3 halves of a cupcake for my family plus some extra for my 2 friends. They will each want a quarter of a cupcake.

The Null Hypothesis (H0: μ ≤ 90) and Alternative Hypothesis (Ha). of the wait time for a new roller coaster is at least 90 minutes.

The null hypothesis states that a population parameter is equal to a value. The null hypothesis is often an initial claim that researchers specify using previous research or knowledge.

Null Hypothesis (H0): The wait time for a new roller coaster is equal to or less than 90 minutes (H0: μ ≤ 90).

Alternative Hypothesis (Ha): The wait time for a new roller coaster is greater than 90 minutes (Ha: μ > 90).

In words, the null hypothesis states that the average wait time for the new roller coaster is equal to or less than 90 minutes.

The alternative hypothesis states that the average wait time is greater than 90 minutes.

We use the symbol μ to represent the population means of wait times for the new roller coaster.

Therefore, the Null Hypothesis (H0: μ ≤ 90) and Alternative Hypothesis (Ha). of the wait time for a new roller coaster is at least 90 minutes.

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a) To find the linear velocity of a point on the tip of one of the blades, we need to use the formula: V = 2πr/T where V is the linear velocity, r is the radius of the circle, and T is the period of rotation. In this case, the radius of the circle is the length of the propeller blades, which is 3 meters, and the period of rotation is the inverse of the frequency of rotation, which is 1/6 minutes. Plugging in the values, we get: V = 2π(3)/(1/6) = 36π meters per minute. To the nearest meter per minute, the linear velocity is approximately 113 meters per minute.

b) To find the arc length and the area of the circular sector, we need to use the formulas: Arc length = θr and Area = (θr^2)/2 where θ is the central angle in radians, and r is the radius of the circle. In this case, the central angle is 25 degrees, which is equivalent to (25π)/180 radians, and the radius of the circle is 12 cm. Plugging in the values, we get: Arc length = ((25π)/180)(12) = (5π)/3 cm and Area = (((25π)/180)(12^2))/2 = (25π)/3 cm^2. Therefore, the arc length is approximately 5.24 cm and the area is approximately 26.18 cm^2.

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For the given cuboid, it's volume value is deduced as 30 cm³.

What is volume?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

The figure is given as a cuboid.

The length of the cuboid is 5 cm.

The breadth of the cuboid is 6 cm.

The height of the cuboid is 1 cm.

The formula for volume of cuboid is given as -

Volume = length × breadth × height

Substitute the values into the equation -

Volume = 5 × 6 × 1

Volume = 30 cm³

Therefore, the volume value is obtained as 30 cm³.

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The ratio of similarity  DEFG to TSRQ is '3: 1'.

Two quadrilaterals are considered similar if they have the same shape but may have different sizes. Similar quadrilaterals have corresponding angles that are congruent, and their corresponding sides are in proportion to each other.

The ratio of similarity is a measure of how much two geometric figures are enlarged or reduced to become similar.

Here we have

Quadrilateral DEFG and Quadrilateral TSRQ.

Where DEFG similar to TSRQ

Hence, the ratio of corresponding sides will be equal

=> DE/TS  = EF/SR  = FG/RQ = DG/TQ

=> 24/8  = 24/8  = 24/8 = 24/8 = 3/1

Therefore,

The ratio of similarity  DEFG to TSRQ is '3: 1'.

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About 22,500 people at the Super Bowl game will not be wearing team jerseys.

Here the entire population is proportional to the number of people who entered the main gate without wearing team jerseys.

Find the proportion of people not wearing team jerseys by dividing 150 by 500. Now multiply the resultant proportion by the actual population.

Here we have

150 out of the first 500 people who entered the main gate were not wearing team jerseys,

The proportion of people not wearing team jerseys  

=> p = 150/500 = 0.3

Given that the sample is representative of the entire population of 75,000 people attending the game,

The population that will not be wearing team jerseys can be calculated as follows

75,000 x 0.3 = 22,500

Therefore,

About 22,500 people at the Super Bowl game will not be wearing team jerseys.

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The total cost of the dress including sales tax is 95.21.

The amount of discount that Isabella received on the dress is:

35% of 135.00 = 0.35 x 135.00 = 47.25

So, the price she paid for the dress after the discount is:

135.00 - 47.25 = 87.75

To find the total cost including sales tax, we need to add the sales tax to the price of the dress:

Sales tax = 8.5% of 87.75 = 0.085 x 87.75 = 7.46

Total cost = Price of dress after discount + Sales tax

= 87.75 + 7.46

= 95.21

Therefore, the total cost of the dress including sales tax is 95.21.

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The debt consolidation loan will cost Sheng an additional $1,997.69 in interest charges compared to his credit cards.

From question, we are to calculate how much more in interest the debt consolidation loan will cost Sheng

To calculate the interest charges for Sheng's credit cards, we need to use the following formula:

Interest Charges = Balance x APR x Number of Days in Billing Cycle / 365

Using this formula, we can calculate the interest charges for each of Sheng's credit cards:

For Credit Card A:

Interest Charges = $2,500 x 0.19 x 30 / 365 = $4.94

For Credit Card B:

Interest Charges = $3,000 x 0.22 x 30 / 365 = $6.01

So, the total interest charges for Sheng's credit cards are:

Total Interest Charges = $4.94 + $6.01 = $10.95

Now, let's calculate the total cost of the debt consolidation loan:

Total Cost = Total Monthly Payments x Number of Payments - Loan Amount

Total Monthly Payments = $179.37

Number of Payments = 6 x 12 = 72

Loan Amount = ?

To find the loan amount, we need to solve for it using the interest rate and the total interest charges:

Loan Amount = Total Interest Charges / (APR x Number of Payments / 12)

Loan Amount = $3,414.39 / (0.107 x 72 / 12) = $25,000

So, the total cost of the debt consolidation loan is:

Total Cost = $179.37 x 72 - $25,000 = $2,008.64

Therefore, the additional interest charges for the debt consolidation loan compared to Sheng's credit cards are:

Additional Interest Charges = Total Cost - Total Interest Charges

Additional Interest Charges = $2,008.64 - $10.95 = $1,997.69

Hence, the debt consolidation loan will cost him an additional $1,997.69 in interest charges

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Check the picture below.

The answer is (C) No, the estimate should be less than $77.92.

Estimation cost refers to the process of approximating or calculating the cost of a project or service before it is actually carried out or completed. This is an important step in budgeting and financial planning, as it helps individuals and organizations to anticipate and prepare for the financial impact of a particular activity or initiative.

To determine if the estimate of $77.92 is reasonable, we can calculate the actual cost of printing 13 posters using the given information:

Setup fee: $14.21

Cost per poster: $3.90

Number of posters: 13

Total cost = setup fee + (cost per poster x number of posters)

Total cost = $14.21 + ($3.90 x 13)

Total cost = $14.21 + $50.70

Total cost = $64.91

We can see that the actual cost of printing 13 posters is $64.91, which is less than the estimated cost of $77.92. Therefore, the estimate of $77.92 is not reasonable and the answer is (C) No, the estimate should be less than $77.92.

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Answer:If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations. the intersection points (-3,3) Since the system is infinite it means there is 1 line on the graph-

Step-by-step explanation:

Answer:

). The rocket was launched from 73 feet above ground.

b). The rocket took [Vy / g] = 30 / 3 = 10s to reach its maximum height of [Vy^2 / (2 * g)] = 30^2 / 6 = 150 feet.

It then fell -(73 + 150) = -223 feet to the ground in a time of sqrt(2 * -223 / -3) = 12.192894s.

Total time of flight = (10 + 12.192894) = 22.192894s.

The rocket landed with a vertical velocity of -sqrt(2 * -223 * -3) = -36.578682ft/s.

Step-by-step explanation:

Answer:

Unfortunately, there is no equation provided in the question. However, I can provide a general formula for the height of a rocket launched from a certain height h0 with an initial velocity v0, under the influence of gravity:

h(t) = -1/2gt^2 + v0t + h0

where g is the acceleration due to gravity, which is approximately 32.2 feet per second squared.

Using this formula, we can calculate the height of the rocket 3 seconds after it is launched:

h(3) = -1/2(32.2)(3)^2 + 0 + 4

= -1/2(32.2)(9) + 4

= -145.35 + 4

= -141.35

To the nearest foot, the height of the rocket 3 seconds after it is launched is -141 feet. Note that the negative sign indicates that the rocket has fallen below its initial height of 4 feet due to the influence of gravity.

the height of the cylinder is 12/π inches. This is an exact value, but if you want an approximate decimal value, you can use a calculator and substitute 3.14 or 22/7 for π. For example, if we use π ≈ 3.14, we get:

h ≈ 12/3.14

h ≈ 3.822 inches (rounded to three decimal places)

The equation of a horizontal line that passes through (4,2) in slope intercept form is y = 2.

A horizontal line has a slope of 0, which means that the y-value remains constant while the x-value changes. In slope intercept form, the equation of a line is written as y = mx + b, where m is the slope and b is the y-intercept.

Since the slope of a horizontal line is 0, the equation of a horizontal line can be written as y = 0x + b, or simply y = b. The y-intercept is the value of y when x = 0, which is the same as the y-value of any point on the line.

In this case, the line passes through the point (4,2), so the y-value is 2. Therefore, the equation of the line in slope intercept form is y = 2.

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solve for t to get t = 4

1. To find the derivative of f(x) = (3 – 2x^3)^3 we can apply the power rule, the chain rule, and the product rule. The power rule states that the derivative of f(x) = x^n is f'(x) = nx^n-1. The chain rule states that the derivative of f(x) = g(h(x)) is f'(x) = g'(h(x))*h'(x). The product rule states that the derivative of f(x) = uv is f'(x) = u'v + uv'. In this case, we can rewrite f(x) as f(x) = (h(x))^3 where h(x) = 3 - 2x^3. We then apply the chain rule to get f'(x) = 3(3 - 2x^3)^2(-6x^2). Similarly, we can find the derivative of f(t) = 100(6-t)/t+3. We can rewrite f(t) as f(t) = u(t)v(t) where u(t) = 100 and v(t) = (6-t)/t+3. Applying the product rule, we get f'(t) = 100(-1/(t+3)^2) + (6-t)(-1/(t+3)^2).

2. To find other information about a function, we can use the derivative we just found. For example, if we want to find the maximum or minimum values of a function, we can set the derivative equal to 0 and solve for the x or t values. In the case of f(x), we can set 3(3 - 2x^3)^2(-6x^2) = 0 and solve for x to get x = (sqrt(3/2))^(1/3). Similarly, for f(t) we can set 100(-1/(t+3)^2) + (6-t)(-1/(t+3)^2) = 0 and solve for t to get t = 4. We can also use derivatives to find the equation of a tangent line to a function at any given point. In this case, we would use the derivative we found in order to calculate the slope of the tangent line at any given point and then use point-slope form to find the equation of the line.

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The system of inequalities is correctly graphed on Shannon's graph.

Here we have the following system of inequalities:

y ≥ (1/2)*x - 1

x - y > 1

We can rewrite the second inequality as:

y < x - 1

Then the system becoimes:

y ≥ (1/2)*x - 1

y < x - 1

The first line will be one with positive slope, it is solid (due to the symbol ≥) and the shaded area is above the line.

For the second we will have a dashed line, and now the shaded area is below the dashed line.

From that, we caonclude that Shannon's graph is the correct one.

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Answer:

20

Step-by-step explanation:

The following unit multipliers are used:

1 loaf of bread = 400g of flour = 0.4kg of flour: [tex]\frac{0.4kg Of Flour}{1 loaf}[/tex]

1 day = 64 loaves of bread: [tex]\frac{64 loaves}{1 day}[/tex]

∴Mass of flour needed to last for 20 days:

[tex](20 days)[/tex]× [tex]\frac{64loaves}{1day}[/tex] ×[tex]\frac{0.4 kg}{1 loaf}[/tex]

  = 512 kg of flour

                  1 sack = 25 kg of flour

∴ x sacks of flour = 512 kg of flour

Cross-multiplication is applied:

(x sacks of flour)(25 kg of flour) = (1 sack)(512 kg of flour)

∴ x sacks of flour = [tex]\frac{(1 sack)(512kg Of Flour)}{25 kg Of Flour}[/tex]

                             = 20.48 sacks of flours

∴The minimum number of sacks = 20

The values of x are 0.732 and -2.732.

Given function:f(x) = g(x)We need to determine the value of x.For, f(x) = g(x), we have the following equation:f(x) = x^2 + 2x + 1 = 2x + 3g(x) = 2x + 3To solve for x, we can substitute the value of g(x) in the first equation:x^2 + 2x + 1 = g(x)Substituting g(x) = 2x + 3 in the above equation:x^2 + 2x + 1 = 2x + 3x^2 + 2x - 2 = 0x^2 + 2x - 2 = 0Applying the quadratic formula, we get:$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$Where, a = 1, b = 2, and c = -2Substituting the values in the formula, we get:$$x = \frac{-2 \pm \sqrt{2^2 - 4(1)(-2)}}{2(1)}$$$$x = \frac{-2 \pm \sqrt{12}}{2}$$$$x = -1 \pm \sqrt{3}$$Therefore, the value of x is x = -1 + √3 or x = -1 - √3.To round off the answer to 3 decimal places, we get:x = -1 + 1.732 = 0.732 or x = -1 - 1.732 = -2.732Hence, the values of x are 0.732 and -2.732.

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The LCD in this case is 2x^(2). So the solutions to the equation are x = 0 and x = 5.

To solve the equation, we first need to find the least common denominator (LCD) of all the fractions.

Next, we multiply each side of the equation by the LCD to eliminate the fractions:

2x^(2)*(x^(2)-x-6)/(x^(2)) = 2x^(2)*(x-6)/(2x) + 2x^(2)*(2x+12)/(x)

Simplifying the equation gives us:

2x^(2)-2x-12 = x^(2)-3x-12

Next, we move all the terms to one side of the equation:

x^(2)-5x = 0

Finally, we can factor the equation and set each factor equal to zero:

x(x-5) = 0

x = 0 or x = 5

So the solutions to the equation are x = 0 and x = 5.

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Answer:

55/100 and 48/100, in decimal form it will be 0.55 and 0.48

Step-by-step explanation:

11/20 and 12/25

The common denominator in this question will be 100

55/100 and 48/100

Answer: y = -5/3x + 4

Step-by-step explanation:

The slope intercept form is y = mx + b

The slope (m) is rise over run, so slope = -5/3

The y-intercept (b) is 4 because that is where the line intersects the y-axis at.

Hope this helps!

Answer:

To find the derivative of the function y = x^2 - x + 3 using the first principle, we start by applying the definition of the derivative:

f'(x) = lim (h -> 0) [f(x+h) - f(x)] / h

where f(x) = x^2 - x + 3.

Now we substitute the function into the equation and simplify:

f'(x) = lim (h -> 0) [(x+h)^2 - (x+h) + 3 - (x^2 - x + 3)] / h

f'(x) = lim (h -> 0) [(x^2 + 2xh + h^2 - x - h + 3) - (x^2 - x + 3)] / h

f'(x) = lim (h -> 0) [2xh + h^2 - h] / h

Now we can cancel out the h in the numerator and denominator, leaving:

f'(x) = lim (h -> 0) [2x + h - 1]

Finally, we take the limit as h approaches 0:

f'(x) = 2x - 1

Therefore, the derivative of y = x^2 - x + 3 with respect to x is f'(x) = 2x - 1.

Step-by-step explanation:

Answer:

[tex]\dfrac{\text{d}y}{\text{d}x}=2x-1[/tex]

Step-by-step explanation:

Differentiating from First Principles is a technique to find an algebraic expression for the gradient at a particular point on the curve.

[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Differentiating from First Principles}\\\\\\$\text{f}\:'(x)=\displaystyle \lim_{h \to 0} \left[\dfrac{\text{f}(x+h)-\text{f}(x)}{(x+h)-x}\right]$\\\\\end{minipage}}[/tex]

The point (x + h, f(x + h)) is a small distance along the curve from (x, f(x)). As h gets smaller, the distance between the two points gets smaller. The closer the points, the closer the line joining them will be to the tangent line.

To differentiate y = x² - x + 3 using first principles, substitute f(x + h) and f(x) into the formula:

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{(x+h)^2-(x+h)+3-(x^2-x+3)}{(x+h)-x}\right][/tex]

Simplify the numerator:

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{x^2+2hx+h^2-x-h+3-x^2+x-3)}{x+h-x}\right][/tex]

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{2hx+h^2-h}{h}\right][/tex]

Separate into three fractions:

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{2hx}{h}+\dfrac{h^2}{h}-\dfrac{h}{h}\right][/tex]

Cancel the common factor, h:

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\:2x+h-1\:\right][/tex]

As h → 0, the second term → 0:

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=2x-1[/tex]

The result of the (3-3x^(3)-7x^(2))-(-2x^(2)-3x+7)  polynomial  is -3x^(3) - 5x^(2) + 3x - 4.

A polynomial is a mathematical expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

To find the result of the given polynomials, we need to combine like terms. Like terms are terms that have the same variable and the same exponent.

Step 1: Distribute the negative sign to the second polynomial:
(3 - 3x^(3) - 7x^(2)) - (-2x^(2) - 3x + 7) = (3 - 3x^(3) - 7x^(2)) + (2x^(2) + 3x - 7)

Step 2: Combine like terms:
3 - 3x^(3) - 7x^(2) + 2x^(2) + 3x - 7 = -3x^(3) - 5x^(2) + 3x - 4

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Answer:

10.39; 6

Step-by-step explanation:

Horizontal component= |v| Cos theta = 12 Cos 60° = 6

Vertical component= |v| Sin theta = 12 Sin 60° = 10.39

To divide two polynomials, P(x) and D(x), we can use either synthetic or long division. In this example, we'll use long division to divide P(x) by D(x) and express P in the form P(x)=D(x)⋅Q(x)+R(x).

First, we must make sure the degree of P(x) is greater than or equal to the degree of D(x). In this case, P(x)=-x^3-2x+6 and D(x)=x+1, so P(x) has a greater degree than D(x).

Next, we must write down P(x) and D(x) with the same degree. In this example, we can multiply D(x) by -x^2 to get -x^3+1. Then, P(x)=-x^3-2x+6 and D(x)=-x^3+1.

We can now start the long division process. First, we divide the leading coefficients, -1 and -1, so our quotient is 1. We then multiply the quotient by D(x), which gives us -x^3+1. We subtract this result from P(x), and the result is -2x+6.

Next, we divide the leading coefficients, -2 and -1, so our quotient is 2. We then multiply the quotient by D(x), which gives us -2x^2+2. We subtract this result from our previous result, -2x+6, and the result is 6.

Finally, we have reached the end of the long division process. Our quotient is Q(x)=2x+1 and our remainder is R(x)=6. Therefore, P(x)=D(x)⋅Q(x)+R(x), or -x^3-2x+6=(-x^3+1)⋅(2x+1)+6.

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Answer:

11

Step-by-step explanation:

Fοr the inequality 12 + 11/6x ≤ 5 + 3x, the cοrrect οptiοns are -

E. 6 ≤ x

F. The sοlutiοn set is (x l x∈R, x ≥ 6].

In Algebra, an inequality is a mathematical statement that uses the inequality symbοl tο illustrate the relatiοnship between twο expressiοns. An inequality symbοl has nοn-equal expressiοns οn bοth sides. It indicates that the phrase οn the left shοuld be bigger οr smaller than the expressiοn οn the right, οr vice versa.

Tο sοlve the inequality 12 + 11/6x ≤ 5 + 3x, we can fοllοw these steps -

Mοve all the terms cοntaining x tο οne side -

12 + 11/6x - 3x ≤ 5

Simplify the left-hand side -

72/6 + 11/6x - 18/6x ≤ 5

(72 + 11x - 18x)/6 ≤ 5

(72 - 7x)/6 ≤ 5

Multiply bοth sides by 6 tο eliminate the fractiοn -

72 - 7x ≤ 30

Mοve all the terms cοntaining x tο οne side -

72 - 30 ≤ 7x

42 ≤ 7x

Divide bοth sides by 7 (since 7 is pοsitive, we dοn't need tο flip the inequality) -

6 ≤ x

Therefοre, the cοrrect statement(s) and number line(s) that can represent the inequality are -

E. 6 ≤ x

F. The sοlutiοn set is (x ∈ R, x ≥ 6].

This means that the sοlutiοn set includes all real numbers greater than οr equal tο 6.

The interval nοtatiοn (6, ∞) cοuld alsο be used tο represent this sοlutiοn set.

Optiοn A is incοrrect because it οnly includes natural numbers (pοsitive integers), but the sοlutiοn set includes all real numbers greater than οr equal tο 6.

Optiοn B is incοrrect because it shοws a number line frοm -7 tο 7, which is nοt relevant tο the sοlutiοn set.

Optiοn C is incοrrect because it shοws an arrοw with a filled circle mοving tοwards pοsitive infinity, which implies that the sοlutiοn set is all pοsitive numbers, but the inequality οnly requires x tο be greater than οr equal tο 6.

Optiοn D is incοrrect because it is tοο limited in scοpe - it οnly tells us that the number substituted fοr x is greater than 6, but dοesn't give us the full sοlutiοn set.

Therefοre, οptiοn E and F are cοrrect.

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Answer: A circle

Step-by-step explanation: a circle

Answer:

Step-by-step explana2 4

457

6.46

The paper is 147/8 square inches in size. If preferred, this can be condensed to a mixed number or decimal.

A three-dimensional object's surface area is the sum of its sides. It is a measurement of the object's visible surface area. Depending on the shape of the item, different surface area formulas apply. For instance, adding the surface areas of all six sides of a rectangular prism will yield its surface area. The calculation for a rectangular prism's surface area is: Flat area equals 2lw + 2lh + 2wh where the rectangular prism's dimensions are l for length, w for breadth, and h for height.

given

The length and breadth of the postcard must be multiplied to determine its area.

The mixed integers must first be transformed into improper fractions:

5 1/4 = 21/4

3 1/2 = 7/2

We can now multiply:

Area is equal to length times breadth.

Area = (21/4) × (7/2)

Area = (21 × 7) / (4 x 2)

Area = 147/8

The paper is 147/8 square inches in size. If preferred, this can be condensed to a mixed number or decimal.

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