Maggie has decided to collect Hot Wheel cars. She is allowed to buy 15 cars a week with her allowance and she currently has 2 cars in her room. Identify
the rate of change, the initial value and write the function that best models the situation.
O Rate of Change: 2; Initial Value: 15; y = 2 + 15x
O Rate of Change: 2; Initial Value: 15; y = 2x + 15
O Rate of Change: 15; Initial Value: 2; y = 2x + 15
O Rate of Change: 15, Initial Value: 2; y = 15x + 2

Answer: 1. No, because figure 1 is 5 squares and figure 2 is 6 squares

Step-by-step explanation:

The height of the arch at a distance of 7.5 m from the center is 7m

It's important to keep in mind that a parabola has the usual form of y = a(x - h)2 + k, where (h, k) denotes the vertex and a determines the shape and vertical orientation. x and y are (100, 0) in. You are then provided with the parabola's equation.

What height of the arch, as measured from a point on the water 40 meters from the center of the arch, would sustain a bridge over a river?

The arch is 200 meters wide at water level and 80 meters tall at its tallest point

The peak of the arch might serve as the vertex and be located at position y0 on the y-axis if we wish to plot this on a graph or represent it in an equation

The equation of the parabolic arch is

x² = - 4ay

Lets take x and y for first case as (14, 30)

⇒ 14² = - 4a(30)

⇒ a = −49/30

Now we have a so lets put the formula for another variable to find height

Here, y = 7.5

​x² = - 4ay

⇒ ​x² - 4(-49/30)(7.5)

x = 7

Thus, The height of the arch at a distance of 7.5 m from the center is 7m.

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The value of x is 6 using logarithmic properties.

The power to which a number must be increased in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents). For instance, the logarithm of 100 in base ten is 2, since ten multiplied by two equals 100: log 100 = 2, since 102 = 100.

The Scottish mathematician John Napier reported his findings on logarithms in 1614. He was there to aid with the multiplication of quantities known as sines at the time.

Given,

Log2+ log3= logx

To find= We need to find the value of x

The value of log2=  0.301

The value of log 3= 0.477

Now, putting the value in the given expression, we get:

0.301+ 0.477= logx

logx= 0.778

Now, taking the antilog os=f x:

x= antilog(0.778)

x= 5.99=6

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The denominator of the formula for the variance of a sample is given as follows:

N - 1.

A fraction is a numerical representation of the division of the two terms x and y that composed the fraction, as follows:

Fraction = x/y.

The terms are named as follows:

The formula for the variance of a sample is given as follows:

[tex]s^2 = \frac{sum (X - \overbar{X})^2}{N - 1}[/tex]

Hence the denominator is the bottom term, which is of N - 1.

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Using relations in a right- triangle, the equation can be used to break for the measure of angle ABC is  tan x = 2.4/10

The relations in a right triangle are given as follows

The sine of an angle is given by the length of the contrary side to the angle divided by the length of the hypotenuse.

The cosine of an angle is given by the length of the conterminous side to the angle divided by the length of the hypotenuse.

The digression of an angle is given by the length of the contrary side to the angle divided by the length of the conterminous side to the angle.

For angle Alphabet = x, we've that

The length of the contrary side is of2.4 cm.

The length of the conterminous side is of 10 cm.

Hence, the equation is tan x = 2.4/10.

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The horizontal asymptote is y = X, and the vertical asymptotes are x = 2 and x = 1.

A curve is a continuous, smooth, and often repeating shape in the plane or in space. It is a geometric object that can be described mathematically by an equation or a set of points.

In mathematics, curves are used to model real-world phenomena and to study geometric and mathematical properties. For example, curves can be used to describe the shape of objects, the path of moving objects, or the graph of a mathematical function.

There are many types of curves, including lines, circles, ellipses, parabolas, hyperbolas, and spirals, among others. Each type of curve has unique properties and characteristics, and they are studied and used in different ways in different fields of mathematics and science.

The horizontal asymptotes are found by examining the degree of the numerator and denominator when x approaches infinity or negative infinity.

Since the numerator is of degree 3 and the denominator is of degree 2, the horizontal asymptote is y = X3 - x / x² – 3x + 2 = X.

For the vertical asymptotes, we look for the values of x that make the denominator equal to zero and the numerator either equal to zero or undefined.

The denominator x² – 3x + 2 = 0 has roots at x = 1 and x = 2.

At x = 1, the numerator x³ - x = 0, so the function has a hole at x = 1 and y = 0.

At x = 2, the function is undefined, so x = 2 is a vertical asymptote.

Thus, the horizontal asymptote is y = X, and the vertical asymptotes are x = 2 and x = 1.

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Picture - 1 from left representation shows what balloon Z resembles after each change occurs when the pressure is halved and the Kelvin temperature is halved.

we have relation ,

PV= nRT ,  from ideal gas law

V = nRT /P

when P is halved P becomes P/2 and when T is halved it becomes T/2

V= nR ( T/2) / ( P/2)

     = nRT

Thus volume is unchanged   hence correct representation is  same size balloon  i.e middle

2)  The pressure is 2.5 atm  surrounding balloon. This makes balloon contract  since pressure outside balloon is higher than pressure inside balloon.

Thus correct representation of change is smaller balloon i.e picture 1 from left

(The pictures are attached below )

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A frequency table is a simple tabular representation of the number of times a particular value or range of values appears in a data set.

It lists the values in one column and the corresponding frequencies in another column. For example, if we have data on the heights of a group of people, a frequency table could list the heights (in cm) in one column and the number of people with that height in the other column.

A frequency distribution is a graphical representation of the same information as a frequency table. It shows the number of occurrences of values in a data set by grouping the values into classes or intervals, and then plotting the frequency of each class or interval. For example, a histogram is a type of frequency distribution where the data is divided into equal-width intervals and the height of each bar represents the frequency of the data that falls within that interval.

A frequency table can be used for both qualitative and quantitative data, whereas a frequency distribution can only be used for quantitative data. This is because the classes or intervals used in a frequency distribution require a numerical representation of the data, which is not possible for qualitative data.

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John scored 110 points in total.

A equation is used to equate two expressions. For example -

4x + 4 = 7

Given is that John, scores 35 more than triple the amount of points than Amy. Amy scores 25 points.

The total points scored by john would be -

{p} = 3{a} + 35                                                        .... Eq { 1 }

{p} = 3 x 25 + 35

{p} = 110 points

Therefore, John scored 110 points in total.

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For the above system of equations 2x+4y+3z=11, 2y+5z=-9, x=11+6z,The value of y=-8, z=7/5, x=97/5.

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the connection between two expressions on opposite sides of the sign. It generally consists of one variable and one equal to symbol.

Here,

x-6z=11

2x+4y+3z=11

2y+5z=-9

x=11+6z

substitute and calculate,

y=-8

z=7/5

x=97/5

The value of y=-8, z=7/5, x=97/5 for the given system of equation: 2x+4y+3z=11, 2y+5z=-9, x=11+6z.

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You have to put the value of the variables in the given column. Then press the button to calculate to find the regression line.

What is the regression line?

The linear equation that best fits the points is linear regression.

There are various methods for selecting the best-fitting line, with ordinary least squares being the most popular (OLS). The dependent variable (Y) and the independent variables are related according to linear regression (X).

Based on the independent variables, the linear regression model calculates the dependent variable (DV) (IV, predictors).

Select the type of regression line

Step 1: First make the column

Step 2: Then input the value of the variables.

Step 3: Press shift + 0 to get the menu option.

Step 4: from the menu select regression line number.

Step 5: Get the equation of the regression line.

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The regression line can be calculated by finding the slope and intercept. The equation of the regression line is y = slope * x + intercept.

To calculate the regression line, we need to find the slope and intercept of the line. Let's denote the independent variable as x and the dependent variable as y. The given data can be represented as a set of (x, y) pairs:

(x1, y1), (x2, y2), ..., (xn, yn)

To calculate the slope, we need to calculate the following sums:

Using these sums, the slope can be calculated as:

slope = (nΣxy - ΣxΣy) / (nΣx^2 - (Σx)^2)

Next, we can calculate the intercept using the following formula:

intercept = (Σy - slopeΣx) / n

Once we have the slope and intercept, we can write the equation of the regression line as:

y = slope * x + intercept

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The discrete probability distribution of the number of successes in a series of n independent experiments is called the binomial distribution with parameters n and p in probability theory and statistics.

What is the binomial distribution?

The binomial distribution formula aids in determining the likelihood that "x" successes will occur in "n" separate trials of a binomial experiment. Recall that there are two possible outcomes for the statistics probability distribution known as the binomial distribution. The binomial distribution in probability theory has two parameters, n and p. When the probability distribution satisfies the following conditions, it becomes a binomial probability distribution. Each experiment may only yield two results, or results that can be reduced to two results. These results could result in success or failure. There must be a specific number of trails. Each trial's results must be distinct from one another.

Additionally, each trial's likelihood success rate must remain constant.

Using binomial probability formula,

k P(X = k)

0 0.0001

1 0.0020

2 0.0236

3 0.1355

4 0.3899

5 0.4489

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The required systolic pressure will be lower when the patient takes the blood pressure medication at 7 a.m. between the interval of 7 a.m. to 9 a.m.

A piecewise function is one that is constructed from pieces of different functions at different intervals.

Here,
A graph of the piecewise function is shown, from the graph it's clear that systolic pressure is low for the interval 5 < x < 9, such that the patient takes the medication at 7 A. M. So, corresponding to that required systolic pressure will be lower between 7 a.m. to 9 a.m.

Thus, the required systolic pressure will be lower when the patient takes the blood pressure medication at 7 a.m. is 7 a.m. to 9 a.m.

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By applying linear equation concept, it can be concluded that the number of stamps in the 25th month is 990 stamps

Linear equation is equations whose highest power of the variables is 1. The graph of a linear equation is a straight line.

y = mx + C where

m = Δy / Δx = slope of the line

C = constant

We have the following data:

Month    Number of stamps

   1                      30

   2                     70

   3                     110

   4                     150

   5                     190

As we look at the attached graph, this data is depicted as a linear graph. Thus we want to find the linear equation.

First, we calculate the m:

m = Δy / Δx

   = (70 - 30) / (2 - 1)

   = 40 / 1

   = 40

To find C, we pick one point, let say point (1,30) and input it into the equation:

 y = mx + C

30 = 40*1 + C

30 = 40 + C

 C = -10

Now we have the linear equation:

y = mx + C

y = 40x - 10

We want to know the number of stamps in the 25th month, so we input this value into the equation:

y = 40x - 10

   = 40*25 - 10

   = 1000 - 10

   = 990

Thus, the number of stamps in the 25th month is 990 stamps.

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The lateral Surface Area of ​​a Cylinder  is is 345  cm²  

What are solids ?

A three-dimensional object that is closed (which may, according to some terminology conventions, be self-intersecting). A solid is any constrained area of space that is bounded by surfaces, according to Kern and Bland (1948, p. 18). The sphere, cube, cone, and cylinder, as well as the polyhedra more broadly, are some of the most basic solids.

lateral Surface Area of ​​a Cylinder  is :

L= 2 × π × r × h

where, r = base radius,

and h = height of the cylinder

L= 2 × 3.14 × 4.9 × 11.2

=> L=  344.646  cm²

Nearest whole number: 345  cm²

The lateral Surface Area of ​​a Cylinder  is is 345  cm²  

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Answer:

X=. 1. X=. 2

Step-by-step explanation:

The first story (movie theater) has the equation 6(x+3)= 24. The equation for the juice story is 3(x+6)=24 . The x in the move theater story is the cost of each ticket. The x in the juice story is the amount of juice poured to each friend originally (before the extra 6 ounces). The solution to the movie theater story is 6((1)+3)=24. So x is one is the first story.In the juice story, 3((2)+6)= 24. So x is two. The solution tells me that in the movie theater story that each ticket cost 1 dollar. In the second story, it tells me that 2 ounces of juice where poured to each freind originally. So each freind got a total of 8 ounces of juice.

Step-by-step explanation:

I see only 2 stories and equations.

a.

6(x + 3) = 24

is for the first story (6 show tickets and snacks).

3(x + 6) = 24

is for the second story (juice for 3 friends).

b.

in the first story it is the price of one ticket to the show.

in the second story it is the original amount of juice each friend gets before adding 6 oz.

c. and d.

6(x + 3) = 24

6x + 18 = 24

6x = 6

x = 1

each ticket to the show was $1.

3(x + 6) = 24

3x + 18 = 24

3x = 6

x = 2

each of the 3 friends got first 2 oz of juice, before they each got additional 6 oz. so, ultimately, each friend got 8 oz.

The gallons of water used column should have four entries: 0, 20, 40, andTo plot the point, you need to plot the values from the table on a graph.

Time (minutes): 0, 2, 4, 6

Gallons of Water Used: 0, 20, 40, 60

Plot: (0, 0), (2, 20), (4, 40), (6, 60)

To complete the table, you need to fill in the time (minutes) and gallons of water used columns.

The time column should have four entries: 0, 2, 4, and 6.

The gallons of water used column should have four entries: 0, 20, 40, andTo plot the point, you need to plot the values from the table on a graph.

The point (0, 0) represents 0 minutes and 0 gallons of water used.

The point (2, 20) represents 2 minutes and 20 gallons of water used.

The point (4, 40) represents 4 minutes and 40 gallons of water used.

The point (6, 60) represents 6 minutes and 60 gallons of water used.

The complete question is :

A shower used 60 gallons of water in 6 minutes. Complete the table and plot the point.

Time (minutes): 0, 2, 4, 6

Gallons of Water Used: 0, 20, 40, 60

Plot: (0, 0), (2, 20), (4, 40), (6, 60)

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The measure of ∠K is 72°.

To find the measure of ∠K in ΔJKL, we can use the Law of Cosines. The formula is:

cos C = (a^2 + b^2 - c^2) / 2ab where C is the angle opposite the side of length c.

In this case,

Plugging in the values, we get:

cos C = (720^2 + 640^2 - 520^2) / 2 * 720 * 640

cos C = 0.4756

Finally, to find the measure of ∠K, we use the inverse cosine function:

∠K = cos^-1 (0.4756)

∠K = 72.22°

Rounding to the nearest degree, ∠K = 72°.

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In ΔJKL, j = 520 inches, k = 730 inches, and l=640 inches. Find the measure of ∠K to the nearest degree.

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To find C the Pythagorean formula is used which would be = 7.6

The formula for the Pythagorean theorem is given as follows:

c² = a²+b²

where;

a = 7

b = 3

C = ?

c² = 7²+3²

c² = 49+ 9

c² = 58

C= √ 58

C = 7.6

Therefore, when the Pythagorean formula is being used, the value of the missing side of the triangle = 7.6.

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The hypotenuse of the right triangle is:

C = 7.6

On the image we can see a right triangle where C is the hypotenuse of said triangle.

Remember the Pithagorean's theorem, it says that if A and B are the two legs of the right triangle, then C can be written as:

C = √(A² + B²)

Here we can see that:

A = 3

B = 7

Replacing that we will get:

C = √(3² + 7²) =7.6

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The rate of change for a health club is, 24.

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)

We have to given that;

A health club charges a $20 one-time sign-up fee and a monthly membership fee of $54 per month.

Hence, The equation to represents that the health club charges,

⇒ y = 24x + 54

Since, The general form of the slope - intercept equation is :

⇒ y = mx + c

Where, m = slope = rate of change in y per change in x

Therefore, By comparing the expressions, the slope of the cost function given is 24.

Hence, The rate of change = 24

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Answer:

We can solve for x by using logarithms.

9^(x + 10) + 3 = 92

9^(x + 10) = 89

Take the log base 9 of both sides:

x + 10 = log9(89)

x = log9(89) - 10

To find the value of log9(89), you can use a logarithm table or calculator.

The solution for x is:

x = log9(89) - 10

The expression is obtained on subtracting 4x + 6 from 7 + 2x is -2x + 1

Given the two expressions in the question;

( 4x + 6 ) and ( 7 + 2x )

To subtract  4x + 6 from 7 + 2x simply means ( 7 + 2x ) - ( 4x + 6 ).

Now, simplify

( 7 + 2x ) - ( 4x + 6 )

Distribute the negative sign to all the terms in the second expression.

( 7 + 2x ) -4x - 6

Now collect and add like terms

2x - 4x - 6 + 7

Add 2x and -4x

-2x - 6 + 7

Add -6 and 7

-2x + 1

Therefore, the resulting expression is -2x + 1.

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The perimeter of the rectangle ABCD is 22 cm.

What is the perimeter of a rectangle?

In order to find the perimeter or distance around the rectangle, we need to add up all four side lengths. This can be done efficiently by simply adding the length and the width, and then multiplying this sum by two since there are two of each side length.

Perimeter = (length+width)×2 is the formula for the perimeter.

The perimeter of a rectangle is the sum of the lengths of all four sides.

If the sides of a rectangle have lengths of 6 cm and 5 cm, then the perimeter can be calculated as follows:

6 cm + 6 cm + 5 cm + 5 cm = 22 cm

The perimeter of a rectangle with sides 6 cm and 5 cm is 22 cm (2 * 6 cm + 2 * 5 cm = 22 cm).

Hence, the perimeter of the rectangle ABCD is 22 cm.

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The surface area of a cone is 103.6 in².

Option B is the correct answer.

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

We have,

Cone:

Diamter = 6 in

Radius = 3 in

Slant height.

s = 8 in

Now,

The surface area of a cone.

= πrs + πr²

= πr (s + r)

= 3.14 x 3 (8 + 3)

= 3.14 x 3 x 11

= 103.62 in²

Thus,

103.62 in² is the surface area of a cone.

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The equation  models the problem is 54

The given parameters that will help us to determine the number are

During the first weekend of December, 43 pine trees were sold. The farm sold 97 trees in all that weekend.

There are two kinds of trees

Tir and Pine.  On the farm and in the weekend as 97 trees were sold with 43 pine tress.

Let f represent fir trees

This implies that f+43 = 97

⇒f= 97-43

f=54 tress

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The solution is (-5,0), the interval in which the function is increasing.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

In case when you tracking the finger across the line, at which there is an increase or decrease in y axis so this is we called intervals. Moreover, the interval notation is also necessary as it depicts the beginning and ending points. In this, the first number denotes the minimum number while the second number denotes the maximum number

For Decreasing:

(-8,-5)

(4,8)

For Increasing:

(-5,0)

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Answer: 30 ft

Let's assume the original dimension of the carpet was LxW. Now let's have Lin cut a 1 foot wide strip from the length. That gives her a strip that's L feet long. She then cuts a strip from the other side, giving her another strip that L feet long. She then cuts a strip from the width, giving her a 3rd strip that's (W-2) feet long. And finally, she cuts a 4th strip that's also W-2 feet long. So the total length of all those strips is L + L + W - 2 + W - 2 = 2L + 2W - 4 feet long. And since all the strips are 1 foot wide, they cover 2L + 2W - 4 square feet. So: 2L + 2W - 4 = 26 2L + 2W = 30 Now the original perimeter of the carpet is 2L + 2W, therefore the original perimeter is 30 feet.

The website is advertising a 46% discount on the jacket, meaning that Farah will pay 46% less than the original price if she decides to buy it now.

A discount is a reduction in the original price of an item, allowing the customer to purchase it for less than the original price.

To calculate the discount mathematically, we can use the following formula:

Discounted price = Original price * (1 - discount percentage)

Let's assume the original price of the jacket is P dollars.

The discount percentage is 46%, which can be written as a decimal 0.46. To find the discounted price, we need to multiply the original price by (1 - discount percentage), which is (1 - 0.46) = 0.54.

So, the discounted price after the 46% saving will be P * 0.54 dollars.

In other words, Farah will pay 0.54 times the original price, P, to buy the jacket with the advertised 46% saving.

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