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The constant of proportionality is k = 7, so:

y = 7x

We know that a proportional relation is of the form:

y = k*x

Where k is the constant of proportionality between the variables x and y.

Here we can see that the line passes through the point (1, 7), this means that when x = 1, y = 7.

Replacing these values we will get:

7 = k*1

With that we can find the value of k.

7/1 = k

That is the constant of proportionality, then the equation is:

y = 7x

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An equation in slope-intercept form for the line of best fit is y = -0.29x + 80.43.

In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At point (5, 79), an equation of this line in slope-intercept form can be calculated by using the point-slope form:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 79 = (77 - 79)/(12 - 5)(x - 5)

y - 79 = -2/7(x - 5)

y = -2x/7 + 10/7 + 79

y = -0.29x + 80.43

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Answer:

Help me

Step-by-step explanation:

Therefore, the number of pages in the book is 240.

So the answer is option B.

An arithmetic value is a number, which is occasionally used to represent quantities and carry out calculations. In writing, numerical symbols like "3" are used to represent numbers. A number system is a form of writing in which symbols or digits are arranged logically to represent numbers.

If Charles has read 180 pages of a book, and this is 3/4 of the total number of pages in the book, we can set up the following equation:

3/4 p = 180

To solve for p, we can multiply both sides by 4/3:

p = 180 × 4/3 = 240

Therefore, the number of pages in the book is 240.

So the answer is option B.

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Therefore , the solution of the given problem of inequality comes out to be rigid nature of the inequality, x cannot equal 12.

An inequality also in math is a connection or a collection of integers even without the equal symbol. Equity always comes after equilibrium. When values are still not equivalent, inequality results. Between equity and inequality, there are differences. Because factors aren't always identical or similar, it was determined to use the most common symbol (). No matter how few or variables numerous the differences, they are all able to be used to assess values.

Here,

To address the disparity:

=> (2x + 6)/5 > 6

To commence, we can remove the fraction by multiplying both sides by 5:

=> 2x + 6 > 30

The next step is to reduce by taking 6 away from both sides:

=> 2x > 24

By multiplying both parts by 2, we can finally find the value of x:

=> x > 12

The following is how the disparity can be resolved:

=> x > 12

Because of the rigid nature of the inequality, x cannot equal 12.

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The two numbers whose sum is 1 and whose product is -20 are 5 and -4.We can start solving this problem by using algebra. Let's say that the two numbers we want to find are x and y. Then, we know that:

x + y = 1 (Equation 1)

xy = -20 (Equation 2)

We can use Equation 1 to solve for one of the variables in terms of the other. For example, we can solve for y:

y = 1 - x (Equation 3)

Then, we can substitute Equation 3 into Equation 2 to get:

x(1 - x) = -20

Expanding the left side of the equation, we get:

x - x{power}2 = -20

Rearranging the terms, we get:

x{power}2 - x - 20 = 0

This is a quadratic equation, which can be factored as:

(x - 5)(x + 4) = 0

Therefore, the solutions for x are x = 5 and x = -4.

We can use Equation 3 to find the corresponding values of y:

y = 1 - x

If x = 5, then y = 1 - 5 = -4. If x = -4, then y = 1 - (-4) = 5.

Therefore, the two numbers whose sum is 1 and whose product is -20 are 5 and -4.

It's important to note that there are different strategies for solving equations and that some problems may require different approaches. Algebra is a powerful tool for solving many types of problems, including those involving numbers and equations.

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After answering the given query, we can state that  Consequently, the rectangle combined figure's area is 469 cm².

In Euclidean mathematics, a rectangle is a parallelogram with four small angles. Another way to characterize it is as a basic rule-following hexagon or one with equal angles. Another choice for the parallelogram is a straight angle. Four of the vertices in a rectangle have the same length.

Four vertices with 90° angles and identical parallel sides make up a quadrilateral with a rectangle-shaped cross section. This leads to it being known as a "equirectangular rectangle" at times. A rectangle is occasionally referred to as a parallelogram because its two edges are so equal and parallel to one another.

Let's start by calculating the rectangle's area:

Rectangle area equals length times breadth

Size = 22 centimetres

17 centimetres wide

Rectangle's area is equal to 22 × 17 cm, or 374 cm².

Next, let's calculate the triangle's area:

Area of trapezoid = base x height x half.

Base: 19 centimetres.

Size equals 10 centimetres (since the left vertical leg is 10 cm below the top right vertex of the rectangle)

Triangle's area is 1/2 x 19 cm x 10 centimeter, or 95 cm².

the combined figure's overall surface area

Area of rectangle plus area of triangular equals total area.

Total space equals 469 cm² (374 cm² plus 95 cm²).

Consequently, the combined figure's area is 469 cm².

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Answer:

407 pounds of food for 11 tigers

Step-by-step explanation:

We know

74 pounds of food is needed to feed two tigers.

74 / 2 = 37 pounds of food

So, each tiger needs 37 pounds of food.

How many pounds of food are needed to feed 11 tigers?

37 x 11 = 407 pounds of food

So, 407 pounds of food are needed to feed 11 tigers.

Answer:

407 pounds of food for 11 tigers

Step-by-step explanation:

The unit rate would be 37 pounds of food per tiger.

37 x 11 = 407

Helping in the name of Jesus.

The original fraction is 3/4.To solve this problem, start by writing an equation that expresses the fraction increasing by 2 1/6.

A fraction is a numerical expression that represents a part of a whole or a ratio of two numbers. It consists of two parts: a numerator (the number on top) and a denominator (the number on the bottom). For example, 3/4 is a fraction that represents 3 parts out of 4. It can also represent the ratio of 3 to 4.

This equation can be written as (N + 4)/(D - 3) = 2 1/6, where N is the numerator and D is the denominator.

Next, you can use algebra to solve for N and D. Multiply both sides of the equation by 6 to eliminate the fraction on the right side, giving you (N + 4) × 6 = (D - 3) ×6 + 13. Simplifying this equation gives you 6N + 24 = 6D - 18 + 13, or 6N + 41 = 6D - 5. Since the denominator must be 1 greater than the numerator, subtract 6 from both sides of the equation, giving you 6N + 35 = 6D. Finally, divide both sides of the equation by 6 to get N + 5.83 = D. Since the denominator must be an integer, round up to get N + 6 = D. Therefore, the original fraction is 3/4.

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Answer:

its actually 5/6

Step-by-step explanation:

the orginal fraction would be x/x+1, as the denominator is 1 more. the new equation is x+4/x-2, then you would have to add 2 1/6 on to x/x+1.therfore the equation is (x/x+1)+2 1/6=x+4/x-2, in which you would find that x=5 so its 5/6

The volume of a rectangular pyramid is 1200m.

What is a rectangular pyramid?

A rectangular pyramid is a sort of pyramid in which the sides are triangular in shape but the base is rectangular. While having diverse bases, such as square or hexagonal, a pyramid typically has triangular sides. The base, face, edges, and vertices of each of these pyramids are what set them apart from one another. A rectangular pyramid has unique characteristics and calculations.

Here, we have

Height = 20m

Width = 12m

Length = 15m

Volume = 1/3(Bh)

B = W×L

Volume = 1/3( W×L×h)

Volume = 1/3(20×15×12)

Volume = 1200m

Hence, the volume of a rectangular pyramid is 1200m.

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The equation Hx = c is inconsistent for some c in Rn, then the equation Hx = 0 has a nontrivial solution, and the null space of H is nonempty.

If Hx = c for some c in Rn is not consistent, it means that there is no solution x that satisfies this equation for the given value of c. This could happen if the vector c is not in the column space of the matrix H.

Now, let's consider the equation Hx = 0. This equation is known as the homogeneous equation associated with the matrix H. If the matrix H is inconsistent for some c in Rn, it means that the column space of H does not contain the vector c. Since the homogeneous equation Hx = 0 is a special case of the equation Hx = c, it follows that the column space of H also does not contain the zero vector.

In other words, the homogeneous equation Hx = 0 has a nontrivial solution, meaning there exists at least one vector x ≠ 0 that satisfies this equation. This solution is known as the null space or kernel of the matrix H. Therefore, A nontrivial solution to the equation Hx = 0 exists, and the null space of H is not empty if the equation Hx = c is inconsistent for some c in Rn.

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Answer:

a) $5.75 for 14 oz

Step-by-step explanation:

1) Find how much soap you get for $1 of each

To find out this, we have to divide the amount by how much it costs. This will give us how much soap each one will give you for $1.

a) 14 ÷ 5.75 = 2.43

b) 13 ÷ 5.50 = 2.36

c) 3.5 ÷ 3.45 = 1.01

d) 12 ÷ 5.25 = 2.29

From this we can see that we would be getting the most soap for $1 if we were to buy the first one. This means that it is the best deal!

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The amount of space contained within this goal is 216ft³.

What is triangular prism?

A polyhedron with three faces connecting corresponding sides, a triangle base, and a translated copy is known as a triangular prism. If the sides of a right triangular prism are not rectangular, the prism is oblique.

Here, we have

Given: Alex made a sketch for a homemade soccer goal he plans to build. The goal will be in the shape of a triangular prism. The legs of the right triangles at the sides of his goal measure 3 ft and 6 ft, and the opening along the front is 24 ft.

We have to find how much space is contained within this goal.

= 1/2(height×side length×width)

= 1/2(3×6×24)

= 216

Hence, The amount of space contained within this goal is 216ft³.

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The P-values for a sample size of 12 and the following test statistics are as follows:

t0 = 2.55: P-value = 0.0220

t0 = 1.87: P-value = 0.1040

t0 = 2.05: P-value = 0.0450

t0 = 2.80: P-value = 0.0044

a. t0 = 2.55: P-value = 0.0220  

Since the hypothesis is one-tailed (μ>100), the P-value is calculated using the area to the right of the test statistic. The P-value for a test statistic of 2.55 with a sample size of 12 is 0.0220.

b. t0 = 1.87: P-value = 0.1040

Since the hypothesis is one-tailed (μ>100), the P-value is calculated using the area to the right of the test statistic. The P-value for a test statistic of 1.87 with a sample size of 12 is 0.1040.

c. t0 = 2.05: P-value = 0.0450

Since the hypothesis is one-tailed (μ>100), the P-value is calculated using the area to the right of the test statistic. The P-value for a test statistic of 2.05 with a sample size of 12 is 0.0450.

d. t0 = 2.80: P-value = 0.0044

Since the hypothesis is one-tailed (μ>100), the P-value is calculated using the area to the right of the test statistic. The P-value for a test statistic of 2.80 with a sample size of 12 is 0.0044.

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The maximum number of factors that p(x) = (t²⁰ - t⁴) could have is 20.

The maximum number of factors that a polynomial can have depends on the degree of the polynomial.

For example, a quadratic polynomial of the form ax² + bx + c can have at most two factors if the coefficients a, b, and c are real numbers.  

Similarly, If the highest degree of the polynomial is 3 the factors of the polynomial will equal to 3.

Here we have

The polynomial p(x) = (t²⁰ - t⁴)  

As we know the maximum number of factors that a polynomial could have is equal to the highest degree of the polynomial.

The highest degree of p(x) is 20

Hence,

The maximum number of factors that p(x) = (t²⁰ - t⁴) could have is 20.  

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The value of the ratio will be a / b = 2 / 3.

Two objects are said to be comparable if they have the same shape. Therefore, two figures are said to be comparable in mathematics if they share the same shapes, lines, or angles.

In the given figure there are two lines intersecting the three parallel lines and making the segments a and b. The values of the segment on both sides will be similar.

The value of the ratio will be calculated as,

a / b = 4 / 6

a / b = 2 / 3

Therefore, the ratio a / b is 2 / 3.

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Answer:

Step-by-step explanation:

This is a vector addition problem because displacement is a vector

d = √(14² + 11²) = √317 = 17.8

direction of resultant d:

tan⁻1(11/14) = 38.2°  (north of east)

We may respond to that by addressing the issue at hand with equation  6 distinct numbers selected from 1 to 44, there are 7,059,052 possible lottery tickets.

A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A scientific statement that proves the equality of two formulae is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the connection that exists between the sentences that were already written on opposite sides of a letter. Frequently, the symbol and the particular software are identical. like in 2x - 4 = 2, for example.

We may use the formula for combinations to find how many different lottery tickets can be made with six different numbers selected from 1 to 44: nCr equals n / r!(n-r)!

where r is the number of things selected, n is the total number of items available, and! stands for the factorial function.

Because n = 44 and r = 6 in this instance, we may change the formula to read as follows:

44C6 = (44 x 43 x 42 x 41 x 40 x 39) / (6 x 5 x 4 x 3 x 2 x 1) = 7,059,052

Hence, with 6 distinct numbers selected from 1 to 44, there are 7,059,052 possible lottery tickets.

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The previous population of the city was 22,500.

All nationals present in, or temporarily absent from, a country, as well as aliens permanently settled in a country, are characterised as population. This indicator depicts the average number of people who live in a given location. The annual changes in population caused by births, deaths, and net migration during the year are referred to as growth rates.

Let P be the previous population of the city. We know that the current population is 36% larger than the previous population, so we can write:

Current Population = Previous Population + 36% of Previous Population

Using the values given in the problem, we can substitute and solve for P:

30,600 = P + 0.36P

30,600 = 1.36P

P = 30,600 / 1.36

P = 22,500

Therefore, the previous population of the city was 22,500.

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Answer:

1000000

Step-by-step explanation:

Answer:

Step-by-step explanation:

12/60

shorten it

it will be 1/5

After 3 hours of reading, Carly has 115 pages left to read.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Great, now I can help you with your question. The equation you provided is:

y = -35x + 220

Where y represents the number of pages Carly has left to read, and x represents the number of hours she has been reading.

We can interpret this equation as follows: Carly's reading speed is 35 pages per hour (since the coefficient of x is -35), and the total number of pages in the book is 220 (since the y-intercept is 220). So, at the start of the reading session (when x = 0), Carly has 220 pages left to read.

To find out how many pages Carly has left to read after a certain number of hours, you can simply substitute that number for x in the equation and solve for y. For example, if Carly has been reading for 3 hours, we can find out how many pages she has left to read by substituting x = 3 in the equation:

y = -35(3) + 220

y = -105 + 220

y = 115

Therefore,  after 3 hours of reading, Carly has 115 pages left to read.

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The inequality of the amount is x > 5

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

He could now afford the squishy ball for $5 at the school store.

This means that he must have more than $5 in savings

Represent the amount with x

So, we have the following representation

x > 5

Hence, the inequality is x > 5

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When the two events are mutually exclusive and collectively exhaustive,

the probability that one or the other occurs is:

b. 1.00

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1. Moreover, the proportion of positive outcomes cannot be negative.

The answer to the question is that two occurrences that are mutually exclusive cannot happen simultaneously. One cannot happen without the other. A coin flip result is a nice example. Tails cannot happen if heads do, and vice versa. A set of occurrences is considered exhaustive if there is a 100% chance that any one of them will occur. To put it another way, at least one of the occurrences is required.

According to the definitions given above, there is a situation in which there is a 100% chance that either one or the other event will occur. This is evident from the set's mutual exhaustibility. Furthermore, because they are mutually exclusive, we know that even if one event occurs, the other cannot.

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The value of surplus each month of $2492.33.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given monthly expenditure:

Fixed expenses = $1720

Living expenses = $1021

Annual expenses = $135

⇒ total monthly expenditure = 1720 + 1021 + 135 = $2,876

Given annual income:

Annual net income = $64,420

⇒ total monthly net income = 64,420 ÷ 12 = $5,368.33 (nearest cent)

Comparing the monthly income and expenditure, we can see that he earns more than he spends, so there will be a surplus.

⇒ total monthly net income - total monthly expenditure

= 5368.33 - 2876 = $2492.33

So, there is a surplus each month of $2492.33.

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Answer:

y=3x+6

Step-by-step explanation:

replacing the x=2,3,4 to produce y

when x=2

y=3(2)+6

y=6+6=12 ✓

when x=3

y=3(3)+6

y=9+6=15 ✓

when x=4

y=3(4)+6

y=12+6=18 ✓

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Part A :  Company B has the lowest one-time delivery fee.

Part B :  Company D has the highest additional fee per person.

Part C: Inviting 20 people Company C will be cheaper.

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

From the given information the four equations of a line can be formed as

Company A,

m = (100 - 70)/(2 - 0).

m = 15.

100 = 15(2) + b.

b = 80.

y = 15x + 70.

Company B,

m = (92 - 60)/(2 - 0).

m = 16.

y = 16x + 60.

Company C,

y = 12x + 120.

Company D,

y = 17x + 90.

Part A. Company B, y = 12x = 60 has the lowest one-time delivery fee

Rs. 60.

Part B. Company D, y = 17x + 90 has the highest additional fee per person,

Rs. 17.

Part C. For company B and company C, Inviting 20 people would cost,

Company B, y = 16(20) + 60 ⇒ y = 380.

Company C, y = 12(20) + 120 ⇒ 240 + 120 = 360.

So, Company C will be cheaper.

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Answer:

£10.35

Step-by-step explanation:

1) Find the tip

To find the tip the members payed we have to do 27 x 1.15

The reason we are multiplying by 1.15 is that the final amount would be 15% added on the original payment (100%). This means that we have to add 100 and 15 which gives us 115. After this we simply divide it by 100 to get the decimal multiplier

2) Split into 3

As they are splitting the bill 3 ways we have to divide 31.05 by 3

Each person will pay £10.35

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