The table below represents the value, y, of an antique table x years after purchase.



The data was modeled with a linear best-fit function. What was the initial purchase price?

$5,625

$5,000

$625

$2,500

The equation x²/3 + y²/3 = 4 represents an ellipse in the shown graph below and the length of the given ellipse is 8 units.

The equation x²/3 + y²/3 = 4 represents an ellipse centered at the origin with a major axis along the x-axis and a minor axis along the y-axis.

The equation can be rewritten as x²/4 + y²/12 = 1 to highlight the lengths of the semi-major and semi-minor axes.

The semi-major axis length is given by the square root of the denominator of the x-term, which is 4, so the semi-major axis length is 2.

The semi-minor axis length is given by the square root of the denominator of the y-term, which is 12, so the semi-minor axis length is 2√3.

Based on the symmetry of the ellipse, we can determine that it is symmetric with respect to both the x-axis and the y-axis.

This means that the length of the entire ellipse can be found by multiplying the semi-major axis length by 4, since there are 4 identical sections due to symmetry.

Length of the ellipse = 4 * semi-major axis length

= 4 * 2

= 8.

Therefore, the length of the given ellipse is 8 units.

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The correct question is as follows:

Sketch the curve with the equation x²/3 + y²/3 = 4 and use symmetry to find its length.

The relation that is displayed by the given table is: B. {(1,2), (3,4), (5,6), (8,7)}

A relation can be described as a set of ordered pairs which contain one object from each sets, of which one pair is represented as (x, y). So, in a table, a relation can be represented by having all the set of x-values one column, and their corresponding y-values on another column.

Given the table below:

x   |  y

1      2

8     7

5     6

3     4

We can list out the set of ordered pairs as follows:

(1, 2), (8, 7), (5, 6), and (3, 4).

Ordering the pairs of values, we would have the following relation of the table, which is expressed as: B. {(1,2), (3,4), (5,6), (8,7)}

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A linear equation relating profit, to the number of student is shown below.

y = 2x + 500

Linear equation is used to present the elements in mathematic. A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

To write a linear equation relating profit to the number of students, we need to find the slope and the y-intercept of the line.

The slope of the line can be calculated using the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line.

In this case, we can use the two data points given to find the slope:

slope = (460 - 500) / (80 - 100) = -40/ -20 = 2

The y-intercept of the line is the point where the line crosses the y-axis, which is the profit when the number of students is 0. In this case, the y-intercept is 500, since that is the profit when 100 students purchase items.

Using these values, we can write the linear equation in slope-intercept form:

y = 2x + 500

This equation can be interpreted as follows: the profit (y) is equal to 2 times the number of students (x) plus 500.

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Check the picture below, so the parabola looks more or less like so.

keeping in mind the vertex is half-way between the focus point and the directrix, this one lands as you see it in the picture, with a negative "p" distance.

[tex]\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=-5\\ k=0\\ p=-2 \end{cases}\implies 4(-2)(y-0)=( ~~ x-(-5) ~~ )^2\implies -8y=(x+5)^2 \\\\\\ ~\hfill {\Large \begin{array}{llll} y=-\cfrac{1}{8}(x+5)^2 \end{array}} ~\hfill[/tex]

The function is: c(x) = 5.50 + 21.60x. This means that for each ticket purchased, an additional $21.60 will be added to the service fee of $5.50.

The total cost for ordering 5 tickets is $108.00. This means that each ticket costs $20.50 plus a service fee of $5.50.

Therefore, we can create a linear function that represents the total cost when x tickets are ordered. The function is: c(x) = 5.50 + 21.60x. This means that for each ticket purchased, an additional $21.60 will be added to the service fee of $5.50.

When x = 5, then c(x) = 5.50 + 21.60x = 5.50 + 21.60(5) = 108.00, which matches the given total cost.

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Answer:

  z = 52.5

Step-by-step explanation:

You want the solution for (4.8)/(2z+15)=(0.2)/(5).

Multiplying by 5(2z +15) we have ...

  5(4.8) = 0.2(2z +15)

  24 = 0.4z +3 . . . . . . . . . . simplify

  21 = 0.4z . . . . . . . . . . . . subtract 3

  z = 21/0.4 = 52.5 . . . . divide by the coefficient of z

The value of z is 52.5.

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Answer:

10x + 35

Step-by-step explanation:

7(3x+5)-11x

21x + 35 - 11x

10x + 35

The subtotal is $20, Savings is $ 1, New Subtotal is $19, Sales tax is $1.14 and the Total is $20.14

A sales discount is a reduced price offered by a business on a product or service

Given:

1 bottle of lotion = $5

1 t-shirt = $12

1 birthday card = $3

Subtotal = $5 + $12 + $3 = $20

If you use your Target RedCard and save 5%, savings will be:

Savings = 5% of Subtotal

Savings = 5/100 × $20 = $1

New Subtotal: $20 - $1 = $19

Sales tax is 6%: 6/100 × $19 = $1.14

Total: New Subtotal + Sales tax = $19 + $1.14 =$20.14

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Answer: 8cm

Step-by-step explanation:

Square root 64 to get 8

Answer:

8cm

Step-by-step explanation:

A base is either the length or the width of the square (doesn't matter because square has 4 equal lengthed sides). To find the area from the base, square it. To find the base from the area, square root it (inverse operations.)

[tex]\sqrt{64cm^2}[/tex]

8cm

The expression of the nth term of the given sequence is

-7.7 + (n - 1)0.3

It is a sequence where the difference between each consecutive term is the same.

Example:

2, 4, 6, 8, 10 is an arithmetic sequence.

We have,

-7.7, -7.4, -7.1, -6.8, -6.5

This is an arithmetic sequence.

Now,

a = -7.7

d = -7.4 + 7.7 = 0.3

The nth term of an arithmetic sequence.

= a + (n - a)d

Now,

a + (n - a)d

= -7.7 + (n - 1)0.3

Thus,

The nth term is -7.7 + (n - 1)0.3.

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Answer:

B

Step-by-step explanation:

For a set of data to have a median that is greater than the mean, it must have an odd number of values and be skewed to the right. This means that the majority of the values in the set must be smaller than the median, with a few larger values on the right side of the distribution.

Out of the given options, the only set of data that satisfies these conditions is (B) {8, 12, 14, 14, 22}. This set has an odd number of values, and the median of 14 is greater than the mean of 14.4. The other options have either an even number of values, or are not skewed to the right.

Therefore, the correct answer is (B) {8, 12, 14, 14, 22}.

Answer:

yes

Step-by-step explanation:

for a relation to be a function then each value of x can only map to one unique value of y.

This is the case here, then the relation is a function

Answer:

(4x^2 +7x + 2)

Step-by-step explanation:

(8x³ +26x² + 25x + 6)/( 2x + 3)

(8x³ +26x² + 25x + 6) = (4x^2 +7x + 2)(2x + 3)

(4x^2 +7x + 2)(2x + 3)/(2x+3) = (4x^2 +7x + 2)

A pair of vertical angles is; Angle 1 and Angle 4

A pair of supplementary angles are; Angle 2 and angle 1

Vertical Angles are defined as the angles that are opposite each other when two lines cross each other.

Two angles are defined as adjacent angles when they share the common vertex and side.

Two angles are defined as supplementary angles if they sum up to 180 degrees.

By those definitions above, we can say that;

Angle 1 & 2 as well as angle 3 & 4 are pairs of supplementary angles.

We can also say that;

Angle 4 and 1 are vertical angles while angle 2 and 3 are vertical angles as well.

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The expression that represents the number of football cards that Frankie has is given as follows:

F = J + 65.

The situation can be modeled by a system of equations, in which the variables are given as follows:

Frankie has sixty-five more football cards than his friend John, hence the expression that represents the number of football cards that Frankie has is given as follows:

F = J + 65.

As the term sixty-five more means that the number 65 is added to the amount of cards that John has, which is symbolized by J, to obtain the amount F, which is the number of football cards that Frankie has.

The problem asks for the expression of the number of cards that Frankie has.

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The equation of the line passing through (3, 4) and perpendicular to the line  y=1/9x + 8 in slope-intercept form is y = -9x + 31

Suppose we have two lines with slope m₁ and m₂ respectively, then those lines are perpendicular to each other if

m₁ x m₂ = -1

In the given problem, the line is perpendicular to a line whose equation is:

y = 1/9 x + 8

Hence,

m₁ x m₂ = -1

1/9 x  m₂ = -1

m₂ = -9

Therefore, the equation of the second line is:

y = -9x + b

To find the value of b, we use the fact that the line passing through (3,4)

Substitute x = 3, and y = 4

4 = -9 (3) + b

b = 4 + 27 = 31

Thus, the equation of the line is:

y = -9x + 31

Your question is incomplete, but most probably your question was:

Find the equation of the line passing through (3, 4) and perpendicular to the line whose equation is y=1/9x + 8 in slope-intercept form.

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The price of the winter coats is going to be $17.325.

The marked price or list price is the amount that appears on a product's label. This is the price that the product will be sold for. But this price might be discounted in some way, and the product's real selling price might be less than the advertised price.

given,

Marked Price of winter coats = $57.75 and  discount = 70%

Discount = 70%

57.75 × 70/100

5.775 × 7

40.425

Selling Price = M.P - Discount

57.750 - 40.425

17.325

therefore ,

The price of the winter coats is going to be $17.325.

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Answer:

normal force decreases

Step-by-step explanation:

N=mgcosθ, and cosine decreases as theta increases

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Answer:

A) decreases

Step-by-step explanation:

As the angle of the incline increases, the normal force decreases, which decreases the frictional force. The incline can be raised until the object just begins to slide.

The rate at which the radius is increasing is; 0.006 in/min

We are given that the formula for the volume of  a spherical balloon is;

V = ⁴/₃πr³

where r is the radius

The volume is increasing at the constant rate of 0.78 inches per minute. Thus;

dV/dt = 0.78

Now, differentiating with respect to t gives;

dV/dt = ⁴/₃(3πr²)(dr/dt)

At radius of 3.2 inches, we have;

0.78 = 4π * 3.2² * dr/dt

dr/dt = 0.78/(4π * 3.2²)

dr/dt = 0.006 in/min

This is therefore the rate at which the radius is increasing.

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Answer: D) $2,118.00

Step-by-step explanation:

1 year = 4.25% interest rate

18 years = 76.5% interest rate

76.5% = 0.765

Take 1200 times 0.765 = $918.00

$918.00 is the interest money he will receive after 18 years. We have to add both numbers to find the total.

$1,200 + $918.00 = $2118.00

The expression is - 2xz⁴

An exponent is a method of expressing large numbers in terms of power. So, exponent means how many times a number is multiplied by itself. For example, 5 is multiplied by itself 3 times i,e 5 *5*5. It can be written as 5³.

Here, 3 is the exponent, and 5 is the base. We can read it as 5 is raised to power 3. The symbol '^' is used to represent the exponents. It is called a carrot.

Based on the power there are different laws of exponents, such as :

So, The expression is - 2xz⁴

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A continuous quantitative variable is a measure of a quantity that can take any value within a certain range. An example of this is the number of gallons of paint purchased.

A continuous quantitative variable is a type of data that is measured on a continuous scale. This type of data is typically used to measure quantities that can take any value within a certain range. Examples of continuous quantitative variables include the number of gallons of paint purchased, the number of miles of interstate highways, or the population of a city. Continuous quantitative variables differ from discrete quantitative variables, which are used to measure counts of items or events. For example, the number of quarts of milk purchased or the number of times you sharpen your pencil while working on statistics problems would be discrete quantitative variables. Continuous quantitative variables can be measured with precise accuracy, while discrete quantitative variables can only be measured in whole numbers, since they are counts of items or events.

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The figure S is translatation and then followed by rotation to map it into

figure T.

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

The figure S is translated (moved a fixed amount from the preimage)

and then followed by rotation(the preimage is rotated to create the final image) to map it into figure T.

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We will discover that the probability that you will at random wind up with an orange hat is as follows: P = 1/12

Observe how we arrived at that now:

4 pieces of clothing (shirt, pants, socks, or hat)

three hues (purple, blue, or orange)

The color of only one item of clothing will change. The likelihood that you will receive an orange hat is what we are looking for.

We must first determine the likelihood that you will choose a hat at random. The likelihood of picking your hat at random is if all the apparel has the same probability of being chosen, just one more than the number of options (4). p = 1/4

The color is now chosen at random using the same methodology as before, with the likelihood that orange will be chosen at random being: q = 1/3.

When we multiply the individual probabilities by the joint probability, we obtain:

P = q*p = (1/4)*(1/3) = 1/12

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The number of cabinets of large size Lee should pack is equal to 40 and that of small size is equal to 25.

To determine how many of each size of cabinet Lee should pack in the truck, you can set up a system of equations. Let X be the number of large cabinets and Y be the number of small cabinets.

The total weight of the large cabinets is 30X pounds, and the total weight of the small cabinets is 20Y pounds. The total weight of all the cabinets is 1550 pounds, so the equation to represent this is:

30X + 20Y = 1550

The total number of cabinets is the sum of the number of large cabinets and the number of small cabinets, so the equation to represent this is:

X + Y = 65

To solve this system of equations, you can use the substitution method. First, solve for X in the second equation by substituting 65 - Y for X:

X = 65 - Y

Then, substitute 65 - Y for X in the first equation:

30(65 - Y) + 20Y = 1550

Solving this equation for Y, you get:

Y = 25

Substituting this value for Y in the second equation, you get:

X = 65 - 25 = 40

So, Lee should pack 40 large cabinets and 25 small cabinets in the truck.

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Answer:

75 km/h

Step-by-step explanation:

48 minutes = 48/60

(48 : 12)/(60:12)

4/5

0.8 hours

average speed between Bristol and Cardiff = 72/0.8 = 90 km/h

average speed of the journey = (60 + 90)/2 = 150/2 = 75 km/h

Answer:

L = 12ft

W = 13ft

Step-by-step explanation:

Let's use the two pieces of information to make 2 equations (we need 2 eqns to solve for 2 variables: Length and Width).

The length and width are consecutive integers

L+1=W

The area of the rectangle is 156 square feet.

L*W=156

We know that W=L+1 from our first equation, so substituting that information into our second equation we get

L*(L+1)=156

Let's distribute that L

L^2 + L = 156

and subtract 156 from both sides

L^2 + L - 156 = 0

Now we can use the quadratic formula to find L. L cannot be negative, so

L = 12

using our very first equation we know L, so we can solve for W.

L+1=W

12+1=W

W = 13