Which of the following are equivalent to
five quarts?

A 1 1/2-gallons
B 18 cups
C 160 ounces
D 32 tablespoons

A. An expression for the perimeter of the fountain is 8x + 12 ft.

B. The perimeter when x=2 ft. is 28 ft

The area of the fountain is given as 4x^2 + 12x + 9 square feet. Since the fountain is a square, we know that the length and the width of the fountain are equal. This means that we can express the area of the fountain in the form of (cx + d)^2.

Expanding (cx + d)^2 gives:

(cx + d)^2 = cx^2 + 2cxd + d^2

We can equate this to the given area of the fountain:

cx^2 + 2cxd + d^2 = 4x^2 + 12x + 9

To find the expression for the perimeter of the fountain, we need to find the dimensions (length and width) of the fountain. This can be done by factoring the area expression:

4x^2 + 12x + 9 = (2x + 3)(2x + 3)

So the dimensions of the fountain are (2x + 3) ft

The perimeter of a square is the sum of all four sides, so we can find the perimeter of the fountain by multiplying the length of one side by 4:

Perimeter = 4(2x + 3) ft = 8x + 12 ft

When x = 2 ft, the perimeter of the fountain is:

8(2) + 12 = 28 ft

So when x = 2 ft, the perimeter of the fountain is 28 ft.

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A. The percent error is 25%

B. Another estimate that gives the same percent error is the Theoretical value.

A. To find the percent error, we use the following formula:

percent error = (|experimental value - theoretical value| / theoretical value) x 100

In this case, the experimental value is 4000 years (from carbon-14 dating) and the theoretical value is 3200 years (from the researcher's estimate). Plugging these values into the formula:

percent error = (|4000 - 3200| / 3200) x 100 = (800 / 3200) x 100 = 25%

B. To find an estimate that gives the same percent error, we can use the formula:

Theoretical value = experimental value / (1 + percent error / 100)

If we use the same percent error (25%) and experimental value (4000 years) as before:

Theoretical value = 4000 / (1 + 25/100) = 4000 / 1.25 = 3200

So, an estimate of 3200 years would give the same 25% percent error as the researcher's original estimate.

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Answer:

19.8

Step-by-step explanation:

Answer:

Do 99 divided by 5

Step-by-step explanation:

Use cross multiplication

Answer:

The answer would be B

Step-by-step explanation:

The charge on the object a is 0.00017 micro Coulombs (0.00017 μC) to two significant figures.

The electric force between two objects is given by Coulomb's law: F = k[tex]q_1[/tex][tex]q_2[/tex] /[tex]r^2[/tex], where k is the Coulomb constant, [tex]q_1[/tex]and [tex]q_2[/tex]  are the charges of the two objects, and r is the distance between them.

We have , [tex]q_2[/tex] = b

r = 50cm = 0.5m

k = 9 x [tex]10^9[/tex] [tex]Nm^2/C^2[/tex]

We know that b has a mass of 300 g and that a has twice the charge of b. So we can substitute these values and solve for [tex]q_1[/tex]:

[tex]q_1[/tex]= 2 * [tex]q_2[/tex]

[tex]q_2[/tex] = 0.38 N * [tex]0.5^2[/tex] / k

Substituting the values in Coulomb's law we get,

[tex]F = k q_1 q_2/r^2[/tex]

0.38 N = k * [tex]q_1[/tex] * [tex]q_2[/tex] /  [tex]0.5^2[/tex]

[tex]q_2[/tex]  = 0.38 N * [tex]0.5^2[/tex] / (9 x      [tex]10^9[/tex])

[tex]q_2[/tex]  = 0.00085 *  [tex]10^{-6}[/tex]

then we can multiply [tex]q_2[/tex]  by 2 to find the charge on object a:

[tex]q_1[/tex] = 2 * [tex]q_2[/tex]

[tex]q_1[/tex]= 0.00017 x [tex]10^{-6}[/tex] C

So, the charge on the object a is 0.00017 micro Coulombs (0.00017 μC) to two significant figures.

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The amount you make each month before taxes and other deductions is known as your monthly gross income so monthly gross income is 3000.

Marcus makes $3,000 each month. He pays a total of 28% in taxes and 5% for

It's rather easy to figure out net income. Simply deduct expenses like taxes, insurance, and retirement contributions from your gross income, which is the entire amount of money you have made. Deductions from gross income equal net income.

Gross income – deductions = net income.

3000 - 840 - 150 = 2010.

The amount you make each month before taxes and other deductions is known as your monthly gross income. In other words, it is your annual income divided by 12.

monthly gross income = 3000.

The amount you make each month before taxes and other deductions is known as your monthly gross income so monthly gross income is 3000.

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Answer:

34.94

Step-by-step explanation:

Answer: 34.94

Step-by-step explanation:

The oscillations have an amplitude of 0.129 m. The block is positioned at 0m and moving at 0m/s at time t=0s.

The maximum deflection of a simple harmonic oscillator from its equilibrium position is its amplitude. Since this is the displacement at time t=1.00s, the oscillations in this instance have an amplitude of 0.129m. The oscillator is in equilibrium at time t=0 s, therefore the block is located at location 0 m. Additionally, since the oscillator has not yet begun to move, these values can be determined by examining the oscillator's equation of motion. According to this equation, the oscillator's position is determined by the expression x=A*cos(t), where A stands for amplitude and for angular frequency. The equation becomes simpler to x=0m for A=0.129m and t=0s. Similar to that, v=-Asin(t) gives the velocity. The equation is again simplified to v=0m/s as A=0.129m and t=0s.

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The opponent to Citizens United v. Federal Elections Commission (2010) would most likely argue that corporate and special interest influence in elections should be limited to prevent corruption and maintain a fair and level playing field for all candidates.

The opponent to Citizens United v. Federal Elections Commission (2010) would most likely argue that the decision to allow unrestricted corporate and special interest spending in elections has had a negative impact on the integrity of the democratic process. They would point to the increased influence of money in politics and the dangers of corruption that come with it. They would argue that the decision has allowed wealthy entities to have an outsized influence in elections, creating an unfair and unequal playing field for candidates. Furthermore, they would argue that the decision has weakened the regulation of campaign spending and has allowed for the creation of so-called "dark money" groups, which can spend money on elections with little to no transparency. In short, the opponent to Citizens United v. Federal Elections Commission (2010) would argue that allowing unlimited corporate and special interest spending in elections has created an unequal playing field and should be limited in order to protect the integrity of the democratic process.

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The table is completed as follows:

The situation is modeled by a linear function, in slope-intercept format, as follows:

y = mx + b.

In which:

The initial capacity is of 770 liters, decaying by 14 liters each minute, hence the parameters are given as follows:

b = 770, m = -14.

The function for this problem is defined as follows:

y = -14x + 770.

The numeric values are given as follows:

The table is given by the image presented at the end of the answer.

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The missing coordinates on the ordered pairs of the linear equation are:

(0, -4) and  (8, 3)

Here we have the linear equation:

3x - 4y = 12

And we want to find the missing coordinates for the given points (0, ?) and (?, 3) where these points belong to the line.

The first point is (0, ?), this means that the value of x is zero, then we can evaluate the equation in x = 0 then we will get:

3*0 - 4y = 12

-4y = 12

y = 12/-3 = -4

So the point is (0, -4)

For the other point (?, 3) we need to evaluate in y = 3.

3*x - 4*3  12

3x - 12 = 12

3x = 12 + 12

3x = 24

x = 24/3 = 8

So we have the point (8, 3)

These are the missing coordinates.

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If y varies inversely as x and y = 9 when x = 7, then the value of y = 10.5 when x = 6.

If y fluctuates inversely of x, then y = kx, where k is a fixed value. According to the expressions "y varies inversely as x" and "y is inversely proportionate to x," y decreases as x increases or vice versa. There are two translations for this idea. For some constant k, referred to as the constant of proportionality, yx = k.

According to the expression "y varies inversely as x," y drops by the same amount that x grows. In other terms, xy = k means that the equation xy is constant.

Let the equation be x = k/y, then k be a constant

[tex]$$\begin{aligned}& x=k \times \frac{1}{y} \\& \Rightarrow k=x y=9 \times 7=63 \\& \Rightarrow x=\frac{63}{y}\end{aligned}$$[/tex]

So [tex]$y=\frac{63}{x}$[/tex]

At x = 6 we have

[tex]$y=\frac{63}{6}=10.5$$[/tex]

If y varies inversely as x and y = 9 when x = 7, then the value of y = 10.5 when x = 6.

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The simplified expression is 14m -10n

From the question, we have the following parameters that can be used in our computation:

12m−3n62m−7n

Express properly

So, we have the following representation

12m - 3n + 2m - 7n

Collect the like terms

This gives

12m + 2m - 3n - 7n

Evaluate the like terms

So, we have the following representation

14m - 10n

Hence, the solution is 14m - 10n

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Answer: b is the coefficient of the x term. In the standard form f(x) = ax^2 + bx + c, b is the value of the coefficient of the x term. So the value of b is 0.

Step-by-step explanation:

The value of b in the given function is 12.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

For example, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Given that, a table defining the function, we need to form an equation and compare with the standard form of a quadratic function,

We can use the vertex form of a quadratic function, which is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Since, we know the vertex of this parabola from the table, we can use that information to write the equation in vertex form: f(x) = a(x + 6)^2 + 8

Expanding this, we get f(x) = a(x² + 12x + 36) + 8

Comparing this with the standard form, we see that a = 1, b = 12, and c = 8.

Therefore, the value of b is 12.

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The complete question is :-

The table represents a quadratic function f(x). x f(x) −10 24 −9 17 −8 12 −7 9 −6 8 −5 9 −4 12 If the equation of the function f(x) is written in standard form f(x) = ax2 + bx + c, what is the value of b?

Answer:

All of the following statements are true for the expression (11 + 7)(8 + 7) + (2 + 9): all factors are the sum of two terms, the solution is the sum of three terms, the solution is the product of two factors, plus another number, and the solution is the difference between three terms.

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The required constant charge for each minute used is $0.02.

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14. ​

Let fixed charge of monthly be x and constant rate of each minute used is y.

So,

In january

x + 100y = 47--------(1)

and in February

x + 350y = 52-----------(2)

equation(2) - equation(1)

(x + 350y) - (x + 100y) = 52 -47

250y = 5

y = 0.02

Thus, $0.02 used per minutes.

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The length of sides a,b and c of triangle are 2, 4 and 5 respectively whereas the perimeter is 11ft.

A one-dimensional length, a two-dimensional shape, or both can have perimeters that are closed paths that contain, surround, or define them. A circle's or an ellipse's perimeter is measured by its circumference.

The perimeter calculation has a lot of useful applications. Calculated perimeter is the term used to describe the size of fence required to completely surround a yard or garden. How far a wheel or circle can go in one spin is determined by its circumference, which measures its perimeter. Similar to this, a spool's circumference is inversely related to the length of thread that is wound around it; if the string were exactly the same length, the circumference would be equal.

Given that

b = 2a

c = 3 +a

We know that the perimeter is equal to the sum of all the sides

Perimeter = a+b +c

11 = a +2a + a+3

8 = 4a

a = 2

Hence, sides a ,b and c are 2, 4, 5 respectively.

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Step-by-step explanation:

the easiest way might be the approach to calculate the area of the whole rectangle and then subtract the area of the triangle.

the area of the whole rectangle is

18×16 = 288 m²

the area of a triangle is

baseline × height / 2

in a case like this (right-angled triangle) we can use one leg as baseline, and the other leg (90°) as height.

so, the height is the same as the width of the rectangle : 16 m.

how long is the baseline ?

it is on the 18 m length of the rectangle, and there are two 3 m "gaps", one left, and one right.

so, what's left for the baseline of the triangle itself ?

baseline = 18 - 3 - 3 = 12 m

therefore the area of the triangle is

12×16/2 = 12×8 = 96 m²

so, the total area of the shaded region is

288 - 96 = 192 m²

The reflection preserves the side lengths and angles of the triangle. The dilation preserves angles but not side lengths. Therefore, option B is the correct answer.

Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.

Given that, triangle is reflected across the y-axis and then dilated by a factor of centered at the origin.

The triangle ABC in a graph with vertices A (-4, -2), B (4, -2), and C (4, 4)

A reflection across the y-axis changes the coordinates of the triangle from (x, y) to (-x, y) without changing the side lengths and angles.

The dilation of the triangle by a factor an then centered at the origin increases the side length of the triangle but the angles in the triangle remain the same since the ratio of the sides before and after dilation are the same.

Therefore, option B is the correct answer.

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The order of the numbers from the smallest to the largest is: 0.04, 25%

It can be said that the ascending or increasing order is the one where the values, elements or numbers of a group or set are ordered starting from the one with the smallest value to the one with the highest value of all.

Ordering the numbers from the smallest to the largest , we have:

25% is equal to 25/100 = 0.25, so 0.25 is largest than 0.04

0.04 < 0.25

0.04 < 25%

The correct option is:

0.04, 25% = correct order

25%, 0.04 = incorrect order

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The measure of a different interior angle of the triangle is 52 degrees.

A right angled triangle is a triangle with one of the angles as 90 degrees.

The sum of the interior angle of a triangle is 180 degrees.

Given the data in the question;

Since the sum of the interior angle of a triangle is 180 degrees.

Angle a + Angle b + Angle c = 180

38 + Angle b + 90 = 180

Angle b + 128 = 180

Angle b = 180 - 128

Angle b = 52 degrees.

Therefore, the measure of the second angle is 52 degrees.

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y = $40 is the equation of the line that represents the information. The line has no slope.

A linear equation can be used to represent the equation that represents Mr. Williams' total payment for city water. A linear equation is one that is composed of a single variable raised to the power of one.

A linear equation takes the following form:

y = ax + b

Where: a = slope = which measures the equation's rate of change

b = the intercept

y = $40 + (x × 0)

y = $40

A linear equation can have an upward, downward, or zero slope when plotted on a graph.

The equation of the line that represents the information is y = $40. There is no slope to the line.

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If a bus company usually transports 12 000 people per day at a ticket price of $1. The ticket price that will maximize revenue is $2 per ticket.

Equation to find the ticket price is:

y = (12000 - 400x)(1 + .1x)

Take the derivative of the function by product rule

y' = (12000 - 400x)(.1) + (-400)(1 + .1x)

y' = 1200 - 40x - 400 - 40x

y' = 800 - 80x

Let y' = 0

0 = 800 - 80x

Solving for x

80x = 800

Divide both side by 80x

x = 800/80

x = 10

Point at x = 10

Substitute x with 10 for 1 + .1x

1 + .1(10)

= 1 + 1

= $2 per ticket

Therefore the ticket price is  $2 per ticket.

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Answer:

x = 15

Step-by-step explanation:

The sum of the four angles of a quadrilateral add up top 360°

Given:

m∠A = (5x+14)°  

m∠b = 109°        

m∠C = (3x+8)°    

m∠D = 109°°

Here we are given actual values for two angles as 109°. Their sum is: 109 + 109 = 218°

The sum of the remaining two angles which are expressions in x should be:

360 - 218 = 142°

This is the sum of m∠A an m∠C

Substituting the terms for the two angle measures we get

(5x+14)  + (3x+8) = 142

5x+14  + 3x+8 = 142

Grouping like terms:

5x + 3x + 14 + 8 = 142

8x + 22 = 142

8x = 142- 22

8x = 120

x = 120/4

x = 15

The length of the arc of a circle with given radius and central angle is 5.23 meters.

A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.

Given that, a circle of diameter 10 meters subtended by a central angle of π/3 radians or 60°.

We have, radius of a circle = 5 meters

We know that, arc length of a circle is θ/360° ×2πr

Now, 60°/360° ×2×3.14×5

= 1/6×2×3.14×5

= 5.23 meters

Therefore, the length of the arc of a circle with given radius and central angle is 5.23 meters.

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890998

Step-by-step explanation:

1999+888999 = 890998

The linear function containing the median of the trapezoid whose vertices are R(-1, 5) , S(1, 8), T(7, -2), and U(2, 0). is given as follows:

y = -1.67x + 6.5.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The median of the trapezoid is composed by these two points:

The coordinates of the midpoint of RS are given as follows:

The coordinates of the midpoint of TU are given as follows:

Hence the points of the function are:

(0, 6.5) and (4.5, -1).

When x = 0, y = 6.5, hence the intercept b is given as follows:

b = 6.5.

When x increases by 4.5, y decays by 7.5, hence the slope m is given as follows:

m = -7.5/4.5

m = -1.67.

Hence the function is:

y = -1.67x + 6.5.

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Payoff matrix: R (row player) receives payoff if total number of fingers shown is even, C (column player) receives payoff if total number of fingers shown is odd.

Two-finger morra is a game in which two players take turns holding up either one or two fingers. The payoff for the game is the total number of fingers shown, with the player whose total is even (R) receiving the payoff, and the player whose total is odd (C) receiving the payoff. This game can be represented in a payoff matrix, which is a table that shows the payoffs for each player in each possible situation. For two-finger morra, the payoff matrix would have two rows and two columns, representing the two players, R and C. The top row would show the payoffs for R when the total number of fingers is even, and the bottom row would show the payoffs for R when the total number of fingers is odd. Similarly, the left column would show the payoffs for C when the total number of fingers is even and the right column would show the payoffs for C when the total number of fingers is odd.

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Answer:

k)  x = 2

l)  x = 6

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8cm}\underline{Log laws}\\\\Product law:\quad\:$\log_axy=\log_ax + \log_ay$\\\\Power law:\quad\;\;\;\:$\log_ax^n=n\log_ax$\\\\Equality Law:\; If $\log_ax=\log_ay$ then $x=y$\\\\Same base as number:\;\;\;$\log_aa=1$\\$\end{minipage}}[/tex]

[tex]\begin{aligned}\log_7(x + 12) + \log_7(x + 1) &= \log_7(42)\\\log_7\left[(x + 12)(x+1)\right]&= \log_7(42)\\(x + 12)(x+1)&=42\\x^2+13x+12&=42\\x^2+13x-30&=0\\x^2+15x-2x-30&=0\\x(x+15)-2(x+15)&=0\\(x-2)(x+15)&=0\\\\\implies x&=2\\\implies x&=-15\end{aligned}[/tex]

As logs of negative numbers cannot be taken, x = -15 is an extraneous solution.  Therefore, the only valid solution is x = 2.

[tex]\begin{aligned}\log_4(x + 3) + 1 &= 2\log_4(x)\\\log_4(x + 3) + \log_44 &= \log_4(x^2)\\\log_4\left[4(x + 3)\right] &= \log_4(x^2)\\4(x + 3)&=x^2\\4x+12&=x^2\\x^2-4x-12&=0\\x^2-6x+2x-12&=0\\x(x-6)+2(x-6)&=0\\(x+2)(x-6)&=0\\\\\implies x&=-2\\\implies x&=6\end{aligned}[/tex]

As logs of negative numbers cannot be taken, x = -2 is an extraneous solution.  Therefore, the only valid solution is x = 6.

Using Angle Sum property, the measure of 3 angles is ∠Q = 35°, ∠R = 19°, ∠S = 126°.

According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees. Three sides and three angles, one at each vertex, make up a triangle. The sum of the interior angles in a triangle is always 180o, regardless of whether it is acute, obtuse, or right.

One of the most commonly applied properties in geometry is the triangle's angle sum property. Most often, the unknown angles are calculated using this attribute.

As given the measure of 3 angles is -

∠Q = 4x - 17

∠R = x + 6

∠S = 10x - 4

We know that by angle - sum property,

The sum of 3 angles of triangle = 180°

⇒ 4x - 17 + x + 6 + 10x - 4 = 180

⇒ 15x -15 = 180

⇒ 15x = 180 + 15

⇒ 15x = 195

⇒ x = 13

∠Q = 4x - 17 = 4 × 13 - 17 = 35°

∠R = x + 6 = 13 + 6 = 19°

∠S = 10x - 4 = 10 × 13 - 4 = 126°

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Complete question -