1.Which best describes a linear function?

(a) Building a tower of blocks, Collin starts with 25 blocks on the first level, 16 on the second level, and
9 on the third level. The function represents the relationship between the number of blocks on each
level after x levels.

(b) On a summer day, the temperature outside increases 3 degrees Fahrenheit per hour after 6 AM.
The function represents the relationship between the
temperature outside after x hours after 6 AM.

(c) Patty's company makes gift boxes in the shape of cubes. As the size of the gift box changes, the
length of each side increases by 6 inches. The function represents the relationship between the volume
of
each gift box after x increases in side length.
Xo

(d) The water in an outdoor pool is evaporating. Each day, only 95% of the water from the day before
remains. The function represents the relationship between the amount of water in the pool after x days.
()

Answer:

350

Step-by-step explanation:

Using the proportion from part (a):

14/n = 20/500

Cross-multiplying, we get:

20n = 14 × 500

Dividing both sides by 20, we get:

n = 14 × 500 / 20 = 350

Therefore, about 350 seventh graders participate in the contest.

The golden ratio of Fibonacci, also known as the divine proportion, golden mean, or golden section, is a mathematical constant that is approximately equal to 1.618033988749895.

It is represented by the Greek letter phi (φ) and is found by dividing a line into two parts so that the longer part divided by the smaller part is also equal to the whole length divided by the longer part.

In mathematical terms, the golden ratio is expressed as:

φ = (1 + √5) / 2

The golden ratio is closely related to the Fibonacci sequence, which is a series of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1. The ratio of consecutive numbers in the Fibonacci sequence converges to the golden ratio as the sequence progresses.

For example, the first few numbers in the Fibonacci sequence are:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...

As we divide each number by the one before it, we get closer and closer to the golden ratio:

1/1 = 1

2/1 = 2

3/2 = 1.5

5/3 = 1.666...

8/5 = 1.6

13/8 = 1.625

21/13 = 1.615...

34/21 = 1.619...

55/34 = 1.617...

89/55 = 1.618...

144/89 = 1.618...

As you can see, the ratio of consecutive numbers in the Fibonacci sequence approaches the golden ratio as the sequence progresses. This is why the golden ratio is often referred to as the golden ratio of Fibonacci.

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Mat must bowl 140 in the next game.

In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

Given:

Matt bowled games of 162, 170, and 148.

Average = 155

let the score on fourth game be x.

So, (162 + 170 + 148 + x)/4 = 155

480 + x= 620

x= 140

Thus, he must bowled 140.

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The constant of proportionality of the graph is 8.

Constant of proportionality is the constant value of the ratio between two proportional quantities.

Given that, a table, of price of the number of pack of biscuits,

We are asked to find the constant of proportionality or unit rate that defines the relationship,

Unit rate is a rate for one of something.

Here, let us consider the number of packets be x and price be y,

x and y are proportional, therefore,

y = kx, here k is the constant of proportionality,

Put y = 8 and x = 1

8 = k

Similarly, if we check for other values we will get 8

[graph is attached]

Hence, the constant of proportionality of the graph is 8.

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To indicate that one value is greater than, less than, or equal to another, an inequality in a word problem is written using mathematical symbols like, >, or.

Determine the values that the inequality will compare before using the correct mathematical symbol to express the relationship between them in a word problem. Once the values have been determined, represent the relationship between them using the proper mathematical symbol. For instance, the inequality would be phrased as "x > 5" if the problem stated that "x is greater than 5". Other possible symbols for inequalities are (less than), (less than or equal to), and (more than) (greater than or equal to). It is crucial to always use the appropriate mathematical symbols when creating an inequality since they are needed to indicate the direction of the comparison. Moreover, make sure to incorporate all essential components, including the values being compared, the mathematical symbol, and the equals sign, if required. These procedures can be used to effectively write an inequality in a word problem.

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The residual plot tell you about the line of best fit, the closer a data point's residual is to 0, the better the fit.

A residual value is a measure of how much a retrogression line vertically misses a data point. Retrogression lines are the stylish fit of a set of data. You can suppose of the lines as pars; a many data points will fit the line and others will miss.

A residual plot has the Residual Values on the perpendicular axis; the vertical axis displays the independent variable.

A residual plot is generally used to find problems with retrogression. Some data sets aren't good campaigners for retrogression, including

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Answer:-8

Step-by-step explanation:

f(x)=-3x-2

f(2)=-3(2)-2

-6 - 2=

-8

The quadratic function is y = 1/3(x + 2)^2 - 5

The parent function of a quadratic function is represented as

y = x^2

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

vertical shrink of 1/3, shifts left 2 and down 5.

This means that

y = a(x + h)^2 + k

Where

a = 1/3

h = 2

k = -5

So, we have

y = 1/3(x + 2)^2 - 5

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Eigenvalues and eigenvectors can be found using a calculator by solving the equation Ax = λx, where A is a matrix, x is the eigenvector, and λ is the eigenvalue.

To solve this equation, you first need to calculate the determinant of the matrix A, which is written as |A|. If the determinant is not equal to zero, then you can calculate the eigenvalue by dividing the trace of the matrix (the sum of the diagonal elements) by the number of rows or columns of the matrix. The eigenvalues can then be substituted into the equation to solve for the corresponding eigenvector. For example, for a 2x2 matrix A, the eigenvalues can be found by calculating |A| and then solving the equation λ^2 - (trace of A) * λ + |A| = 0. The eigenvectors can then be found by plugging the eigenvalues into the equation Ax = λx and solving for x.

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The function to represent a direct variation relationship between y and x is y = kx.

A direct variation relationship is one where the ratio of two quantities is always constant. In mathematical terms, if y varies directly with x, then there is a constant k such that y = kx.

Below is a function to represent a direct variation relationship between y and x:

y = kx

where k is the constant of proportionality.

A real world example of a direct variation relationship is the relationship between the distance traveled by a vehicle and the time it takes to travel that distance.

If a car travels at a constant speed, then the distance it travels is directly proportional to the time it takes to travel that distance. In mathematical terms, we can write:

distance = rate × time

where the constant of proportionality (rate) is the speed of the car.

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The measure of angle ∠T found in the triangle  ΔRST found using the law of cosines is 127.3°.

What is meant by the law of cosines?

The law of cosines, commonly referred to as the cosine formula or cosine rule, is a relation in trigonometry that links the lengths of a triangle's sides to the cosine of one of its angles. It claims that we can determine the length of the third side of a triangle if we know the length of the first two sides and the angle between them.

If ABC is a triangle, then as per the statement of the law of cosines,  we have:

c = [tex]\sqrt{a^{2}+b^{2}-2 a b \cdot \cos \gamma}[/tex]

where,

c = length of side c

a = length of side a

b = length of side b

γ = angle opposite c

Given a  triangle,  ΔRST

The length of side r = 530 cm

The length of side s = 530 cm

The length of side t = 950 cm

According to the law of cosines,

t² =s² + r² - 2.s.r . cos T

950²  = 530² + 530² - 2 * 530 * 530  * cos T

902500  =  280900 + 280900 - 561800 * cos T

cos T = -0.6064

m∠T = 127.3°

Therefore the measure of angle ∠T found using the law of cosines is 127.3°.

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Total cost to build the ramp is $1467.4. Santiago’s has over budget to build the ramp.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

Here,

Area of 2 rectangles is

2(Length×Width)

= 2(20×12)

= 480 square feet

Area of small rectangle = 12×8.5

= 102 square feet

Area of 2 triangles = 1/2×Base×Height

= 1/2 ×20×8.5

= 85 square feet

Total area = 480+102+85

= 667 square feet

Total cost to build the ramp = 667×2.20

= $1467.4

Santiago’s total budget for the materials to build the ramp and the foam pit is $3,000.

Hence, Santiago’s has over budget to build the ramp.

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"Your question is incomplete, probably the complete question/missing part is:"

The material Santiago will use to build the ramp cost $2.20 per square foot. Find the total cost of materials for the ramp? All sides are; 21.7, 20, 12 for perimeter and 8.5 for the height.

Santiago’s total budget for the materials to build the ramp and the foam pit is 3,000. With his current design, will he be over budget or under budget, and by how much?

Answer:

Step-by-step explanation:

12

The following equations should be used to calculate the cylinder's surface area = SA = 2πr² + 2πrh. As a result, the suggested options do not include the correct approach.

Where h is the cylinder's height and r is the cylinder's radius.

The radius is equal to half of the diameter, or 1.6 feet, given that the diameter is 3.2 feet. And it stands 3.8 feet in height.

As a result, the following is the appropriate formula to get the cylinder's surface area:

SA is = 2.16 plus 2.16.3.8 square feet.

When we abbreviate the phrase, we get:

SA = 2.56 + 2.08 square feet

SA = 5.12 plus 12.16 square fee

SA = 17.28 square feet.

As a result, the suggested options do not include the correct approach.

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The surface area of the given cylinder is given by the equation:

    SA =  2π (1.6)² + 3.2π(3.8) square feet

What is meant by a cylinder?

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. One of the fundamental three-dimensional shapes in geometry is the cylinder, which has two distant, parallel circular bases. At a predetermined distance from the centre, a curved surface connects the two circular bases. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases.

The surface area of the cylinder is the sum of the area of the curvilinear surface and the areas of the top and bottom circular bases.

Now the area of the curved surface  = 2πrh

Area of bases = πr² + πr² = 2πr²

where,

  r = radius of the cylinder

   h = height of the cylinder

Given,

 r = 3.2 / 2 = 1.6 feet

h = 3.8 feet

Substituting,

Surface area SA = 2πrh + 2πr² = 2π * 1.6 * 3.8 + 2π (1.6)²

                                                =  2π (1.6)² + 3.2π(3.8) square feet.

Therefore the surface area of the given cylinder is given by,

    SA =  2π (1.6)² + 3.2π(3.8) square feet.

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Using the geometric mean theorem, the value of x is approximately 8.2.

The right triangle altitude theorem, also known as the geometric mean theorem, is a basic concept in geometry that connects the altitude of a right triangle to the two line segments it creates on the hypotenuse. According to the theorem, the altitude is equal to the geometric mean of the two line segments.

Using the theorem, we have:

14 = √(x * 24)

14² = 24x

196 = 24x

x = 196/24

x ≈ 8.2

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Ross achieved a higher sales target.

A fraction is a number which represents the part of a whole or collection of objects. It is in the from of [tex]\frac{a}{b}[/tex] where a represents the numerator part and the b represents the denominator parts.

A contact center provides incentives based on the number of sales achieved by its representatives.

Ross made 27 sales in 3 days.

Sales per one day =[tex]\frac{27}{3}=9.[/tex]

Mona secured 49 sales in one week

Sales per day =[tex]\frac{49}{7}=7[/tex]

Therefore, in one day sale of Ross is 9 and sale of Mona is 7.

Hence, Ross achieved a higher sales target.

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The total cost to put a new floor on both the court and its border is; $61776

The parameters given are;

Initial length = 84 ft

Initial Width = 46 ft

Now, since the court has a border that is 10 ft wide, it means that we will add 20 ft to the initial length and width to get the new measurements. Thus;

New length = 84 + 20 = 104 ft

New Width = 46 + 20 = 66 ft

Thus;

Area = 104 * 66

Area = 6864 sq.ft

Thus;

Total Cost = 6864 * 9

= $61776

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Noel delivered an average of 500 yards of ribbon per day from Tuesday to Monday.

The central value represents the typical or average value of all the numbers in the set.

From Tuesday to Friday, Noel delivered 350 yards of ribbon per day, a total of 4 days. So, the total length of ribbon that he delivered during this period is

=> 4 * 350 = 1400 yards.

From Saturday to Monday, he delivered 700 yards of ribbon per day, a total of 3 days. So, the total length of ribbon that he delivered during this period is

=> 3 * 700 = 2100 yards.

To find the average length of ribbon that Noel delivered per day, we need to find the total length of ribbon he delivered in both periods and divide it by the total number of days.

The total length of ribbon he delivered in both periods is

=> 1400 + 2100 = 3500 yards.

The total number of days is

=> 4 + 3 = 7 days.

So, the average length of ribbon that Noel delivered per day is

=> 3500/7 = 500 yards.

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Nvm. I got it wrong me self. Srry:(

Answer:

3

Explanation:

Based on the given conditions, formulate: 3

Cross out the common factor: 3

get the result:3

Answer: 3

Answer:

2$

Step-by-step explanation:

10/5=2

Expressions that are tested by the 'if' statement is called conditions.

A condition is an expression that evaluates to either 'True' or 'False', and it determines whether the code block within the 'if' statement is executed. The 'if' statement allows the program to make decisions and execute different codes based on whether the condition is 'true' or 'false'. For example, in Python, an 'if' statement might look like this:

if x > 10:

   print("x is greater than 10")

In this example, the condition being tested is 'x > 10', which will evaluate as 'True' or 'False' depending on the value of x. If the condition is 'True', then the code block within the 'if' statement (in this case, the print statement) will be executed. If the condition is 'False', then the code block within the 'if' statement will be skipped.

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Answer: C

Step-by-step explanation:

Answer:

Since the ratio of the altitudes of the two triangles ABC and DEF is 1:3, we can say that the altitude of triangle DEF is three times that of triangle ABC.

Let's assume the altitude of triangle ABC is h, then the altitude of triangle DEF is 3h.

Now, we know that the area of a triangle is given by the formula:

Area = (1/2) * base * height

Let's apply this formula to both triangles:

Area of triangle ABC = (1/2) * base * altitude

= (1/2) * 7cm * h

= 3.5h cm^2

Area of triangle DEF = (1/2) * base * altitude

= (1/2) * 7cm * 3h

= 10.5h cm^2

Since the two triangles are similar, their areas are proportional to the squares of their corresponding sides. That is:

Area of triangle ABC / Area of triangle DEF = (AB / DE)^2

Substituting the values, we get:

3.5h / 10.5h = (AB / DE)^2

1/3 = (AB / DE)^2

Taking the square root of both sides, we get:

AB / DE = 1 / sqrt(3)

AB = (1 / sqrt(3)) * DE

Now, we know that the sides of triangle ABC are 3cm, 5cm, and 7cm.

Let's assume that the sides of triangle DEF are a, b, and c.

Since the sides of the two triangles are proportional, we can write:

a / 3 = b / 5 = c / 7 = 1 / sqrt(3)

Solving for a, b, and c, we get:

a = 3 / sqrt(3) = sqrt(3) cm

b = 5 / sqrt(3) = (5 * sqrt(3)) / 3 cm

c = 7 / sqrt(3) = (7 * sqrt(3)) / sqrt(3) = 7 cm

Therefore, the measures of the sides of triangle DEF are sqrt(3) cm, (5 * sqrt(3)) / 3 cm, and 7 cm.

The statement that is true regarding "96 multiplied by 11/8" is: G. The product is greater than 96.

To find the product of 96 and 11/8, we can multiply these two numbers:

96 x 11/8 = (96/1) x (11/8)

= 1056/8

= 132

So the product is 132.

Now we can check which statement is true:

F. The product is less than 11/8. This statement is false, since 132 is greater than 11/8.

G. The product is greater than 96. This statement is true, since 132 is greater than 96.

H. The product is between 11/8 and 96. This statement is false, since 132 is greater than both 11/8 and 96.

I. The product is equal to 96. This statement is false, since we have calculated that the product is actually 132.

The statement that is true is G. The product is greater than 96.

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Answer:

x= 6

Step-by-step explanation:

3^3x = 9^9

3^3x = 3^(2×9)

3^3x = 3^18

3x = 18

3x/3 = 18/3

x = 6

Answer:

The marginal cost in this range is $0.50 per bouquet. This can be calculated by finding the difference in total cost of arranging 500 bouquets and 600 bouquets, which is $800, and dividing that by the difference in quantity of bouquets, which is 100. This gives a marginal cost of $0.50 per bouquet.

Answer:

The answer is 4×7×8 units³

Step-by-step explanation:

This is a really easy question. All you have to do is take a look at the prism and you see the height of 4 units, the width of 8 units, and the length of 7 units. To find the volume of a cube you have to multiply the Length, Width, and Height. Therefore, 7×8×4. Also, it doesn't matter the order of the numbers to multiply. Hope this helps!!

The required expression is 30 - 10√5 which is in the form a + b√5, where a = 30 and b = -10.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

The expression is given in the question, as follows:

(5-√5)²

Expanding the above expression,

(5)² + (√5)² - 2 × 5 × √5

25 + 5 - 10√5

30 - 10√5

Compare the above expression to the form a + b√5, and we get

a = 30 and b = -10

Thus, the required expression is 30 - 10√5.

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The equation 6x + 14x - 9 = 4( 5x + 1 ) has no solution.

Given the equation in the question;

6x + 14x - 9 = 4( 5x + 1 )

To solve the equation, first apply distributive property to remove the parenthesis.

6x + 14x - 9 = 4( 5x + 1 )

6x + 14x - 9 = 4 × 5x + 4 × 1

Multiply 4 and 5x

6x + 14x - 9 = 20x + 4 × 1

Multiply 4 and 1

6x + 14x - 9 = 20x + 4

Next, collect and add like terms.

Subtarct 20x from both sides

6x + 14x - 20x - 9 = 20x - 20x + 4

6x + 14x - 20x - 9 =  4

Add 9 to both sides

6x + 14x - 20x - 9 + 9 =  4 + 9

6x + 14x - 20x =  4 + 9

20x - 20x =  4 + 9

20x - 20x =  13

0 = 13

Therefore, there is no solution to the equation.

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