Three cups of soup and two sides of rice cost $15.85. Six cups of soup and four

sides of rice cost $31.70. Find the cost of 1 cup of soup and 1 side of rice.

The length of the side opposite to the reference angle is 7.77 units.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

If we take the reference angle 45°, The side 'x' is opposite and the side having a length of 11 units is the hypotenuse.

We know, sin = opposite/hypotenuse.

Therefore,

sin45° = x/11.

1/√2 = x/11.

x = 11/√2.

x = 7.77 units.

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A table between both the cheeses is given as,
Swiss Cheese (oz) 2 4 6
Cheddar Cheese (oz) 4 8 12, Option A is correct.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,
Let x be the amount of Swiss cheese and y be the amount of cheddar cheese.
According to the question,
y = kx
put y = 4 and x = 2
k = 2

Now,
y = 2x

From the above relation, a table between both the cheeses is given as,
Swiss Cheese (oz) 2 4 6
Cheddar Cheese (oz) 4 8 12

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To find out how many miles Charles Lindbergh flew per hour, we can use the formula:

miles per hour = total miles / total hours

In this case, the total miles is 3,610 and the total hours is 33.5. Plugging in these values, we get:

miles per hour = 3,610 / 33.5

miles per hour = 107.7 (approximately)

So Charles Lindbergh flew about 107.7 miles per hour during his first solo flight across the Atlantic Ocean.

Therefore , the solution of the given problem of function comes out to be the correct options  are B, E and F

A science called mathematics studies numbers, its variations, arithmetic and the local tissue, shapes, and both their existing and projected places. The relationship between a group of inputs, which each have a corresponding output, is described by a function. A function is variable  a collection of inputs that together produce a single, recognizable output with each input. A city, municipality, or scope—often referred to as a realm—is assigned to each function.

Here,

By observing the 1/4 placed ahead of the cubed root symbol, we can get the solution B. Every y value is reduced by a factor of 1/4, bringing it closer to the x axis.

By examining the 3 within the cube root symbol, we can determine solution E. The value is always moved left by that many spaces when we add a digit under the cube root symbol.

Finally, if we look at the 6 at the conclusion, we can locate F. Any integer used as a constant at the conclusion of an equation causes the graph to advance by that too many spaces.

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He saved 180 naira by buying three dozen eggs in sixes Instead of separately.

A group of twelve is referred to as a dozen and is frequently abbreviated as doz or dz. Given that there are roughly twelve lunar cycles (or months) in each cycle of the sun (or year), the number twelve may be one of the earliest primitive integer groupings.

Twelve is useful because it has the greatest number of divisors among numbers up to its double, a property shared only by the numbers 1, 2, 6, 12, 60, 360, and 2520.

1 dozen = 12

3 dozen = 36

6 eggs costs 150 naira

36 eggs costs 150 naira = 36/6 × 150

                                         = 900 naira

Each egg costs 30 naira, then 36 eggs costs = 36 × 30

                                                                            = 1080 naira

Savings = 1080 - 900 = 180 naira

Thus, He saved 180 naira by buying three dozen eggs in sixes Instead of separately.

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As a result, there are 1440 degrees total internal angles in a decagon.

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The inequality using interval notation is given as 55 < x < 70

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

Inequalities are used to show that an expression containing numbers and variables are not equal.

Interval notation involves using parentheses for opened ends and square brackets for closed ends.

Let x represent the allowed height to ride at an amusement park. A person has to be taller than 55 inches but shorter than 70 inches, hence:

55 < x < 70

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Answer: $180.02

Step-by-step explanation:

The total bill for the food will be $178.84 and then add the tip which is 18% to get the total.  One method of changing the 18% to money wise is 1.18 and then adding the two numbers together to get a total of $180.02.

Answer: Yes

Step-by-step explanation: 28/20 Simplified is 1 2/5

Answer:

Yes

Step-by-step explanation:

The number that represents the change in altitude a hiker must complete to return to sea level if he is at an altitude of 25 feet below sea level is 25.

When the hiker is at an altitude of 25 feet below sea level, he needs to go up 25 feet to reach sea level. This represents a change in altitude of 25 feet, regardless of the direction it is going.

So the number that represents the change in altitude to return to sea level is 25.

Answer:

4

Step-by-step explanation:

substitute the values from the set into the inequality and check validity.

x = 1

5(1)² > 12(1) + 9

5(1) > 12 + 9

5 > 21 ← False

x = 2

5(2)² > 12(2) + 9

5(4) > 24 + 9

20 > 33 ← False

x = 3

5(3)² > 12(3) + 9

5(9) > 36 + 9

45 > 45 ← False

x = 4

5(4)² > 12(4) + 9

5(16) > 48 + 9

80 > 57 ← True

thus the value 4 from the set makes the inequality true

Vertex (3, -4) with x-intercepts (1, 0), (5, 0), and (0, 5) and an axis of symmetry of 3. As a result, choice B is the right response.

In a graph, what exactly is a vertex?

The right response is, therefore, option B.

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Full Question-

What characteristics can you see in the graph of the quadratic function in the figure? Options for question 14: A: The vertex is at (-4,3), the y-intercept is at (5,0), the x-intercepts are at (0,1) and (0,5), and the symmetry axis is at (-4,3) B: The vertex is at (-3,-4), the y-intercept is at (0,5), the x-intercepts are at (1,0) and (5,0), and the symmetry axis is at (3); C: Vertex: (3, -4), y-intercepts: (1, 0), and (5, 0), x-intercept: (0, 5), axis of symmetry: (3 D) Axis of symmetry is at x = -3, vertex is at (-3,4), y-intercept is at (0,5), and x-intercepts are at (1,0) and (5,0).

The polynomial [tex]-15\:y^4+12\:y^2-9\:y[/tex] as the sum of other polynomials. Each of the product's polynomials is written as = 3y (-5y³ + 4y - 3)

Given,

[tex]-15 y^4+12 y^2-9 y[/tex]

[tex]& y^2=y y \\[/tex]

[tex]& y^4=y^3 y \\[/tex]

[tex]& =-15 y^3 y+12 y y-9 y[/tex]

[tex]=-3 \cdot 5 y^3 y+3 \cdot 4 y y-3 \cdot 3 y[/tex]

Factor out common term 3y

= 3y (-5y³ + 4y - 3)

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Therefore , the answer is the distance between P and R is 12,2m.

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending point.

Here,

Using the sine rule, sin a/A = sin b/B in this instance, we can determine the distance between P and R.

Sin angle PQR/PR is equal to Sin angle QRP/PQ.

We are aware that the QRP angle is 45° because:

Since it is an alternative interior angle, angle NPR is 75°.

Since 75° – 60° = 15, the angle QPR would be 15°.

As a result, angle QRP would be 45° since 180° – 120° – 15° = 45°.

When we know the angle QRP, we can quickly calculate the PR by entering the values into a calculator.

Sin 120°/RP = Sin 45°/10

RP = sin(120,10) sin(45,45),

=root 6 × 5

= 12.2m(3s.f) (3s.f)

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The scale factor of the rectangle and its copy is [tex]\frac{2}{3}[/tex].

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

The rectangle on right hand side is the scaled copy of the original rectangle. The scaled version of the rectangle is given as follows:

[tex]\frac{42}{63} \text{ and } \frac{15}{\frac{45}{2} } = \frac{30}{45}[/tex]

Rationalize the factors to find the scale factor.

Rationalize the factor [tex]\frac{42}{63}[/tex] by multiplying and dividing by 45.

[tex]\frac{(42)(45)}{(63)(45)}[/tex]

[tex]\frac{1890}{2835}[/tex]

Rationalize [tex]\frac{30}{45}[/tex] by multiplying and dividing by 63.

[tex]\frac{(30)(63)}{(45)(63)}[/tex]

[tex]\frac{1890}{2835}[/tex]

Scale factor = [tex]\frac{1890}{2835} = \frac{2}{3}[/tex]

Hence the scale factor of the rectangle and its copy is [tex]\frac{2}{3}[/tex].

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Answer:

Interpretation of the slope: For students at this school, the predicted GPA decreases by 0.005 for each additional text message sent OR the GPA decreases by 0.005, on average, for each additional text message sent.

Interpretation of intercept: The model predicts that students at this school who send no text messages have, on average, a GPA of 3.8.

Step-by-step explanation:

The purpose of this task is to assess the ability to interpret the slope and intercept of the line of best fit in context. There are two common errors that students make when interpreting the slope. Students may not make it clear that the slope is the predicted change (not necessarily an actual change) in GPA associated with an increase of 1 in the number of text messages sent. They also often do not communicate that the slope describes the change

You might want to point out that it is not always reasonable to interpret the intercept as the predicted y value when x = 0, as this often involves extrapolation far beyond the range of the x values in the data set. In this example, however, it is appropriate because there are observations with x = 0 in the data set.

You can also point out that the interpretation of the slope and intercept represents a generalization from the sample of 52 students to the population of all students at the school. This is appropriate because the sample was a random sample of students from the school.

Although this task is short and looks simple, some of the points brought out in this task are subtle. It might be a good strategy to engage in a whole class discussion of the correct interpretations.

Answer:

[tex]\dfrac{1}{4}=0.25[/tex]

Step-by-step explanation:

The Riemann sum is a method by which we can approximate the area under a curve using a series of rectangles.

The Lower Riemann Sum uses the minimum height of the rectangle on each subinterval.  

As the Lower Riemann Sum is entirely below the curve, it is an underestimation of the area under the curve.

The number of partitions is the number of rectangles used.  

Partitions can be of equal length or not of equal length.

Given:

The given partition divides the interval [-1, 1] into 4 subintervals:

To calculate the areas of the rectangles, multiply the width of each rectangle by its height.

The width is the difference between the x-values of each subinterval.

The height is the minimum value of the function across the subinterval.

First rectangle [-1, -1/4]:

[tex]\begin{aligned}\implies \left(-\dfrac{1}{4}-(-1)\right) \cdot f\left(-\dfrac{1}{4}\right)&=\dfrac{3}{4} \cdot \left(-\dfrac{1}{4}\right)^2\\\\&=\dfrac{3}{4} \cdot \dfrac{1}{16}\\\\&=\dfrac{3}{64}\end{aligned}[/tex]

Second rectangle [-1/4, 1/2]:

[tex]\begin{aligned}\implies \left(\dfrac{1}{2}+\dfrac{1}{4}\right) \cdot f\left(0\right)&=\dfrac{3}{4} \cdot (0)^2\\\\&=\dfrac{3}{4} \cdot 0\\\\&=0\end{aligned}[/tex]

Third rectangle [1/2, 3/4]:

[tex]\begin{aligned}\implies \left(\dfrac{3}{4}-\dfrac{1}{2}\right) \cdot f\left(\dfrac{1}{2}\right)&=\dfrac{1}{4} \cdot \left(\dfrac{1}{2}\right)^2\\\\&=\dfrac{1}{4} \cdot \dfrac{1}{4}\\\\&=\dfrac{1}{16}\end{aligned}[/tex]

Fourth rectangle [3/4, 1]:

[tex]\begin{aligned}\implies \left(1-\dfrac{3}{4}\right) \cdot f\left(\dfrac{3}{4}\right)&=\dfrac{1}{4} \cdot \left(\dfrac{3}{4}\right)^2\\\\&=\dfrac{1}{4} \cdot \dfrac{9}{16}\\\\&=\dfrac{9}{64}\end{aligned}[/tex]

Therefore, the Lower Reimann Sum for the given function over the given interval and partitions is the sum of the area of the rectangles:

[tex]\implies \dfrac{3}{64}+0+\dfrac{1}{16}+\dfrac{9}{64}=\dfrac{1}{4}=0.25[/tex]

The rational numbers from smallest to largest is

5/7 < 11/15 < 3/4

What is a rational number?

In contrast to irrational numbers, which cannot be stated as fractions, rational numbers can be expressed as the ratio of two integers with the condition that the denominator not be equal to zero. Irrational numbers don't have ending or recurring decimals, but rational numbers do.

convert them into decimal numbers

3/4 = 0.75

5/7 = 0.714

11/15 = 0.733

0.714 < 0.733 < 0.75

So, the rational numbers from smallest to largest is

5/7 < 11/15 < 3/4

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Answer: y=(-5/3)x+8

Step-by-step explanation: earrange 5x+3y=6 in slope intercept form

y=mx=b

5x+3y=6

     3y=6-5x

       y=2-(5x)/3

then slope for a line parallel is -5/3

Use point slope form y-y1=m(x-x1)

plug un values of (x,y) = (6,-2)

and m=-5/3

y-y1=m(x-x1)

y-(-2)=(-5/3)(x-6)

y+2=(-5/3)x+10

y=(-5/3)x+10-2

y=(-5/3)x+8 <-- solution

f (x+ h) = 4(x+ h) - 6 and f (x+ h) - f (x) = 4(x+ h) - 6 - 4 (x) - 6 are the results of simulating f (x+ h) = 4.

The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

Given

A) f( x+ h ) = 4( x+ h ) - 6

B) f ( x+ h ) - f (x) = 4 (x+ h ) - 6 - 4 (x) - 6

f (x+ h) = 4(x+ h) - 6 and f (x+ h) - f (x) = 4(x+ h) - 6 - 4 (x) - 6 are the results of simulating f (x+ h) = 4.

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the area of the green parallelogram will be 15inch².

What is Area of Parallelogram?

The region in a two-dimensional plane that a parallelogram occupies is known as its area. A parallelogram is a form with four sides with two geometry dimensions. Because the opposing sides are equal and parallel, so it is a unique quadrilateral example. The space bounded by the four sides of a parallelogram is known as its area. A parallelogram's area is calculated as the sum of its length and height.

A blue parallelogram has a height of 6 inches and a base of 10 inches.

a scale of 2:1 was applied to the blue parallelogram to create a green parallelogram.

So the height will be half and the base ill also be.

For the green parallelogram will be 3 inch and 5 inch.

The area will be 3*5 = 15inch²

Hence, the area of the green parallelogram will be 15inch².

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Answer:

456,754

Step-by-step explanation:

A ticker symbol is an abbreviation of one to four letters, which means it can be one letter, two letters, three letters or four letters. Each letter can be any of the 26 letters in the English alphabet, so there are 26 choices for each position.

For one letter ticker symbols:

26 (number of choices for the first letter) * 1 (number of positions) = 26 different possibilities.

For two letter ticker symbols:

26 (number of choices for the first letter) * 26 (number of choices for the second letter) = 676 different possibilities.

For three letter ticker symbols:

26 (number of choices for the first letter) * 26 (number of choices for the second letter) * 26 (number of choices for the third letter) = 17,576 different possibilities.

For four letter ticker symbols:

26 (number of choices for the first letter) * 26 (number of choices for the second letter) * 26 (number of choices for the third letter) * 26 (number of choices for the fourth letter) = 456976 different possibilities.

So, the total number of different stock ticker symbols that are possible is 26 + 676 + 17,576 + 456976 = 456,754.

Using Simple division, Number of sections that Niquelle create along the trail is 6 sections.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.

The other operations are multiplication, addition, and subtraction. Simply write the first fraction, the division symbol (), and the second fraction to divide a fraction. For instance, your issue could be 3/4 5/8. Use horizontal rather than diagonal lines to conveniently divide each fraction's numerator (top number) and denominator (bottom number).

Partitive division and quotative division are the two types of division. In some circumstances, one form may be more beneficial than the other.

Length of the trail =  4 1/2 miles long = 9/2 miles

The signposts divide the trail into sections that are 3/4 mile long.

Number of sections that Niquelle create along the trail = 9/2 miles ÷ 3/4

⇒ 9/2 × 4/3

⇒ 6 sections

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To find the probability of selecting the letter "C" or the coin landing tails up, we need to calculate the probability of each event individually and then add the probabilities of the two events together.

The probability of selecting the letter "C" is:

1/5

This is because there are 5 letters in total, A, B, C, D, and E, and "C" is one of them, so the probability of selecting "C" is 1/5.

The probability of the coin landing tails up is:

1/2

This is because there are two possible outcomes when flipping a coin, heads or tails, and since the coin is fair, the probability of getting heads or tails is 1/2.

To find the combined probability of the two events we need to add them together using the rule of "or" in probability which is defined as:

P(A or B) = P(A) + P(B) - P(A and B)

However in this case A and B are mutually exclusive events, meaning they can't happen at the same time. There is no way to have "C" and coin landing tails up at the same time. Then we don't have to subtract P(A and B)

Therefore, the probability of selecting the letter "C" or the coin landing tails up is:

1/5 + 1/2 = 2/5 + 1/2 = 7/10

So the probability of selecting the letter "C" or the coin landing tails up is 7/10

The slope of parallel lines is the same. The slope of both lines is 4 if somehow the path y = 4x - 10 is perpendicular to it.

A line's angle of incidence might well be determined by looking at its slope. Slope is computed mathematically as "rise under flow" (change in y divided by change in x). A bridge's slope usually indicates the slopes and direction of the line. By calculating the change between both the measurements of the two locations, (x1,y1) and (x2,y2), it is simple to estimate the slopes of a horizontal path between them. The letters "m" is sometimes used this to represent slope.

In the point slope form, replace m = 1 with to create the equation (1,13).

y - y₁ = m(x - x₁)

y - 13 = 4 (x-1)

y - 13 = 4x - 4

y = 4x + 9

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The complete question is-

What is an equation of the line that is parallel to y=4x-10 and passes through (1,13)?​

Both a ray and a line segment have two endpoints . A ray is bounded on one side , but a line segment is not bounded on either side.

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Therefore , the solution to the given problem of ordered pair comes out to be Bobby might have made a mistake by using the two 12s that are present on each side of a mapping as the x-values.

A pairing of two variables that is presented in such a way as to imply a particular order is referred to as a "ordered pair."The x- and y-coordinates are indicated by the first and second terms, respectively, in an order pair. Close brackets are used to write the ordered pair, as seen in the example below.

Here,

The following are the ordered pairs:

(x,y) = (1, 2), (6, 12), (12, 24), (18, 36) (18, 36)

The following is what arrows show us:

1 -> 2

6-> 12

12->24

18 -> 36

The relational mapping shown above is a function.

This is the case since every x-value points to the same y-value.

Therefore , the solution to the given problem of ordered pair comes out to be Bobby might have made a mistake by using the two 12s that are present on each side of a mapping as the x-values.

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Answer:  15,24,plan A

Step-by-step explanation: you will need to use the 15 from 150 to see which one costs less because 24+ 15= 39 so its obvious that plan B costs less then plan A   the next step is pretty easy because they both  cost 24 at the same time but its obvious that plan A costs more  so your answer for each of them is

The solution of the given system of equations is (2, 1, 0).

What is system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system.

Consider, the given system of equations.

3x + 3y + 6z = 9          ..(1)

x + 3y + 2z = 5            ..(2)

3x + 12y + 12z = 18       ..(3)

Divide equation (1) by 3

x + y + 2z = 3         ..(4)

Subtract equation (4) from equation (2)

   x + 3y + 2z = 5

-   x + y + 2z = 3

______________

      2y = 2

⇒ y = 1

Multiply equation (1) by 2

6x + 6y + 12z = 18         ..(5)

Subtract equation (3) from equation (5)

        6x + 6y + 12z = 18

  -    3x + 12y + 12z = 18

_______________________

       3x - 6y = 0         ..(6)

Multiply equation (2) by 6

6x + 18y + 12z = 30            ..(7)

Subtract equation (3) from equation (7)

    6x + 18y + 12z = 30

-    3x + 12 y + 12z = 18

_______________________

    3x + 6y = 12              ..(8)

Adding equation (6) and (8)

       3x - 6y = 0

   +  3x + 6y = 12

________________

       6x = 12

⇒    x = 2

Now plug x = 2, y = 1 in equation (1)

3(2) + 3(1) + 6z = 9

       6 + 3 +6z = 9

            9 + 6z = 9

                  6z = 0

                    z = 0

Hence, the solution of the given system of equations is (2, 1, 0).

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