Gavin wants to buy a skateboard that sells for $49. 99. An advertisement says that next week the skateboard will be on sale for $42. 50 how much will Gavin save if he waits until next week to buy the skateboard

The vertical asymptote(s) for R(x) is x=1 and x=-2. The horizontal asymptote(s) is y=0.

To find the vertical asymptotes, we look at each factor and look for any x-values that would make the factor equal to zero.

The factors are (2x+6), (x-1), (4-x), and (x+2).

So, x=1 would make (x-1) equal to zero and x=-2 would make (x+2) equal to zero.

To find the horizontal asymptote, we look at the degree of the highest exponent and divide it into the coefficient of the term with the highest degree.

Since the highest exponent is 1 and there is no coefficient, the answer is y=0.

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The investment οf $1,000 will be wοrth $1,225.04 after 3 years.

Cοmpοund interest is interest οn the principal amοunt οr lοan which is calculated accοrding tο the number οf cοmpοunds in οne year.

In this, the interest earned in each periοd is based οn the tοtal amοunt, which includes bοth the principal and the accumulated interest.

The fοrmula used fοr cοmpοund interest is

Here we have

The principal amοunt is $ 1000

The annual interest rate here is 7.5%  

The interest is cοmpounded annually.

The time periοd is 3 years  

Using the fοrmula,

[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]

A = 1,000 (1 + 0.075/1)⁽¹⁽³⁾⁾

= 1,000 (1.075)³

= $1,225.04  

Therefοre,

The investment of $1,000 will be wοrth $1,225.04 after 3 years.

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Using dilation, the scale factor here is 2,

X' = (2,2)

Y' = (4,4)

Z' = (6,0)

A thing must be scaled down or altered during the dilation process. It is a transformation that reduces or enlarges the objects using the supplied scale factor. The pre-image is the original figure, while the image is the new figure that emerges via dilatation. Two types of dilation exist:

Expansion describes an increase in an object's size.

Reduction in size is referred to as contraction.

In the given question,

The scale factor here is 2.

So, the new dilated triangle will be:

X' = (2,2)

Y' = (4,4)

Z' = (6,0)

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Answer:

5.5, 6, and 7.25

Step-by-step explanation:

3 numbers equal 18.75 tells us:

a + b + c = 18.75, where a, b, and c are the 3 unknown numbers respectively.

Next, we know that the range is 1.75. Let us consider that c is the greatest value and a is the smallest value. Thus, we can write

c - a = 1.75

Lastly, we know that there is a median of 6. This tells us that the "middle" number (which in this case would be b if c is greatest and a is smallest) should be 6.

b = 6.

Substituting we can write,

a + c + 6 = 18.75

a + c = 12.75

Also,

c - a = 1.75

c = a + 1.75

Substituting back into the other equation we get,

a + ( a + 1.75) = 12.75

2a + 1.75 = 12.75

2a = 11

a = 5.5

Now, we can find the last number.

c = (5.5) + 1.75

c = 7.25

Plug all 3 numbers back into the original equation to verify if our numbers are correct:

5.5 + 6 + 7.25 = 18.75

Thus, we know we are correct.

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Answer:

see explanation

Step-by-step explanation:

the x- intercepts are the values of x on the x- axis where the graph crosses the x- axis.

On the x- axis the y- coordinate of any point is zero.

Set the factored form of the polynomial to zero and solve for x

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

equate each factor to zero and solve for x

x = 0

x - 3 = 0 ⇒ x = 3

x + 3 = 0 ⇒ x = - 3

x - 2 = 0 ⇒ x = 2

the x-intercepts are then x = - 3, x = 0, x = 2, x = 3

these can be confirmed from the graph of the polynomial

The best forecast is the one with the lowest MSE level. In this case, the "3 Month Moving Average" has the lowest MSE level of 2.1, making it the best forecast. Therefore, the correct answer is B. 3 Month Moving Average.

One common metric used to compare forecasting methods is the Mean Squared Error (MSE). The MSE measures the average squared difference between the actual values and the forecasted values, so a lower MSE indicates a better fit.

In this case, we have four different forecasting methods and their respective MSE values. The 3 Month Moving Average has the lowest MSE of 2.1, which suggests it is the best forecasting method among the four options.

Thus, the answer is B. 3 Month Moving Average.

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Step-by-step explanation:

Let L and W be the length and width of the rectangle, respectively.

We know that the perimeter, P, of a rectangle is given by:

P = 2L + 2W

In this case, P = 16 cm, so we have:

16 = 2L + 2W

Simplifying, we get:

8 = L + W

To find the greatest area of the rectangle, we need to maximize the product of L and W, which is the formula for the area, A:

A = L * W

We can solve for one variable in terms of the other using the equation we found earlier:

L = 8 - W

Substituting this into the formula for the area, we get:

A = (8 - W) * W

Expanding and simplifying, we get:

A = 8W - W^2

To find the maximum value of A, we can use calculus or complete the square. Completing the square, we get:

A = -(W - 4)^2 + 16

Since the square of a real number is always nonnegative, the maximum value of A occurs when (W - 4)^2 = 0, which is when W = 4.

Substituting this value back into the equation for the perimeter, we get:

8 = L + 4

L = 4

Therefore, the rectangle with a perimeter of 16 cm and the greatest area is a square with sides of length 4 cm, and its area is:

A = L * W = 4 * 4 = 16 square centimeters.

NO, the ordered pair (9,2) is not the solution to the system 8x-4y=64 3y=6x-47.

The given ordered pair is (9,2) and the system of equations is:

8x-4y=64
3y=6x-47

To determine whether the given ordered pair is a solution to the system, we can substitute the values of x and y into the equations and see if they are true.

For the first equation:

8(9)-4(2)=64
72-8=64
64=64

For the second equation:

3(2)=6(9)-47
6=54-47
6=7

The first equation is true, but the second equation is not true. Therefore, the given ordered pair is not a solution to the system.

The final answer is: No, the given ordered pair is not a solution to the system.

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A package that weighs 5 pounds will cost $15 for both options.

The equation can be used to symbolize the price, y: Y is equal to 5 plus 2 times the weight of the package, x.

Another choice is for the buyer to pay a one-time price of $15, which is represented by the equation y = 15, in order to send the package.

We'll compare the equation as a whole.

In this case,

5 + 2x = 15

Compile similar terms,

2x = 15 - 5

2x = 10

x = 10 / 2

x = 5

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The response is A.

Option A's median value is 9, and its range is 13, therefore the smallest value is 9-6, which equals 3, and the greatest value is 9+6, which equals 15. This information is accurately represented by the box-and-whisker plot in option A.

The difference between the highest and lowest values for a given data collection is the range in statistics. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3.

As a result, the range may alternatively be thought of as the distance between the highest and lowest observation. The range of observation is the name given to the outcome. Statistics' range reflects the variety of observations.

from the question:

According to the information provided, the number of pupils in each class might range from 9+6 = 15 to 9+6 = 3. Because the maximum value exceeds 15, options C and D cannot accurately represent the number of students in the classes.

Option A's median value is 9, and its range is 13, therefore the smallest value is 9-6, which equals 3, and the greatest value is 9+6, which equals 15. This information is accurately represented by the box-and-whisker plot in option A.

Option B's median value is 9, but its range (from 9-5 = 4 to 9+5 = 14) is only 11, which is less than the range that could be achieved by the number of students. As a result, option B cannot accurately reflect the number of students enrolled in each class.

Thus, the response is A.

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Answer:

  100°

Step-by-step explanation:

You want the missing arc measure in the geometry where two chords cross at 85° and they intercept one arc of measure 70°.

The angle where chords cross is the average of the two arcs that they intercept. Here, that means ...

  85° = (AE +BC)/2

Solving for BC, we get ...

  2(85°) = AE +BC

  BC = 170° -AE = 100°

The missing arc measure is 100°.

The number of lbs in 15. oz is 9 3/8 lb

A unit conversion expresses the same property as a different unit of measurement. For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometers, or feet, or any other measure of length.

lb and oz are both units of weight of a substance.

1 oz = 0.0625 lb

therefore 1 oz = 625/1000

= 25/40 lb

15 oz = 25/40 × 15

= 75/8 lb

= 9 3/8 lb

therefore the number of lbs in 15 oz is 9 3/8 lb

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In linear equation, 2000 pupils are there in the school.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                            Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Ax+By=C is the typical form for linear equations involving two variables. Standard form, slope-intercept form, and point-slope form are the three main types of linear equations.

= 540/27%

= 54000/27

= 2000

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Answer:

4√5

Step-by-step explanation:

To simplify √20+√45-√5, we need to look for factors that can be simplified under the square root. We can simplify 20 and 45 by factoring out perfect squares:

√20 + √45 - √5 = √(4×5) + √(9×5) - √5

= 2√5 + 3√5 - √5

= 4√5

Therefore, the simplest form of the expression is 4√5

The answers are (a) (fog)(4) = 6√2, (b) (gof)(2) = 6√2, (c) (f of)(1) = 3√3, and (d) (gog)(0) = 0.

The given expressions are f(x) = 3√x and g(x) = 2x. We need to find the following expressions: (a) (fog)(4) (b) (gof)(2) (c) (f of)(1) (d) (gog)(0)

(a) (fog)(4) = f(g(4)) = f(2(4)) = f(8) = 3√8 = 3√(4*2) = 3√4 * √2 = 3*2*√2 = 6√2

(b) (gof)(2) = g(f(2)) = g(3√2) = 2(3√2) = 6√2

(c) (f of)(1) = f(f(1)) = f(3√1) = f(3) = 3√3

(d) (gog)(0) = g(g(0)) = g(2(0)) = g(0) = 2(0) = 0

Therefore, the answers are (a) (fog)(4) = 6√2, (b) (gof)(2) = 6√2, (c) (f of)(1) = 3√3, and (d) (gog)(0) = 0.

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The equation that illustrates the commutative property of addition is (1+2)+3=1+(2+3)

The equation that illustrates the commutative property of addition is (1+2)+3=1+(2+3).

The commutative property of addition states that the order of the numbers does not matter when adding them together.

In this equation, the numbers are rearranged but the result is still the same. This is because the commutative property of addition allows for the numbers to be added in any order and still have the same result.

Here is the step-by-step explanation:

Identify the commutative property of addition, which states that a+b=b+a.

Look at the given equations and see which one follows the commutative property of addition.

The equation (1+2)+3=1+(2+3) follows the commutative property of addition because the numbers are rearranged but the result is still the same.

Therefore, the equation that illustrates the commutative property of addition is (1+2)+3=1+(2+3).

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The future value of the investment after 6 years is $14,370.88; while the effective annual interest rate is 2.56%.

To calculate the future value of the investment, we can use the formula: FV = PV (1 + r/n)^(nt), where FV is the future value, PV is the present value, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, PV = $12,000, r = 0.025, n = 12 (compounded monthly), and t = 6.

Plugging these values into the formula, we get:

FV = $12,000 (1 + 0.025/12)^(12*6)

FV = $12,000 (1.002083333)^72

FV = $14,370.88

Therefore, the future value of the investment after 6 years is $14,370.88.

To calculate the effective annual interest rate, we can use the formula: EAR = (1 + r/n)^(n) - 1, where r is the annual interest rate and n is the number of times the interest is compounded per year.

In this case, r = 0.025 and n = 12 (compounded monthly).

Plugging these values into the formula, we get:

EAR = (1 + 0.025/12)^(12) - 1

EAR = (1.002083333)^12 - 1

EAR = 0.02568245

Therefore, the effective annual interest rate is 2.568245%.

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Answer:

To determine who has a greater mean, we need to calculate the mean (average) number of miles ridden by Liz and Sara and compare them.

Day Liz Sara

1 7 6

2 12 8

3 10 5

4 8 10

5 5 7

To find the mean for Liz, we add up the miles she rode and divide by the number of days:

Mean for Liz = (7 + 12 + 10 + 8 + 5) / 5 = 8.4 miles per day

To find the mean for Sara, we add up the miles she rode and divide by the number of days:

Mean for Sara = (6 + 8 + 5 + 10 + 7) / 5 = 7.2 miles per day

Therefore, Liz has a greater mean than Sara by 1.2 miles per day (8.4 - 7.2 = 1.2).

The annual interest rate.

To find the annual interest rate r that will allow your balance to reach $2000 in 10 years, we need to use the formula for continuously compounded interest: A = Pert, where A is the final amount, P is the principal amount, r is the annual interest rate, and t is the time in years.

We are given that P = $1000, A = $2000, and t = 10 years. Plugging these values into the formula, we get:

$2000 = $1000e10r

Dividing both sides by $1000, we get:

2 = e10r

Taking the natural logarithm of both sides, we get:

ln(2) = 10r

Dividing both sides by 10, we get:

r = ln(2)/10 ≈ 0.0693

Therefore, the annual interest rate r that will allow your balance to reach $2000 in 10 years is approximately 6.93%.

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The ratio of strawberries to bananas in the basket is 12:18 or 2:3. To find this ratio, you simply take the number of strawberries and place it over the number of bananas. In this case, there are 12 strawberries and 18 bananas, so the ratio is 12:18.

However, this ratio can be simplified by dividing both numbers by their greatest common factor, which is 6. So, the simplified ratio of strawberries to bananas is 2:3. This means that for every 2 strawberries, there are 3 bananas in the basket.

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The zeros of the polynomial are -5i, √5i, -√5i.

The given polynomial is: f(x)=x⁴+16x²-225.

Zeros of a polynomial are the values of x that make the polynomial equal to zero. These will be the x-intercepts of the polynomial's graph. To find the zeros of a polynomial, use the factored form of the polynomial and set each factor equal to zero. The solutions of this equation are the zeros of the polynomial.

The given zero is: -5i

To find the remaining zeros of the polynomial, we need to factor the polynomial.

We can factorize the polynomial as:

f(x) = (x² + 5i)(x² - 5i)

Finding Zeros:

Therefore, the remaining zeros of the polynomial are:

x = ±√5i

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For each of the given , we need to use the Law of Sines to determine whether the given information results in two triangles, one triangle, or no triangles. The Law of Sines states that for any triangle, the ratio of the length of a side to the sine of the opposite angle is the same for all three sides:

a/sin A = b/sin B = c/sin C

Let's look at each scenario and apply the Law of Sines:

Scenario 1: a = 7, b = 10, A = 50°

Using the Law of Sines, we can find the value of angle B:

7/sin 50° = 10/sin B

sin B = 10*sin 50°/7

sin B = 0.918

B = sin^-1(0.918) = 66.4°

Since the sum of the angles in a triangle must equal 180°, we can find the value of angle C:

C = 180° - 50° - 66.4° = 63.6°

Since all three angles add up to 180° and are positive, we can conclude that this scenario results in one triangle.

Scenario 2: a = 5, b = 7, A = 120°

Using the Law of Sines, we can find the value of angle B:

5/sin 120° = 7/sin B

sin B = 7*sin 120°/5

sin B = 1.209

Since the sine of an angle cannot be greater than 1, this scenario does not result in a triangle.

Scenario 3: a = 9, b = 12, A = 30°

Using the Law of Sines, we can find the value of angle B:

9/sin 30° = 12/sin B

sin B = 12*sin 30°/9

sin B = 0.667

B = sin^-1(0.667) = 41.8°

Since the sum of the angles in a triangle must equal 180°, we can find the value of angle C:

C = 180° - 30° - 41.8° = 108.2°

Since all three angles add up to 180° and are positive, we can conclude that this scenario results in one triangle.

In conclusion, scenario 1 and scenario 3 result in one triangle, while scenario 2 does not result in a triangle. We can determine this by using the Law of Sines and checking whether the values of the angles are valid and add up to 180°.

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The two real roots of the polynomial function S(r) = r^(5) + 5r^(4) - 7r^(3) - 43r^(2) - 8r - 48 are r = -8 and r = 3.

The two real roots of the polynomial function S(r) = r^(5) + 5r^(4) - 7r^(3) - 43r^(2) - 8r - 48 can be found by factoring the polynomial and finding the values of r that make the function equal to zero.

First, we can factor the polynomial using the Rational Root Theorem, which states that if a polynomial has rational roots, they must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

In this case, the constant term is -48 and the leading coefficient is 1, so the possible rational roots are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, and ±48.

We can use synthetic division to test these possible roots and find the ones that make the function equal to zero. After testing the possible roots, we find that the two real roots are r = -8 and r = 3.

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Answer:      a. 8.4 meters       b. 14 wreaths

Step-by-step explanation:

The following equation shows the problem, with x representing the number of wreaths made:

12 = 9(0.4) + 0.6x

To answer a, get 0.6x alone:

12 = 9(0.4) + 0.6x

12 = 3.6 + 0.6x

8.4 = 0.6x

There were 8.4 meters available to make wreaths

To answer b, get x alone

8.4 = 0.6x

14 = x

Diego could make 14 wreaths with the available ribbon

Hope this helps!

cost = 3/√34,  csct = √34/5, sect =√34/3 , and cott = 3/5

explanation:-

The given equation is: tant = 5/3, so, cot t = 3/5 as cot t= 1/tan t

we know sec² t - tan² t = 1

or, sec²t= 1 + tan²t = 1+(25/9) = 34/9

or, sect = √(34/9) = √34/3

or, cos t=√(9/34) = 3/√34 as cos t= 1/sec t

now, also, csc²t - cot²t = 1

or, csc²t = 1+cot²t = 1+ 9/25 = 34/25

or, csc t= √34/5

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Answer:

not a function

Step-by-step explanation:

Answer:

not a function

Step-by-step explanation:

Based on the information, we can infer that the surface area of the pyramid is: 105 inches²

To find the surface area of the pyramids we must perform the following procedure:

We must find the surface of each of the faces and the base.

According to this procedure, each face of the pyramid measures 20 inches². Then we must multiply this value by the number of faces of the pyramid (4).

We must add the surfaces of the faces and the base.

According to the above, the surface area of the pyramid would be 105 inches².

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Answer:

dddiejehehegeheheheh

Moving the ladder 1 foot towards the building will not be enough to raise it by 1 foot, and moving it 2 feet away from the building will not be enough to lower it by 2 feet.

The relationship between the distance the ladder is moved along the ground (run) and the resulting change in height (rise) is determined by the ladder's angle of inclination, which is constant. This angle can be calculated using trigonometry, specifically the tangent function:

[tex]angle = arctan(rise/run)[/tex]

For a 20-foot ladder, the angle of inclination is approximately 75.96 degrees. If the painter moves the ladder 1 foot towards the building, the run will decrease from 20 feet to 19 feet, which means the rise will decrease proportionally according to the tangent function:

[tex]new rise = tan(angle) * new run[/tex]

[tex]new rise = tan(75.96) * 19[/tex]

new rise ≈ 18.7 feet

So, moving the ladder 1 foot towards the building will only raise it by about 0.3 feet, not enough to achieve the desired 1-foot increase. Similarly, moving the ladder 2 feet away from the building will increase the run from 20 feet to 22 feet, causing the rise to increase proportionally according to the tangent function:

new rise = tan(angle) x new run

new rise = tan(75.96) x 22

new rise ≈ 21.3 feet

Therefore, moving the ladder 2 feet away from the building will only lower it by about 1.3 feet, not enough to achieve the desired 2-foot decrease.

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