Caleb earns points on his credit card that he uses toward future puchases. He earns four points per dollar spent on flights, two points per dollar spent at hotels,and one point per dollar spent on all other purchases. Last year, he charged a total of $9,480 and earned 14,660 points. The amount of money spent on flights was $140 more than twice the amount of money spent on hotels. Find the amount of money spent on each type of purchase.

The roots of the quadratic equation are 3/2 and 2.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

2x² - 7x + 6

We can find the roots by middle-term factorization.

2x² - (4 + 3)x + 6 = 0

2x² - 4x - 3x + 6 = 0

2x(x- 2) - 3(x - 2) = 0

We have,

2x - 3 = 0 and x - 2 = 0

Now,

2x = 3

x = 3/2

x - 2 = 0

x = 2

Thus,

The roots are 3/2 and 2.

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Answer:

Point-slope form: y + 2= 0.5(x + 3)

Slope-intercept form: y = 0.5x - 0.5

Step-by-step explanation:

The vertical asymptote of a function can be determined by setting its denominator equal to zero (0) and solving for x.

The horizontal asymptote of a function can be found by determining the degrees of the numerator and denominator.

In Mathematics, an asymptote can be defined as a line which the graph of a given function approaches but would never touch. Additionally, the vertical asymptote of a function simply refers to the value of x which makes its denominator equal to zero (0).

In order to graph any rational function, you should determine the values for which it is undefined. This ultimately implies that, a function is considered as undefined when the value of the denominator is equal to zero, which represents vertical asymptote lines.

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The expression b/a is equivalent to the given expression b⁻²/ab⁻³ when a≠ 0 and b ≠ 0. So, option D is correct.

The two or more expressions are said to be equivalent expressions if their value is the same even if they look different.

This is the same concept as equivalent fractions.  

The given expression is b⁻²/ab⁻³.

This expression is a fraction.

Simplifying the given expression:

b⁻²/ab⁻³

we know a⁻ⁿ = 1/aⁿ

So, we can write b⁻² = 1/b² and b⁻³ = 1/b³

Then, b⁻²/ab⁻³ = (1/b²)/a(1/b³)

⇒ b⁻²/ab⁻³ = 1/b² × 1/a × b³ = b × 1/a

∴ b⁻²/ab⁻³ = b/a

Thus, the equivalent expression for the given expression is b⁻²/ab⁻³ = b/a.

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The weight of Y = 108 pound and weight of P is 27 pound

What does the math ratio mean?

Definitions: An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)

Given that :

A = 36 pound

A:P =4:3

so when A is 36 = 4*9

then P is 3*9 = 27

Hence the weight of P is 27 pound

Now we have Y:A = 9:3

when A = 36 = 3*12

Then Y is 9*12 = 108

Hence weight of Y is 108 pound

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Answer:

The answer is: Acute.

Step-by-step explanation:

All sides of a equilateral triangle are 60 degrees, meaning it is acute.

The sum of the first 7 terms of the following series is 52

'A geometric sequence is a sequence where every term has a constant ratio to its preceding term. A geometric sequence with the first term a and the common ratio r and has a finite number of terms.'

According to the given problem,

Sequence = 32,40,50

Let the common ratio be r,

Let the first term of the sequence be a,

⇒ a × r = second term

⇒ 32 × r = 40

⇒ r = 40/32

⇒ r = 5/4

We know,

Sum of n number of terms in a geometric sequence can be represented by,

sn=a(1-[tex]r^{7}[/tex])/1-r

⇒ [tex]s_{7}[/tex] =32(1 - (5/4)[tex]^{7}[/tex]/1 - 5/4

⇒ [tex]s_{7}[/tex] = 32 (1 - (5/4)[tex]^{7}[/tex]/3/5

⇒ [tex]s_{7}[/tex] = 5*32(1 - (5/4)[tex]^{7}[/tex])/3

⇒ [tex]s_{7}[/tex] = 160(0.972)/3

⇒ [tex]s_{7}[/tex] = 156/3

=52

Hence, we can conclude, the sum of the first 7 terms of the geometric sequence is 52

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Answer: between 5 and 6

Step-by-step explanation: The square root of 5 is 25 and the square root of 6 is 36 . Hence, the square root of 33 lies between 5 and 6.

When the null hypothesis is rejected, the F-ratio and probability of rejection both rise.

The F-ratio is calculated using the formula F = variance between treatments/variety within treatments. An increase in the numerator will raise the F-ratio, while a reduction in the denominator will raise it even further. The probability of rejecting the null hypothesis rises with increasing F.When the null hypothesis is rejected, the F-ratio and probability of rejection both rise.

The null hypothesis for an ANOVA test is that the means of the different groups are equal. If the F-ratio is high enough (i.e., if it is significantly different from 1), then it is likely that the means of the different groups are indeed different. Therefore, if the variance between treatments increases and the variance within treatments decreases, then the F-ratio will be higher, and the likelihood of rejecting the null hypothesis will be greater.

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For a given discrete probability distribution, The random variable also contains discrete values, The mean and standard deviation are computed in terms of Expected values E(X).

The mathematical formalization of a number or object that is subject to chance events is known as a random variable. It is a function or mapping between a space of potential outcomes, commonly real numbers, to a space of measurement.

The arithmetic mean, also known as the arithmetic average or simply the mean or average, is the sum of a set of numbers divided by the total number of numbers in the set. The collection frequently consists of a series of findings from a survey, experiment, or observational study.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

For discrete probability distribution with P(x) as the probability of the event 'x'.

Mean = E(X) = x*P(x).

Variance = [tex]E(X^{2})-(E(X))^2[/tex]

standard deviation = [tex]\sqrt {Variance}[/tex]

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In order for measuring devices to produce correct findings, they must have zero error. Zero error also makes it possible to determine if an instrument is functioning properly or not.

Instruments used by researchers and practitioners to assist in the assessment or evaluation of subjects, clients, or patients are known as measurement tools. From physical functioning to psychosocial welfare, the tools are used to assess or gather data on a number of aspects.

Electrical instruments are one of three categories for measuring devices. Instrument for electronics. a mechanical instrument.

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Answer:

d. (2,1) and (4,2)

Step-by-step explanation:

Slope is rise/run or (y2 - y1) / (x2 - x1)

We see option D, the y increase by 1, and the x increase by 2

So, the slope of this equation is 1/2, and it matches our question.

So, D is the answer!

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Answer:

d. (2,1) and (4,2)

y = 1/2x

2y = x

x = 2y

CHECKING

x = 2y        (substitute (2,1) and (4,2)

2 = 2(1)

2 = 2          correct

x = 2y

4 = 2(2)

4 = 4         correct

Step-by-step explanation:

we can draw in finite number circle from one point. so there are n number of possibility to draw circle from on given single point.

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.

Area of circle =  

[tex]\pi r^2\\r = 10\\A = 3.14 X 20 X 20\\A = 628unit sq\\[/tex]

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Answer:

$16.50

Step-by-step explanation:

y=mx+b

y is total cost, m is the miles, x is the cost per mile driven, and b is the pickup charge.

y=(7 miles x $2) + $2.50

y= $16.50

Answer:

Step-by-step explanation:

y=(7 miles x $2) + $2.50

y= $16.50

The formula for a horizontal line at y=4 is as follows: There is no slope. 4.0 is the y-intercept.

What are the Slope and intercepts ?

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

The slope expresses how quickly the dependent variable changes when the independent variable changes. The Greek capital letter D or D is frequently used by mathematicians and economics to represent change. Slope contrasts the change in the vertical axis, y, with the change in the horizontal axis, x.

On the x-axis, negative numbers are below the origin, and on the y-axis, they are to the left of the origin. If the x-value is negative, begin at the origin and go to the left; if the y-coordinate is negative, move downward.

Line graphs, also known as XY graphs, are used to visually represent data (the outcomes of an experiment) in order to demonstrate the link between various factors, such as the severity of the disease and time.

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2 × 3 × 2 can be written as 2 × 6, so the answer is 6/1, which is an equivalent fraction to 6.

We can solve this problem by converting the expression into a fraction. First, we need to multiply 2 and 3 together, which gives us 6. Then, we need to multiply this result by 2, so we get 12. Finally, we need to express this result as a fraction. To do this, we put the numerator (12) over the denominator (1). So, the answer is 12/1, which simplifies to 4/32 × 3 × 2 can be written as 2 × 6, so the answer is 6/1, which is an equivalent fraction to 6

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The value of the account in 2020 is given as $8622.86.

The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.

The amount of one interval of time becomes the principal to the next one.

Suppose in 2005 t = 0.

Then, in the year 2020 t = 15.

Now, the given question can be solved by finding the Amount using the expression as below,

P(1 + r/100)ⁿ

Where p, r and n are the principal, rate and time for the compounding.

Substitute all the corresponding values to obtain,

A = 5000(1 + 3.7/100)¹⁵

   = 5000 × 1.037¹⁵ = 8622.86

Hence, in 2020 the money invested in the account becomes as $8622.86.

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If the real estate agent's average weekly sales are $850 in the city and $1340 in the suburbs, then her total average weekly sales are $850 + $1340 = $2190.

The standard deviation of her weekly sales in the city is $260, and the standard deviation of her weekly sales in the suburbs is $390. If the sales in the city and the suburbs are independent, then the standard deviation of her total weekly sales is the square root of the sum of the squares of the standard deviations of her weekly sales in the city and the suburbs, which is the square root of $260^2 + $390^2 = $67600 + $152100 = $219100. This is equal to $468.

Therefore, the mean and standard deviation of the real estate agent's total weekly sales are $2190 and $468, respectively.

Additive inverse of 16 is -16.

Multiplicative Inverse of 16 is 1/16.

To produce a result equal to 0, add the original number and the additive inverse by simply reversing the sign of the integer. On the basis of negation of the original number, the characteristics of additive inverse are listed below. For instance, if x is the starting number, then -x is x's additive inverse.

A multiplicative inverse or reciprocal for a number x is a number that, when multiplied by x, produces the multiplicative identity, or 1. It is represented by 1/x or x/1. A fraction a/b has a multiplicative inverse of b/a. Divide 1 by the real number to obtain the multiplicative inverse of the number.

A function that "undoes" another function is called an inverse. In other words, if f(x) generates y, then y entered into the inverse of f creates x. An invertible function is one that has an inverse, and the inverse is indicated by the symbol [tex]f^{-1}[/tex].

Additive inverse of 16 is -16.

Multiplicative Inverse of 16 is 1/16.

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The given data is used to obtain the equation as y = x - 2 and the table and graph has been drawn clearly.

A straight line can be written in the slope-intercept form as, y = mx + c.

In order to obtain the slope, the ratio of the difference of the coordinates are taken and c is the y-intercept which can be found by substituting x = 0 in the equation.

The data is given as below,

slope = 1 and y-intercept = -2.

The equation, graph and table for the given data can be formed as follows,

(a) The slope-intercept equation is y = mx + c, where m is the slope and c is the y-intercept.

Substitute the corresponding values to obtain,

y = 1 × x + (-2)

  = x - 2

(b) The graph for the given equation is plotted below as,

(c) The table for the given equation can be formed with different values of x and y as below,

y = x - 2

Substitute x = 0 to get y = -2, x = 1, y = -1 and x = 2, y= 0.

Now, the table can be formed as below,

Hence, the equation is given as y = x - 2 and the graph and table for the equation is drawn properly.

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In the inequality 3x + 1 ≤ 4 at x = {1, 0, -1, -2, -3} all the values are satisfied therefore, the graph matches with this inequality.

What is Linear Inequality?

A linear inequality is a mathematical inequality that incorporates a linear function. A linear inequality contains one of the inequality symbols. It displays data that is not equal in graph form.

Solution:

To find the answer we need to put the values of x in options

3x + 1 ≤ 4

Putting x = {1, 0, -1, -2, -3}

At x =  1

3*1 + 1 ≤ 4

At x = 0

3*0 + 1 ≤ 4

At x = -1

3*-1 + 1 ≤ 4

At x = -2

3 * -2 + 1 ≤ 4

At x = -3

3*-3 + 1 ≤ 4

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Answer: yes

Step-by-step explanation: it is a 2 dimensional shape if it was 3d it would end up being a prism

Answer: √3 is irrational whereas √9 is rational

Step-by-step explanation:

3x3=9. 3^2=9. but, ?x?=3 and ?^2=3. there is no number for that

The product of [tex]\sqrt{3}[/tex] and [tex]\sqrt{9}[/tex] is irrational

•

An irrational number is a type of real number which cannot be represented as a simple fraction and [tex]\sqrt{3}[/tex] falls under this category. As fractions are just ratios, being multiplied by another number will not affect the ratio, thus making the product irrational.

The solution of the function  2x² + 3x + 2 = 0 is the zeros obtained after factorizing them which is found to be as -2 and -1 / 2.

The given equation is ,  2x² + 3x + 2 = 0

On factorizing this we will get ,

2x² +4x - x +2 = 0

=> 2x(x +2) - ( x + 2) = 0

=> (2x-1) (x + 2) = 0

Therefore , the zeroes are -2 and -1 / 2.

Factorization is a process in which we write a given equation in terms of their prime factors. The result of factorization is known as zeros off a polynomial and are the solution for the given equation.

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Continuity refers to the property of a function or a curve in which a small change in the input results in a small change in the output, while discontinuity is a break or interruption in a function or curve.

An example of continuity is the function f(x) = x^2, which is a continuous function because, for any value of x, there is a corresponding y-value that is obtained by squaring x. This means that if x changes slightly, the value of y will change in a corresponding way.

An example of discontinuity is the function g(x) = 1/x, which is a discontinuous function because it has a break or singularity at x=0, where the function is undefined. This means that there is a gap in the curve at x=0, and the function is not defined for any value of x that is equal to zero

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The function f(x) = x2 serves as an illustration of continuity because there is always a corresponding y-value that can be calculated by squareing x. This implies that if x marginally changes, the value of y will also change.

The function g(x) = 1/x, which has a break or singularity at x=0, where the function is undefined, is an example of a discontinuous function. This indicates that the curve has a gap at x=0 and that the function is not defined for any x value equal to zero.

A line is positive negative or undefined as per its slope is positive negative or undefined.

The slope is the ratio of change of the dependent variable with respect to the change in the independent variable.

It is calculated for both straight lines as well as curves.

for example, let us say , we have a straight line y = mx +c , then the coefficient of the dependent variable 'm' is the slope of the line. It is also calculated by (y2-y1)/ (x2-x1) where y2, x2 are the final positions and y1,x1 are the initial positions.

So, we can say that if the slope is positive, i.e. the line extends up to right , its a positive line ;  if the slope is negative, i.e. the line extends down to right , its a negative line and if the slope is undefined i.e. the change in the independent variable is zero like for a vertical line, then its an undefined line.

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The product of (2x - 5)² can be written in the form az²+bx+c as follows:

(2x - 5)² = (2x)² - 2(2x)(5) + (5)²

= 4x² - 20x + 25

In this expression, a = 4, b = -20, and c = 25.

Given the provided coordinates of the points, The shape that is formed is a parallelogram because the slopes of the opposite sides are same.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. Divide the difference in elevation between two points by the distance between them to find the percent slope, then multiply the result by 100. The term "rise" refers to the difference in elevation between two sites. The run is the separation between the points. Percent slope is therefore equal to (rise / run) x 100.

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

slope between (1,1) and (4,4),

m1 = 4-1/4-1 =3/3 =1

slope between (4,-2) and (7,1),

m2= 1+2/7-4 = 3/3 =1

m1=m2

similarly, slope between (1,1) and (4,-2),

m3= -2-1/4-1 = -3/3 =-1

slope between (7,1) and (4,4)

m4= 1-4/7-4 = -3/3 =-1

m3=m4

So, slopes of opposite sides are same that means they are parallel, The shape is parallelogram.

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