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Lesson is solving rational equations and inequalities

The fraction of the 30 cakes does Simon have left with os 7/10

A fraction is a part of a whole number, and a way to split up a number into equal parts.

Given that, Simon makes 30 cakes, he gives 1/5 of the cakes to Sali, he gives 10% of the 30 cakes to Jane,

We need to find, what fraction of the 30 cakes does Simon have left,

Number of cakes given to Sali = 1/5 of 30

= 30 / 5 = 6

That mean, Sali got 6 cakes out of 30.

Number of cakes given to Jane = 10% of 30

= 30 × 10/100

= 300 / 100

= 3

That mean, Jane got 3 cakes, out of 30.

The remaining number of cake = 30 - (6+3)

= 30 - 9

= 21

Therefore, the fraction of cakes left = 21 / 30

= 7/10

Hence, the fraction of the 30 cakes does Simon have left with os 7/10

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The value of the expression for the condition is 15.

A statement, at least two variables or integers, and one or more arithmetic operations make up a mathematical expression. This mathematical procedure makes it possible to multiply, divide, add, or subtract quantities. The expression structure is as follows:

(Number/Variable, Math Operator, Math Operator) is an expression.

Given the expression,

a + ab and a = 5, b = 2

substitute the values of a and b in the expression we get,

a + ab = 5 + (5)(2)

multiply 5 and 2 we get 10

a + ab  = 5 + 10

a + ab  = 15

Hence the value is 15.

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Answer:

Target is selling the iPad Pro for $1,175.93.

Step-by-step explanation:

Multiply $1099 by the perecntage. (Shift decimal 2 places to the left)

1099 × .07 = 76.93

Add 76.93 to 1,099.

1,175.93

Answer:

Sofia has a total of 7 cups + 1 cup = 8 cups of paint.

The proportion of red paint to the total amount of paint is 1 cup / 8 cups = 1/8.

So the fraction representing the proportion of red paint out of the total amount of paint is 1/8.

Answer: 1/8

Step-by-step explanation:

She uses 8 cups of paint and one of those 8 cups is red so it would be 1 red cup out of 8 cups or 1/8

If Normally Distributed data set a mean of 55 where 99.7% of the data fall between 47.5 and 62.5, then the standard deviation of data set is (c) 2.5  .

The Standard Deviation can be calculated using the empirical rule, also known as the 68-95-99.7 rule, which states that for a normal distribution:

⇒ 68% of data falls within one standard deviation of mean

⇒ 95% of data falls within two standard deviations of mean

⇒ 99.7% of data falls within three standard deviations of mean

Since 99.7% of the data falls within 3 standard deviations of the mean, we can use this information to solve for the standard deviation.

Let's call the standard deviation "σ".

that means ; μ + 3σ = 62.6   ;   μ - 3σ = 47.4

on solving the above two equations  ,the standard deviation is

⇒ 6σ = 62.6 - 47.4  

⇒ 6σ = 15.2  ⇒ σ = 2.5   .

The given question is incomplete , the complete question is

In a normally distributed data set a mean of 55 where 99.7% of the data fall between 47.5 and 62.5, what would be the standard deviation of that data set ?

(a) 5.0

(b) 7.5

(c) 2.5

(d) 5.7

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The height of the cylinder is 3 and its base is a circular disk with radius 1.

The solid of revolution obtained by revolving the region bounded by the curves y = x - 1, y = 0, and x = 3 about the x-axis is a cylinder.

The curves y = x - 1 and y = 0 bound a triangular region in the xy-plane with vertices (0, -1), (3, 0), and (1, 0). When this region is revolved about the x-axis, it generates a cylinder with height 3 and base a circular disk with radius 1.

A cylinder has traditionally been a three-dimensional solid, one of the most normal of curvilinear geometric shapes.

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The two real number solutions to a quadratic equation are rational numbers, then the discriminant is a rational number.

The discriminant of a quadratic equation is a scalar value that describes the nature of the solutions to the equation. Specifically, if the discriminant of a quadratic equation of the form [tex]ax^{2} + bx + c = 0[/tex] is a positive value, then the equation has two real solutions.

This is because the discriminant is given by the expression [tex]b^2 - 4ac[/tex], and the coefficients of a quadratic equation can be either rational or irrational numbers. If the coefficients are rational, then the discriminant will also be rational, and vice versa.

Hence, if the two real number solutions to a quadratic equation are rational numbers, then the discriminant is a rational number.

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Answer: I need a picture of reference? I can't give a logical answer.

Step-by-step explanation:

Answer:

To find the missing side length of two similar rectangles, you can use the proportion of corresponding sides. This means that the ratio of the two longer sides should equal the ratio of the two shorter sides. Therefore, you can solve for the missing side length by setting up a proportion between the known side lengths.

Step-by-step explanation:

The inverse function of the given function is

              f ⁻¹(x)  = x³ + 15x² + 75x + 123

What are inverse functions?

A function that can reverse into another function is known as an inverse function or anti-function. In other words, the inverse of a function f will take y to x if any function f takes x to y. When a function is written as f or F, its inverse is written as f⁻¹ or F⁻¹.

The given function is ∛(x+2) - 5

One of the properties of the inverse function is

f( f ⁻¹ x) = x

We utilise this property to find f ⁻¹ x.

f(x) = ∛(x+2) - 5

f( f ⁻¹x) = ∛( f ⁻¹(x) + 2) - 5

Using the above property

x = ∛( f ⁻¹(x) + 2) - 5

x + 5 = ∛( f ⁻¹(x) + 2)

Cubing both sides,

(x+5)³ =  f ⁻¹(x) + 2

x³ + 15x² + 75x + 125 = f ⁻¹(x)  + 2

f ⁻¹(x)  = x³ + 15x² + 75x + 123

Therefore the inverse function of the given function is

              f ⁻¹(x)  = x³ + 15x² + 75x + 123

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The sample space S of problem 3a is given by the set of all possible outcomes when drawing two balls from a bag containing two red and two green balls.

a. obtaining the same number on both draws:

The event of obtaining the same number on both draws is given by the set {(2,2), (1,1)}. This set is a subset of the sample space S.

b. obtaining a sum of numbers equal to seven:

The event of obtaining a sum of numbers equal to seven is given by the set {(2,5), (5,2)}. This set is a subset of the sample space S.

c. obtaining at least one three:

The event of obtaining at least one three is given by the set {(2,3), (3,2), (3,3)}. This set is a subset of the sample space S.

d. obtaining exactly one red ball:

The event of obtaining exactly one red ball is given by the set {(2,1), (1,2)}. This set is a subset of the sample space S.

e. obtaining the same colour on both draws:

The event of obtaining the same colour on both draws is given by the set {(1,1), (2,2)}. This set is a subset of the sample space S.

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There probability are 120 unique ways for the 5 friends to sit in the row of 6 seats.

The group of 5 friends has 120 unique ways to sit in the row of 6 seats. This is because for each seat in the row, the group has 5 different options for who will sit in it. Additionally, for each option there are 4 more options for the remaining 4 friends. This means the group has 5x4x4x4x4 or 5x4^4 possible combinations, which is 120. To calculate this, it is helpful to think of the row of 6 seats as 6 boxes and the 5 friends as 5 balls. For each box, there is a choice of 5 different balls and for each ball there is a choice of 4 different boxes. This is why the total number of combinations is 5x4^4.  The friends may not be able to sit in the same combination twice, so it's important for them to find the arrangement that works best for them.

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71.5° should be the angle of elevation to the summit of the tree. The tree to the nearest foot is 149.4ft.

Between the horizontal line and the line of sight, an angle called the angle of elevation is created. An angle of elevation is produced when the line of sight is upward from the horizontal line. When it lies between the line of sight and the horizontal line, the angle of elevation is generated. The angle created, known as the angle of elevation, occurs when the line of sight is above the horizontal line. However, the line of sight is downward toward the horizontal line in the depression angle. The angle of elevation is the angle formed by the horizontal line of sight and the object when a person stands and looks up at something.

tan 71.5°=opp/hyp

tan 71.5°=y/50

y=50(tan 71.5°)

y=50(tan 71.5°)

y=50(2.98868)

y=149.4ft

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The required correct answers are;

1 - (1 1/3 x, 1 1/3 y)

4 - (3 1/10 x, 3 1/10 y)

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.

The following algebraic rules represent a dilation that is an enlargement:

1 - (1 1/3 x, 1 1/3 y)

4 - (3 1/10 x, 3 1/10 y)

The scale factor in both of these rules is greater than 1, which means that the dilation is an enlargement. In rule 1, the scale factor is 1 1/3, and in rule 4, the scale factor is 3 1/10.

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Complete question:

Which of the following algebraic rules that represent a dilation that is an enlargement?

Select 2 correct answers

1 - (1 1/3 x, 1 1/3y)

2 - (1/2 x, 1/2y)

3 - ( 0.1 x, 0.1 y)

4 - (3 1/10 x, 3 1/10y)

Answer:

57

Step-by-step explanation:

morning bestie hgcj hcvjhcv jdvzdh

Answer: 38 and 24

Step-by-step explanation:

Hope this helps.

Expressed as fraction : [tex]$\frac{116050}{59049}$[/tex]

[tex]\begin{align*} S &= \frac{a(1-r^{n})}{1-r}= \frac{2}{3} \cdot \frac{1-\left(\frac{2}{3}\right)^{10}}{1-\frac{2}{3}}\\ & = \frac{2}{3}\cdot\frac{1-\frac{1024}{59049}}{\frac{1}{3}}=\frac{2}{3}\cdot\frac{3}{1}\cdot\frac{58025}{59049}=\frac{2\cdot58025}{59049}\\ & = \boxed{\frac{116050}{59049}}. \end{align*}[/tex][tex]S &= \frac{a(1-r^{n})}{1-r}= \frac{2}{3} \cdot \frac{1-\left(\frac{2}{3}\right)^{10}}{1-\frac{2}{3}}\\ & = \frac{2}{3}\cdot\frac{1-\frac{1024}{59049}}{\frac{1}{3}}=\frac{2}{3}\cdot\frac{3}{1}\cdot\frac{58025}{59049}=\frac{2\cdot58025}{59049}\\ & = {\frac{116050}{59049}}[/tex]

The sum S is calculated using the formula for an infinite geometric series, which states that the sum of the series is equal to the first term divided by 1 minus the common ratio.

The first term in the series is [tex]$\frac{2}{3}$[/tex], and the common ratio is [tex]$\frac{2}{3}$[/tex], so the sum is equal to [tex]$\frac{2}{3} \cdot \frac{1-(\frac{2}{3})^{10}}{1-\frac{2}{3}}$[/tex]

This expression simplifies to [tex]$\frac{2 \cdot 58025}{59049}$[/tex], or [tex]$\frac{116050}{59049}$[/tex]

Complete question:

What is the value of sum [tex]\frac{2}{3}+\frac{2^2}{3^2}+\frac{2^3}{3^3}+ \ldots +\frac{2^{10}}{3^{10}}[/tex]?

Express your answer as a common fraction

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The highest frequency of any score in the histogram would be 5/20 = 0.25.

The score that has the highest frequency is 8. This is determined by counting the number of bars corresponding to each score. In this histogram, there are 5 bars corresponding to the score 8, which is the highest number compared to any other score.

Formulaically, we can calculate the frequency for each score by dividing the number of observations for that score by the total number of observations. For the score 8, this would be 5/20 = 0.25. This is the highest frequency of any score in the histogram.

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The diameter is the length across the entire circle. This divides the circle into two equal parts and makes two equal-sized semicircles. The radius is the length from the center of the circle to the circumference. The diameter is always twice the size of the radius.

The equation to solve for the area of a circle is [tex]A =[/tex] π [tex](d/2)^{2}[/tex]

Substituting 5 and 3.14 into the equation gives us:

Solving for 5/2 gives us:

Therefore, [tex]A = 19.6m^{2}[/tex]

Answer:

The area of a circle with a diameter of 5 m is 19.63 m², rounded to the nearest tenth, it would be 19.6 m². So the answer is c. 19.6 m².

What is circle ?

A circle is a two-dimensional geometric shape defined as the set of all points that are a fixed distance, called the radius, from a central point, called the center. A circle is the set of all points in a plane that are at a given distance from a given point, the center.

The area of a circle is given by the formula A = , where r is the radius of the circle. To find the area of a circle with a diameter of 5 m, we first need to find the radius. We can do this by dividing the diameter by 2:

r = 5 m / 2 = 2.5 m

Then we can substitute this value of r into the formula for the area of a circle:

A =  = π(2.5 m)^2 = 3.14 * 6.25 m^2 = 19.63 m²

So the area of a circle with a diameter of 5 m is 19.63 m², rounded to the nearest tenth, it would be 19.6 m². So the answer is c. 19.6 m².

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Step-by-step explanation:

There are 126 ways to select ten comics if we choose at least one of each book.

Here we have a total of 6 different comics.

Now we have selected 10 comics such that we have at least one comic each.

Let's select one copy of each copy. This can be done in 1 way. Thus we are left with 4 comics to select from 6 different comics.

This is a  repetition and unordered form of selection since each comic can have n number of copies.

This can be done in C(6+4-1 , 4-1) ways.

So the correct answer is C(9, 3) ways.

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Using the concept of permutation and combinations, the friends can split donuts in 1680 ways

It is given that 3 different friends are splitting 9 different donuts among themselves equally so each person gets 3 donuts and we need to determine in how many ways it can be done.

We will use here the concept of permutation and combinations.

Number of ways to choose donuts for the first person = ⁹C₃

Number of ways to choose donuts for the second person = ⁶C₃

Number of ways to choose donuts for the third person = ³C₃

Total number of different ways to split donuts = ⁹C₃ × ⁶C₃ × ³C₃

                                  = 84 × 20 × 1

                                  = 1680 ways

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The correct option: b. Reaction times were the longest when people had to read words presented in colored ink.

A seemingly unimportant phenomena called the Stroop effect explains a great deal about how the brain functions.

Thus, the stroop experiment's findings most accurately represent when respondents used to have to read words given in colorful ink, reaction times tended to be the longest.

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The complete question is-

This following question refers to the outcome of the actual experiment (described on the conclusions slides), not the data generated from your performance in particular (which may or may not have matched the real experimental results).

a. Reaction times were the longest when people had to read words presented in black ink.

b. Reaction times were the longest when people had to read words presented in colored ink.

c. Reaction times were the longest when people had to name the color of colored chips/shapes.

d. Reaction times were the longest when people had to name the color of words presented in colored ink.

Having specialized accounting knowladge is most vital for performing it is a advance testing techniques.

Data validation is the exercise of checking the integrity, accuracy and shape of facts before it's miles used for a enterprise operation. records validation operation effects can offer statistics used for facts analytics, commercial enterprise intelligence or training a system gaining knowledge of version.

in this method, take a look at cases are evolved using the use cases of the system. A use case embody the diverse actors and their interactions with the machine. Use instances cover the entire transactions from begin to finish. those check cases depict the real use of software via the end consumer.

The superior Accounting Specialization makes a speciality of superior standards which includes subsidiaries, partnerships, intercompany transactions, mergers and acquisitions and consolidations

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Answer:

[tex]c[/tex] ≈ [tex]8.944[/tex]

Step-by-step explanation:

Use the Pythagorean theorem. The pythagorean theorem can be used if the triangle is a right triangle and you are provided with 2 of sides.

Pythagorean theorem is [tex]a^2+b^2=c^2[/tex]. This is where a and b are the 2 legs of the triangle and c is the hypotenuse. You know where the hypotenuse is because it will always be opposite of the right angle.

So in this triangle, a would be 4 and b would be 8. (a and b can be interchangeable).

[tex](4)^2+(8)^2=c^2[/tex]

[tex]16+64=c^2[/tex]

[tex]80=c^2[/tex]

[tex]\sqrt{80} =c[/tex]

[tex]c[/tex] ≈ [tex]9.944[/tex]

The answer choice which represents a table which represents a linear and proportional relationship is; Choice C ; whose y-intercept is 0.

With respect to relationships, two variables are said to be proportional if the y-intercept of the relation between them is 0.

here, we have,

The answer represents a linear relationship that is also proportional

Hence, y = kx represents a proportional relationship where k is the constant of proportionality.

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The true statement regarding the negation of the statement "It is not the case that x is equal to 400" is given as follows:

x is equals to 400.

Hence the remaining statements are false.

The statement in this problem is given as follows:

"It is not the case that x is equal to 400".

The synonym, considering that the clause is "x is equals to 400", is given as follows:

"x is not equal to 400".

The negation of the statement is given as follows:

Not("x is not equal to 400").

Hence, in this case, we would have a double negation, which becomes and affirmation, and thus the negation of the statement is given as follows:

x is equals to 400.

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The required statement "are cartesian and rectangular coordinates the same" is true.

Cartesian coordinates are a set of numbers that describe the position of a point in a plane relative to an origin (or "pole"). The coordinates are represented by an ordered pair (x, y), where x represents the horizontal position and y represents the vertical position.

This coordinate system was invented by mathematician and philosopher René Descartes, and is named after him. The coordinates are often used to graph equations, plot points on a plane, and describe the relationships between variables.

The Cartesian coordinate system is useful because it allows us to visualize and analyze problems in a straightforward and intuitive way.

Thus, we can say Cartesian coordinates" and "rectangular coordinates" refer to the same thing.

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Answer:

linear, function

Step-by-step explanation:

linear.. straight line

function.. for every x there is only one y

The angles between 0 and 2π that is coterminal to 780° are 2π and π/3.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The coterminal angle to 780°.

The coterminal angle is between 0 and 2π.

Now,

The coterminal angles can be positive or negative.

The coterminal angles are calculated by adding or subtracting 360 degrees as many times as needed from the reference angle.

Now,

780 - 360

= 780 - 360

= 360

= 2π

780 - (2 x 360)

= 780 - 720

= 60

= π/3

Thus,

The angles are 2π and π/3.

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