sides and solving for x, we find that x = 8. Therefore, the original denominator is 8, and the numerator is 3, making the original fraction 3/8.

The equation of the circle that you are looking for is x^2 + y^2 = 100.

You can find this by using the base formula for a circle:

(x - x1)^2 + (y - y1)^2 = r^2

In which x1 is the x-coordinate of the origin, y1 is the y-coordinate of the origin, and r is the radius. So we put in the values we know and simplify.

(x -0)^2 + (y - 0)^2 = 10^2

x^2 + y^2 = 100

The equation of a circle centered at the origin such that the length of its radius is 10 units will be x² + y² = 100.

Circle is a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center).

Given is a circle is centered at the origin, and the length of its radius is 10 units.

The equation of the circle whose center is at origin is given by -

x² + y² = r²

We have radius [r] = 10 units

Therefore, we can write the equation of the circle as -

x² + y² = 10 x 10

x² + y² = 100

Therefore, the equation of a circle centered at the origin such that the length of its radius is 10 units will be x² + y² = 100.

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Answer:

D. -1

Step-by-step explanation:

All the variable terms are on the left, so subtract the constant on the left (5) from the equation and collect terms.

... 4t = -4 . . . . . . . variable term on one side; constant term on the other

Divide by the coefficient of t.

... t = -1

Answer:the answer is C. collision

Step-by-step explanation:

Given is the price increase of a ticket from 50p to 60p.

Using the concept of fractions, we can find the ratio of new price to old price as follows :-

[tex] \frac{new \;\; price}{old \;\; price} = \frac{60p}{50p} =\frac{6}{5} [/tex]

So the increase in price is [tex] \frac{6}{5} [/tex] times old price of the ticket.

Using the formula of percentage, we can find the percentage change in price as follows :-

[tex] Percentage = \frac{(new\;\;price \;-\; old\;\;price) }{old \;\; price}*100 \\\\
Percentage = \frac{60p-50p}{50p}*100 \\\\
Percentage = \frac{10p}{50p}*100 \\\\
Percentage = 20\;\% [/tex]

Hence, Percentage increase is 20% of the original price.

The family's weekly income is $1500.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

given that,

A Family spends 240.00 per week on food. If this is 16% of their income.

let,

x = weekly income (in dollars)

16% of x = amount spent on food per week

16% of x = 240

(16/100)*x = 240

0.16*x = 240

0.16*x/0.16 = 240/0.16

x = 1500

Hence, The family's weekly income is $1500.

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Answer:

  24

Step-by-step explanation:

The given age relationships can be used to reason about their ages.

__

When Holly was 4 times Spencer's age, the difference in their ages was 4-1=3 times Spencer's age. That is, Spencer was 51/3 = 17 years old, and Holly was 68.

That was 7 years ago, so Spencer is now 17+7 = 24 years old.

The median number of jumps that the student made before missing is calculated as: C. 33.5.

Median is the middle value or the average of the two center values of a data set.

Given the data set:

2, 5, 6, 7, 9, 11, 12, 14, 14, 15, 17, 19, 21, 22, 23, 24, 27, 32, 35, 39, 39, 44, 47, 53, 60, 61, 82, 85, 88, 90, 93, 96, 101, 103, 114, 125

The average of the two center values is: (32+35)/2 = 33.5

Therefore, the median number of jumps is: C. 33.5.

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The square, rectangle, and rhombus are all considered parallelograms. Squares have four sides, four 90 degree angles, 2 pairs of opposite congruent angles (all the angles are congruent), the angles add up to a sum of 360 degrees. Rectangles have four sides, four 90 degree angles that add up to 360 degrees, 2 pairs of opposite congruent angles (all the angles are congruent). Rhombuses have four sides, four angles in total measuring up to 360 degrees no matter the combination of angles because the oposite angles are congruent (2 acute angles and two obtuse angles).

While the rhombus is the only shape within this trio to have a pair of congruent acute and a pair of congruent obtuse angles the square and rectangle both have 4 congruent angles. All 3 shapes have a sum of 360 degrees when the angles are added together, all 3 have pairs of opposite angles being congruent, and all 3 shapes have 4 angles in total.

Answer:

The first graph, so A is the answer

Step-by-step explanation:

The probability that a randomly chosen student like at least two of the three styles of music will be 0.21.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences. Then the probability is given as,

P = (Favorable event) / (Total event)

A school radio station polled 500 students to find out what kind of music they appreciate. According to the study, 207 people prefer rock, 172 prefer country, and 126 choose jazz. Furthermore, 33 like rock and country, 27 prefer rock and jazz, 32 prefer country and jazz, and 13 prefer all three forms of music.

The number of favorable events is given as,

Favorable events = 33 + 27 + 32 + 17

Favorable events = 105

Then the probability is given as,

P = 105 / 500

P = 0.21

P = 21%

The probability that a randomly chosen student like at least two of the three styles of music will be 0.21.

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The expression simplifies to approximately -20.822. It involves multiplying -3.64 by the absolute value of -5.3 and then subtracting 1.53 from the result.

To calculate this expression, follow the order of operations (PEMDAS),

which stands for Parentheses, Exponents, Multiplication and Division (left-to-right), and Addition and Subtraction (left-to-right).

In expression, there are no parentheses or exponents, so we proceed with multiplication and then subtraction:

-3.64 × |-5.3| - 1.53

Calculate the absolute value of -5.3, which is 5.3.

Multiply -3.64 by 5.3.

Finally, subtract 1.53 from the result.

-3.64 × 5.3 - 1.53

Now, do the multiplication:

-19.292 - 1.53

Now, subtract:

-19.292 - 1.53 = -20.822

Therefore, the answer for the given expression -3.64 × |-5.3| - 1.53 is approximately -20.822.

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The equation of plane with normal vector n = (1, 3, 4) passing through the point (4, −1, 3) in the scalar form is;

⇒ x + 3y + 4z = 13

What is Equation of plane?

A equation of plane containing the point (x₁ , y₁ , z₁) and having a normal vector (a, b, c) is defined as;

⇒ a (x - x₁) + b (y - y₁) + c (z - z₁) = 0

Given that;

The normal vector n = (1, 3, 4)

And, The point = (4, −1, 3)

Now,

Since, we know that;

A equation of plane containing the point (x₁ , y₁ , z₁) and having a normal vector (a, b, c) is defined as;

⇒ a (x - x₁) + b (y - y₁) + c (z - z₁) = 0

So, We get;

A equation of plane containing the point (4, −1, 3) and having a normal vector (1, 3, 4) is defined as;

⇒ a (x - x₁) + b (y - y₁) + c (z - z₁) = 0

⇒ 1 (x - 4) + 3 (y - (-1)) + 4 (z - 3) = 0

⇒ x - 4 + 3y + 3 + 4z - 12 = 0

⇒ x + 3y + 4z = 13

Thus, The equation of plane with normal vector n = (1, 3, 4) passing through the point (4, −1, 3) in the scalar form is;

⇒ x + 3y + 4z = 13

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