14. The function f(x)=√x+2-3 is moved 3 units left and 1 unit up. Which of
the following is the correct equation for the new function?

The constant of variation for the subscription cost based on the number of weeks is $7.5.

What is Slope?

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

The straight line passes through the point

(4, 30), (8, 60) and (12, 90)

so, slope of line passing through the points

m = (60- 30)/ (8-4)

m = 30/ 4

m = 7.5

Thus, the constant of variation is $7.5.

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When two positive fractions are multiplied the product is always less than the factors.

Fraction is defined as the number of compositions that constitutes the Whole. In mathematics, fraction is a number that is expressed as a proportion, as 1/2 or 2/3. The number on the bottom represents the total number of parts of one unit, while the number on the top is the portion of the unit being considered.

here,

Let's assume an example,

1 / 8 × 1 / 9 = 1 / 72

So as we see in the above example,

1 / 8 and 1/ 9 is a positive fractions and their product is less than their own factors.

Thus, when two positive fractions are multiplied the product is always less than the factors.

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Jacinta's pattern is correct for question A.

Jacinta's pattern is not correct for question B.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

We have two types of fractions.

Proper fraction and improper fraction.

A proper fraction is a fraction whose numerator is less than the denominator.

An improper fraction is a fraction where the numerator is greater than the denominator.

Example:

1/2, 1/3 is a fraction.

3/6, 99/999 is a fraction.

1/4 is a fraction.

We have,

Jacinta's:

Fractions are 1/3 and 1/5 (say).

Product.

= 1/3 x 1/5

= 1/15

Now,

1/15 < 1/3

1/15 < 1.5

For Question A:

We can assume that,

The fractions are 1/3 and 3/4.

Their product.

= (1/3) x (3/4)

= 3/12

= 1/4

1/4 < 1/3

1/4 < 3/4.

So,

Jacinta's pattern is correct.

For Question B.

The fractions are 2/5 and 4/7.

Their product.

= (2/5) x (4/7)

= 8/35

We see that,

8/35 < 2/5

8/35 >  4/7

So,

Jacinta's pattern is not correct.

Thus,

Jacinta's pattern is correct for question A.

Jacinta's pattern is not correct for question B.

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The complete question.

A) The two fractions are 1/3 and 3/4

B The two fractions are 2/5 and 5/7

Answer:

56

Step-by-step explanation:

The sequence types are (a) arithmetic seqience and (b) geometric seqience

a) an annual raise of $3,500

Given that the annual rase ie $3500

This is an arithmetic seqience

And it means that there will be an addition of $3500 in the salary each year

So, we have

Common difference = 3500

b) an annual raise of 5% of his current salary.

Given that the annual rase is 5% of the current salary

This is a geometric seqience

And it means that the raise would be 5% of previous salary

So, we have

Common ratio = 1.05

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The number of students that have veggies as a snack is equal to 51 students.

In Mathematics, a circle graph is sometimes referred to as a pie chart and it can be defined as a type of graph that is used for the graphical representation of the proportional relationship between each part to a whole, especially by dividing a circle into various sectors or sections.

Since there are 300 students at York Middle School, the number of students that have veggies as a snack can be calculated as follows;

Number of students that had veggies = 17/100 × 300

Number of students that had veggies = 0.17 × 300

Number of students that had veggies = 51 students.

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A two-column table method used to prove that the segments of the triangle are proportional, AE/EC = BD/DC, can be presented as follows;

Statement [tex]{}[/tex]                                       Reasons

1. AD bisects ∠BAC[tex]{}[/tex]                         Given

2. AE = ED     [tex]{}[/tex]                                   Given

3. ∠BAD ≅ ∠DAE [tex]{}[/tex]                            Definition  of bisected angle ∠BAC

4. ΔADE is an isosceles Δ [tex]{}[/tex]              Definition of isosceles triangle

5. ∠ADE ≅ ∠DAE [tex]{}[/tex]                            Base angles of an isosceles triangle

6. AB ║ DE [tex]{}[/tex]                                      Converse of alternate int. ∠ theorem

7. AE/EC = BD/DC [tex]{}[/tex]                           Thales theorem

A proportional relationship is one in which the elements of each ordered pair in the relationship are in the same proportion.

The details of the reasons used to prove the proportionality of the segments of the triangle are presented as follows;

Definition of bisected angle ∠BAC

An angle is bisected by a segment that divides it into two angles of the same measure.

Definition of isosceles triangle
An isosceles triangle is a triangle that has two sides that are congruent, or which have the same length.

Base angles of an isosceles triangles

The base angles of an isosceles triangle are congruent.

Converse of the alternate interior angle theorem

The converse of the alternate interior angles theorem states that if the alternate interior angles formed between two lines and a transversal are congruent, then the lines are parallel

Thales theorem

The Thales theorem states that a line drawn parallel to one of the sides of a triangle, such that it intersects the other two sides, then the line divides the other two sides proportionately.

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Plotting the relationship between the number of hours studied and exam results reveals a negative correlation curve, where the exam results get worse as the number of hours studied rises.

The point (10,70) would be plotted on the negative correlation curve, for instance, if a student spent 10 hours studying and received a 70 on their exam. A downward sloping negative correlation curve would result as study time increased and exam score decreased. A graph illustrating the relationship between two variables, where an increase in one variable is accompanied by a drop in the other, is called a negative correlation curve. Numerous various types of situations, such as the amount of hours studied and exam results, might demonstrate this type of link. Exam scores typically decline as the amount of study time increases.

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The minimum number of rides Scott has to go on is 7 or more rides.

What is inequality ?

An inequality is a mathematical statement that compares two quantities, expressing that one is greater than, less than, or equal to the other. Inequalities are often represented using inequality symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

According to the question:

Let's start by finding an expression for the total cost of each amusement park in terms of the number of rides, x. For Amusement Park A, the total cost is:

Total cost for Amusement Park A = 40 + 2.5x

This is because there is a $40 entry fee plus $2.50 for each ride.

For Amusement Park B, the total cost is:

Total cost for Amusement Park B = 30 + 4x

This is because there is a $30 entry fee plus $4.00 for each ride.

To find the minimum number of rides Scott has to go on so that the total charge at amusement park A costs less than the total charge at amusement park B, we can set up an inequality comparing the total cost of the two amusement parks:

40 + 2.5x < 30 + 4x

This inequality is saying that the total cost for Amusement Park A is less than the total cost for Amusement Park B. We want to solve for x, which represents the minimum number of rides that Scott has to go on to make Amusement Park A cheaper than Amusement Park B.

To solve for x, we can simplify the inequality:

40 + 2.5x < 30 + 4x

10 < 1.5x

6.67 < x

So the minimum number of rides Scott has to go on to make Amusement Park A cheaper than Amusement Park B is 7 (rounded up from 6.67). Therefore, if Scott goes on 7 or more rides, Amusement Park A will be cheaper than Amusement Park B.

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The perimeter of the original parallelogram is 22/9 * √3

The vertices of the parallelogram are A, B, C, and D, with AB parallel to CD and AD parallel to BC.

The parallel lines intersect the sides of the parallelogram at E, F, G, and H.

The side length of the equilateral triangle is s.

The three regions have the same area, hence, the area of each region is 1/3 of the total area of the parallelogram.

Let's the area of the parallelogram as A.

The area of the equilateral triangle is (s²√3)/4

This area is one-third of A

(s²√3)/4 = A/3

s² = 4A/(3√3)

Considering the whole parallelogram;

AB is parallel to CD, hence, triangle AEF is similar to triangle BGF

Also, AD is parallel to BC, hence, triangle ADE is similar to triangle BCF.

AE/EB = BF/FG AD/DE

AE/EB = BC/CF

Expressing AE, BF, AD, and BC in terms of s:

AE = s/3 (perimeter of the equilateral triangle is 1)

EB = 2s/3

BF = 2s/3

FG = s/3

AD = (2s + 2EB)/3

AD = (2s + 4s/3)/3

AD = 10s/9

DE = (2s + 2AE)/3

DE = (2s + 2s/3)/3

DE = 8s/9

BC = (2s + 2FG)/3

BC = (2s + s/3)/3

BC = 7s/9

CF = (2s + 2BF)/3

CF = (2s + 4s/3)/3

CF = 10s/9

Now we can find the perimeter of the parallelogram:

Perimeter = 2(AB + AD)

Perimeter = 2(EB + BC)

Perimeter = 2(2s/3 + 7s/9)

Perimeter = 4s/3 + 14s/9

Perimeter = (22s/9)

Substituting s² = 4A/(3√3) from the earlier equation, we get:

Perimeter = (22/9)√3

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The probability of Halston choosing two pieces of fruit that are not bananas is 69 %

First, find the total number of fruit :

=   3 + 4 + 2

= 9 fruit

The probability of picking a fruit that is not a banana the first time is :

= ( 3 + 4 ) / 9

= 7 / 9

The probability of picking a fruit that is not a banana the second time is :

= ( 3 + 4 - 1 ) / 9

= 6 / 9

The probability that two fruits are picked that aren't bananas is:

= 7 / 9 x 6 / 9

= 69 %

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Answer:

2(x-4)

Step-by-step explanation:

2 is common and (x-4) is the leftover.. simple as that.

Answer:

Step-by-step explanation:

A surface analysis chart is a type of weather map that displays information about the current pressure and wind patterns over a particular region. The chart provides a snapshot of the weather conditions at a specific point in time and helps meteorologists to identify and track the location, movement, and development of high- and low-pressure systems, fronts, and other weather features.

The surface analysis chart typically shows a map of the Earth's surface with various meteorological symbols and information, including isobars (lines of equal pressure), fronts (boundaries between different air masses), and wind direction and speed. The chart may also include information about temperature, precipitation, and cloud cover.

Surface analysis charts are used in weather forecasting, air traffic control, and other applications where an understanding of current weather conditions is important. They provide important information for short-term weather forecasting, such as predicting the location of fronts and the development of thunderstorms, and for long-term weather planning, such as determining the most suitable routes for shipping or aviation.

Answer:30

Step-by-step explanation:

use the word Pemdas

P-parenthesis

e-exponent

m-Multiplication

d-divide

a-Add.

s-Subtract.

Answer:

108

Step-by-step explanation:

5^2 + 45 - 67 + 15x                     when  x = 7

= 5^2 + 45 - 67 + 15(7)

= 25 + 45 - 67 + 105

= 70 - 67 + 105

= 3 + 105

= 108

So, the answer is 108

Answer:

Uncle Mike was 7 times as old as Sally 17 years ago.

Step-by-step explanation:

Let's call Uncle Mike's current age "x."

Sally is 12 years old, so x = 12 * 3 = 36 years old.

We are looking for years that must pass before Uncle Mike is only twice as old as Sally. So we need to find the age when x = 2 * (12 + n), where n is the number of years that have passed. Solving for n:

36 = 2 * (12 + n)

36 = 24 + 2n

12 = 2n

n = 6

So, six years must pass before Uncle Mike is only twice as old as Sally.

To find out how many years ago Uncle Mike was 7 times as old as Sally, we need to find the age when x = 7 * (12 - m), where m is the number of years ago. Solving for m:

36 = 7 * (12 - m)

36 = 84 - 7m

120 = 7m

m = 17

So, Uncle Mike was seven times as old as Sally 17 years ago.

The most appropriate measure of center is median.

option B.

The choice of measure of center (i.e., the most appropriate way to summarize the "typical" value of a dataset) depends on the distribution of the data and the research question being addressed. In general, the most commonly used measures of center are the mean and the median.

The mean is the arithmetic average of a dataset, and is often used as the measure of center for datasets that follow a normal or symmetrical distribution, where the data are roughly evenly distributed around a central value.

The median, on the other hand, is the middle value of a dataset when the values are arranged in order from smallest to largest.

For the given data, it is not evenly distributed but it is arranged from the smallest to the largest, so we can use median as the most appropriate measure of center.

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A conversion factor is a mathematical expression that is used to convert a quantity from one unit of measure to another. It is a ratio that expresses the relationship between two different units of measurement.

There are many conversion factors used to convert one unit of measure to another. Here are some common conversion factors that you may find useful:

1 inch = 2.54 centimeters

1 foot = 0.3048 meters

1 mile = 1.609 kilometers

1 pound = 0.4536 kilograms

1 ounce = 28.35 grams

1 gallon = 3.785 liters

1 liter = 1000 milliliters

1 meter = 100 centimeters

1 kilometer = 1000 meters

1 square meter = 10.764 square feet

1 cubic meter = 35.315 cubic feet

1 atmosphere = 101.3 kilopascals

These are just a few examples of the many conversion factors that are used in various fields of science, engineering, and everyday life. It's important to know and use the appropriate conversion factor when converting units of measure to ensure accurate and meaningful results.

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Answer:

the answer is number of orange marble/number of times

which might be 1/12 because you didn't specify

Answer:

.28

Step-by-step explanation:

you subtract Lucas's from karim's hight wich is .56 then devid in by 2 wich is .28

we can conclude that 2.2 is less than 14/4.

what is fraction ?

A fraction is a mathematical representation of a part of a whole or a ratio between two quantities. It is typically represented as a top number (numerator) divided by a bottom number (denominator), separated by a horizontal line.

For example, the fraction 3/4 represents three parts out of four equal parts of a whole. The numerator (3) represents the number of parts, while the denominator (4) represents the total number of parts that make up the whole.

According to the question:
To compare 2.2 and 14/4, we can convert 14/4 to a decimal:

14/4 = 3.5

Now we can see that 2.2 is less than 3.5. Therefore, we can say that:

2.2 < 14/4

Another way to compare them is to convert both numbers to a common denominator. In this case, the common denominator of 2.2 and 14/4 is 10:

2.2 = 22/10

14/4 = 35/10

Now we can see that:

22/10 < 35/10

Therefore, we can conclude that 2.2 is less than 14/4.

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The surface area of the rectangular prism is 174 in²

A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism.

Given is a net for a rectangular prism, we need to find the surface area of the rectangular prism,

We know that,

The surface area of the rectangular prism = 2(lxb+bxh+hxl)

Length = l, height = h and b = breadth

Therefore, here we have, l = 9 in, b = 3 in and h = 5 in

Surface area = 2(9x3+3x5+5x9)

= 2(27+15+45)

= 2x87

= 174 in²

Hence, the surface area of the rectangular prism is 174 in²

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The number of chocolates that Steve have left is 4848 - 88 chocolates

Algebraic expressions are expressions having a composition of terms, variables, coefficients, factors and constants.

They are also composed of mathematical operations, such as;

From the information given, we have that;

Then, the number of chocolates he has is 4848 - 88

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Answer: The x-intercepts of the line are points where the y-coordinate is equal to 0. The x-intercepts of this line are (-2, 0) and (3, 0). The y-intercept is the point where the x-coordinate is equal to 0, which in this case is (0, 4).

Step-by-step explanation:

If you can only pick one answer, the most correct choice would be (d) all real numbers up to and including 2, and any other values for which we have data.

This choice is the most general and inclusive, as it covers all possible values of time, including non-integer values, and any other values for which we have data on the population of E. coli bacteria.

However, if the answer choices are restricted to the given options, the most appropriate answer would be (c) all integers up to and including 2, and any other values for which we have data, since the given table only provides data for integer values of time up to 2 hours.

Answer:

Step-by-step explanation:

At a simple annual interest rate of 3%, the following formula might be used to determine the annual interest for a $4200 principal:

Interest is calculated as follows: Principal * Rate * Time

Where,

Capital = $4200

Rate = 3% (expressed as a decimal by dividing by 100) (expressed as a decimal by dividing by 100)

t = one year

When we enter the values, we obtain:

Interest is equal to $4200 multiplied by 0.03 times one.

Therefore, $126 would be the annual interest for a $4200 principal at a basic annual interest rate of 3%.

The EAN-13 code of Mr. Chips Nacho Cheese Flavor (100 g) 4-800016-653094 is valid.

To check the validity of the EAN-13 barcode, we need to perform a computation based on the numbers in the code. The EAN-13 code consists of 13 digits, where the first digit represents the number system, the next five digits represent the manufacturer code, the following five digits represent the product code, and the last digit is the check digit.

The check digit is calculated based on the previous 12 digits using a specific algorithm.

For the given EAN-13 code 4-800016-653094, we can extract the previous 12 digits as 480001665309. To calculate the check digit, we need to multiply the first, third, fifth, etc. digits by 3, and the second, fourth, sixth, etc. digits by 1, and then sum these products. In this case, the calculation is as follows:

(4x3) + 8 + (0x3) + 0 + (0x3) + 1 + (6x3) + 6 + (5x3) + 3 + (0x3) + 9 = 74

The check digit is then the smallest number that, when added to the sum above, results in a multiple of 10. In this case, the check digit is 6, since 74 + 6 = 80, which is a multiple of 10.

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The binary representation of the number 4 is 101, which is a three-digit binary number where leftmost digit represents the MSB and the rightmost digit represents the LSB.

The binary fraction, 0.1, now has 1 added to it because the outcome is 1. The representation is finished because there is zero in the last decimal place of the number.

To convert 10 to binary, we can use the following steps:

Divide the decimal number 10 by 2. The remainder is 0, while the quotient is 5.

Write the remainder (0) as the least significant bit (LSB) of the binary representation.

To Divide the quotient (5) by 2. The remainder is 1, while the quotient is 2.

Write down the remainder (1) as the next bit in the binary representation.

As a result, 4 is represented in binary as 101

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The correct equation to gives the proportional relationship of the graph is,

⇒ y = 6x

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The graph is shown in figure.

Now, Let two points on the graph of line are (2, 12) and (4, 24).

Hence, The equation of line given the proportional relationship of the graph.

Thus, The equation of line is,

⇒ y - 12 = (24 - 12) / (4 - 2) (x - 2)

⇒ y - 12 = 12/2 (x - 2)

⇒ y - 12 = 6 (x - 2)

⇒ y - 12 = 6x - 12

⇒ y = 6x

Thus, The correct equation to gives the proportional relationship of the graph is,

⇒ y = 6x

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