Enter the number that belongs in the green box 7 4 8

The range of the given dataset is: 44

The boxplot variation restricts the whiskers length to no more than 1.5 times the interquartile range. That is, the whiskers reach the farthest value from the center while still being within 1.5 times the interquartile range of the lower or upper quartile.

The range of the box and whisker plot is the difference of the maximum value from the minimum value of the data set.

Interquartile range is the difference of the 3rd quartile from the 1st quartile.

From the dataset, the maximum value is 48 while the minimum value is 4.

Thus:

Range = 48 - 4

Range = 44

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The Intel pays $7,760 to Bally Manufacturing on August 14.

The first step in calculating what Intel Corporation pays Bally on August 14 is to determine the net price of the machinery after the trade discount and the return of $100 due to defects.

The trade discount of 40% is calculated as follows:

Discount = List price × Discount rate

Discount = $13,100 × 0.40 = $5,240

So the net price of the machinery after the trade discount is:

Net price = List price - Discount

Net price = $13,100 - $5,240 = $7,860

After Intel returns $100 of machinery, the cost of the machinery is further reduced to:

Net price after return = Net price - Return

Net price after return = $7,860 - $100 = $7,760

Since the payment terms are 3/10 EOM (end of month), Intel receives a discount of 3% if payment is made within 10 days. The 10-day period begins on August 1 and ends on August 10 (the payment due date). Since Intel pays the bill on August 14, payment is late and the 3% discount does not apply.

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[tex]\boxed{A}\\\\ U=5(2n+22)+2\left( n+\cfrac{3}{2} \right) \\\\\\ U=10n+110+2n+3 \implies U=12n+113 \\\\[-0.35em] ~\dotfill\\\\ \boxed{B}\hspace{5em}\textit{in 2009, that's 9 years after 2000, n = 9}\\\\ U(9)=12(9)+113\implies U(9)=221 ~~ millions[/tex]

To find the center and radius of the circle represented by the inequality [tex]\displaystyle \sf x^{2} +y^{2} -12y-12\leq 0[/tex], we can complete the square for the y terms.

The inequality can be rewritten as:

[tex]\displaystyle \sf x^{2} +( y^{2} -12y) -12\leq 0[/tex]

To complete the square for the y terms, we need to add and subtract [tex]\displaystyle \sf ( 12/2) ^{2} =36[/tex] inside the parentheses:

[tex]\displaystyle \sf x^{2} +( y^{2} -12y+36) -36-12\leq 0[/tex]

Simplifying, we have:

[tex]\displaystyle \sf x^{2} +( y-6)^{2} -48\leq 0[/tex]

Now we can rewrite the inequality in the standard form of a circle equation:

[tex]\displaystyle \sf ( x-h)^{2} +( y-k)^{2} \leq r^{2}[/tex]

Comparing this with the obtained equation, we can identify the center and radius of the circle:

Center: [tex]\displaystyle \sf ( h,k)=( 0,6)[/tex]

Radius: [tex]\displaystyle \sf r=\sqrt{48}[/tex]

Therefore, the center of the circle is at [tex]\displaystyle \sf ( 0,6)[/tex], and its radius is [tex]\displaystyle \sf \sqrt{48}[/tex].

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Answer:

7

Step-by-step explanation:

The line represented by the equation y = 7 is a horizontal line that passes through the y-axis at 7, so the y intercept of this line is 7

84.13% of the printing jobs will be acceptable.

The new standard deviation required to achieve a minimum of 95% of jobs acceptable is 0.121.

The darkness of the print is measured quantitatively using an index. If the index is greater than or equal to 2.0 then the darkness is acceptable. Anything less than 2.0 means the print is too light and not acceptable. The machines print at an average darkness of 2.2 with a standard deviation of 0.20.

The mean of the darkness of the print is µ = 2.2 and the standard deviation is σ = 0.20.Therefore, the z-score can be calculated as; `z = (x - µ) / σ`.The index required for acceptable prints is 2.0. Thus, the percentage of prints that are acceptable can be calculated as follows;P(X ≥ 2.0) = P((X - µ)/σ ≥ (2.0 - 2.2) / 0.20)P(Z ≥ -1) = 1 - P(Z < -1)Using the standard normal table, P(Z < -1) = 0.1587P(Z ≥ -1) = 1 - 0.1587= 0.8413.

To find the new standard deviation, we can use the z-score formula.z = (x - µ) / σz = (2.0 - 2.2) / σz = -1Therefore, P(X ≥ 2.0) = 0.95P(Z ≥ -1) = 0.95P(Z < -1) = 0.05Using the standard normal table, the z-score value of -1.645 corresponds to a cumulative probability of 0.05. Hence,z = (2.0 - 2.2) / σ = -1.645σ = (2.0 - 2.2) / -1.645= 0.121.

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The coefficient of variation for Bank A is approximately 8.04%, while the coefficient of variation for Bank B is approximately 25.55%.

To find the coefficient of variation for each set of data, we need to calculate the mean and standard deviation for each set. The coefficient of variation is then calculated by dividing the standard deviation by the mean and multiplying by 100.

Let's calculate the coefficient of variation for each set of data:

Bank A (single line):

Mean: Calculate the mean of the data set.

Mean = (6.5 + 6.6 + 6.7 + 6.7 + 7.1 + 7.4 + 7.5 + 7.7 + 7.7 + 7.7) / 10 = 7.03 minutes

Standard deviation: Calculate the standard deviation of the data set.

Standard deviation = √[(6.5 - 7.03)² + (6.6 - 7.03)² + ... + (7.7 - 7.03)²] / 10 ≈ 0.565 minutes

Coefficient of variation:

Coefficient of variation = (0.565 / 7.03) * 100 ≈ 8.04%

Bank B (individual lines):

Mean: Calculate the mean of the data set.

Mean = (4.0 + 5.4 + 5.9 + 6.2 + 6.8 + 7.7 + 7.7 + 8.5 + 9.4 + 9.8) / 10 = 7.5 minutes

Standard deviation: Calculate the standard deviation of the data set.

Standard deviation = √[(4.0 - 7.5)² + (5.4 - 7.5)² + ... + (9.8 - 7.5)²] / 10 ≈ 1.916 minutes

Coefficient of variation:

Coefficient of variation = (1.916 / 7.5) * 100 ≈ 25.55%

Comparing the variation:

The coefficient of variation for Bank A is approximately 8.04%, while the coefficient of variation for Bank B is approximately 25.55%. Since the coefficient of variation measures the relative variability of the data, we can conclude that the waiting times at Bank B (individual lines) have a higher variation compared to Bank A (single line).

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Using Maxwell's equations, we can determine the magnetic flux density. One of the Maxwell's equations is:

[tex]\displaystyle \nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}}{\partial t}[/tex],

where [tex]\displaystyle \nabla \times \mathbf{H}[/tex] is the curl of the magnetic field intensity [tex]\displaystyle \mathbf{H}[/tex], [tex]\displaystyle \mathbf{J}[/tex] is the current density, and [tex]\displaystyle \frac{\partial \mathbf{D}}{\partial t}[/tex] is the time derivative of the electric displacement [tex]\displaystyle \mathbf{D}[/tex].

In this problem, there is no current density ([tex]\displaystyle \mathbf{J} =0[/tex]) and no time-varying electric displacement ([tex]\displaystyle \frac{\partial \mathbf{D}}{\partial t} =0[/tex]). Therefore, the equation simplifies to:

[tex]\displaystyle \nabla \times \mathbf{H} =0[/tex].

Taking the curl of the given magnetic field intensity [tex]\displaystyle \mathbf{R} =2\cos( 10^{10} t-600x)\hat{a}_{z}\, \text{Am}[/tex]:

[tex]\displaystyle \nabla \times \mathbf{R} =\nabla \times ( 2\cos( 10^{10} t-600x)\hat{a}_{z}) \, \text{Am}[/tex].

Using the curl identity and applying the chain rule, we can expand the expression:

[tex]\displaystyle \nabla \times \mathbf{R} =\left( \frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial y} -\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial z}\right) \mathrm{d} x\mathrm{d} y\mathrm{d} z[/tex].

Since the magnetic field intensity [tex]\displaystyle \mathbf{R}[/tex] is not dependent on [tex]\displaystyle y[/tex] or [tex]\displaystyle z[/tex], the partial derivatives with respect to [tex]\displaystyle y[/tex] and [tex]\displaystyle z[/tex] are zero. Therefore, the expression further simplifies to:

[tex]\displaystyle \nabla \times \mathbf{R} =-\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial x} \mathrm{d} x\mathrm{d} y\mathrm{d} z[/tex].

Differentiating the cosine function with respect to [tex]\displaystyle x[/tex]:

[tex]\displaystyle \nabla \times \mathbf{R} =-2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z[/tex].

Setting this expression equal to zero according to [tex]\displaystyle \nabla \times \mathbf{H} =0[/tex]:

[tex]\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z =0[/tex].

Since the equation should hold for any arbitrary values of [tex]\displaystyle \mathrm{d} x[/tex], [tex]\displaystyle \mathrm{d} y[/tex], and [tex]\displaystyle \mathrm{d} z[/tex], we can equate the coefficient of each term to zero:

[tex]\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x) =0[/tex].

Simplifying the equation:

[tex]\displaystyle \sin( 10^{10} t-600x) =0[/tex].

The sine function is equal to zero at certain values of [tex]\displaystyle ( 10^{10} t-600x) [/tex]:

[tex]\displaystyle 10^{10} t-600x =n\pi[/tex],

where [tex]\displaystyle n[/tex] is an integer. Rearranging the equation:

[tex]\displaystyle x =\frac{ 10^{10} t-n\pi }{600}[/tex].

The equation provides a relationship between [tex]\displaystyle x[/tex] and [tex]\displaystyle t[/tex], indicating that the magnetic field intensity is constant along lines of constant [tex]\displaystyle x[/tex] and [tex]\displaystyle t[/tex]. Therefore, the magnetic field intensity is uniform in the given medium.

Since the magnetic flux density [tex]\displaystyle B[/tex] is related to the magnetic field intensity [tex]\displaystyle H[/tex] through the equation [tex]\displaystyle B =\mu H[/tex], where [tex]\displaystyle \mu[/tex] is the permeability of the medium, we can conclude that the magnetic flux density is also uniform in the medium.

Thus, the correct expression for the magnetic flux density in the given medium is:

[tex]\displaystyle B =6\cos( 10^{10} t-600x)\hat{a}_{z}[/tex].

Given that the side of a square field is 52 m so, the area of the square field is 2704 m².

The side of a square field is given as 52 m.

Now, Let’s find the area of the square field using the given information.

As we know, area of a square can be calculated by using the formula:

A = a², where ‘a’ is the side of the square.

Now, by substituting the given value of ‘a’ in the given formula above we will get the area of the square field as,

A = (52)²

A = 2704 m²

Therefore, the area of the square field of given side i.e. 52m is 2704 m².

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The rocket is at a height of 1876.1 meters after 9 seconds,the velocity of the rocket after 9 seconds is 143.8 m/s and  the acceleration of the rocket after 9 seconds is -9.8 m/s².

To find the height of the rocket when it was initially launched, we can plug in t = 0 into the equation h(t) = -4.9t² + 232t + 185.

h(0) = -4.9(0)² + 232(0) + 185

     = 0 + 0 + 185

     = 185

Therefore, the rocket was initially launched at a height of 185 meters.

To find the height of the rocket after 9 seconds, we can plug in t = 9 into the equation h(t) = -4.9t² + 232t + 185.

h(9) = -4.9(9)² + 232(9) + 185

     = -4.9(81) + 2088 + 185

     = -396.9 + 2088 + 185

     = 1876.1

Therefore, the rocket is at a height of 1876.1 meters after 9 seconds.

To find the velocity of the rocket after 9 seconds, we can take the derivative of the height function h(t) with respect to time (t) and evaluate it at t = 9.

The velocity function v(t) is the derivative of h(t) with respect to t:

v(t) = dh/dt = d/dt(-4.9t² + 232t + 185)

       = -9.8t + 232

v(9) = -9.8(9) + 232

       = -88.2 + 232

       = 143.8

Therefore, the velocity of the rocket after 9 seconds is 143.8 m/s.

To find the acceleration of the rocket after 9 seconds, we can take the derivative of the velocity function v(t) with respect to time (t) and evaluate it at t = 9.

The acceleration function a(t) is the derivative of v(t) with respect to t:

a(t) = dv/dt = d/dt(-9.8t + 232)

       = -9.8

a(9) = -9.8

Therefore, the acceleration of the rocket after 9 seconds is -9.8 m/s².

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The missing values in the quantitative reasoning given are : -2, 13 and 9

Given the rule :

We can deduce that :

For the left circle :

circle = -6 - (-4) = -6 + 4 = -2

For the right circle :

circle = 11 - (-2) = 11 + 2 = 13

For the left square :

square = 13 + (-4)

square = 13 -4 = 9

Therefore, the missing values are : -2, 13 and 9

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The graph of the function f(x)=√(x + 1) is in the first option

A radical graph, also known as a square root graph, represents the graph of a square root function. A square root function is a mathematical function that takes the square root of the input variable.

The general form of a square root function is f(x) = √(ax + b) + c,

where a, b, and c are constants that determine the characteristics of the graph.

In the given function:

a = 1

b = 1

c = 0

The graph is plotted and attached

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The algebraic expression for the given phrase is: 17x - 8x. To simplify this expression, we can combine like terms by subtracting the coefficients of x. The simplified expression is: 9x.

In the given phrase, "The product of 8 and a number" can be represented as 8x, where x represents the number. Similarly, "The product of 17 and the number" can be represented as 17x. Since we are subtracting the product of 8x from the product of 17x, the algebraic expression becomes 17x - 8x.

To simplify the expression, we combine like terms. The coefficients of x are 17 and -8. Since we are subtracting 8x from 17x, we subtract the coefficient of 8x from the coefficient of 17x, resulting in 17x - 8x. Combining like terms gives us 9x.

In conclusion, the simplified expression for the phrase "The product of 8 and a number, which is then subtracted from the product of 17 and the number" is 9x.

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Answer:

Ryan had a head start of 10 meters

Step-by-step explanation:

Answer:

only god knows

Step-by-step explanation:

because they didn't give us an answer on how many text messages anyone sent

At a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

According to the given model C = 0.37219T + 1,560, where C represents the number of calories an idle mouse burns each day and T represents the temperature of its environment in °C.

To find the most comfortable temperature for an idle mouse, we need to determine the temperature at which the mouse burns the least amount of calories per day.

To find this temperature, we can minimize the equation C = 0.37219T + 1,560. To do so, we take the derivative of C with respect to T and set it equal to zero:

dC/dT = 0.37219 = 0

Solving this equation, we find that the derivative is a constant value, indicating that the function C = 0.37219T + 1,560 is a linear equation with a slope of 0.37219. This means that the mouse burns the least calories at any temperature, as the slope is positive.

Therefore, there is no specific "most comfortable" temperature for an idle mouse in terms of minimizing calorie burn. However, if we consider the range of temperatures mice typically encounter, we can find a temperature where the calorie burn is relatively low.

For example, if we take a temperature of 20°C, we can calculate the calorie burn:

C = 0.37219 * 20 + 1,560

C = 7.4438 + 1,560

C ≈ 1,567.4438 calories per day

Therefore, at a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

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Answer:

41)  Yes, the relation is a function.

42)  The domain of the function is [-2, 4].

43)  The range of the function is [-1, 3].

Step-by-step explanation:

A relation is a set of ordered pairs where each input (x-value) is associated with one or more outputs (y-values).

A function is a special type of relation where each input (x-value) is associated with exactly one output (y-value).

We can determine if a graphed relation is a function by applying the Vertical Line Test. It states that if a vertical line intersects the graph at more than one point, then the relation does not pass the test and is not a valid function.

As the given graph passes the Vertical Line Test, the relation is a function.

[tex]\hrulefill[/tex]

The domain of a function is the set of all possible input values (x-values).

The range of a function is the set of all possible output values (y-values).

From inspection of the given graph, the continuous curve begins in quadrant II at point (-2, 1) and ends in quadrant IV at point (4, -1).

The endpoints of the graph are represented by closed circles, which means that the corresponding x and y values are included in the domain and range.

Therefore, the domain of the function is the x-values of the endpoints: [-2, 4].

The minimum point of the curve is endpoint (4, -1) and the maximum point is (0, 3). Therefore, the range of the function is the y-values of the minimum and maximum points: [-1, 3].

To calculate how many months it will take for the number of insect species to reach a specific value "n" based on the trend of a 4% decrease per month, we can use an exponential decay function.

The general form of an exponential decay function is given by:

f(x) = a * (1 - r)^x

In this case, "x" represents the number of months, and "r" represents the rate of decrease per month, which is 4% or 0.04 (since it is expressed as a decimal).

Since the initial number of insect species is 186, we can substitute "a" as 186 into the function:

f(x) = 186 * (1 - 0.04)^x

To find the number of months it will take for the number of insect species to reach a specific value "n," we can set the equation equal to "n" and solve for "x":

n = 186 * (1 - 0.04)^x

By rearranging the equation and using logarithms, we can solve for "x" and determine the number of months it will take for the number of insect species to reach the desired value.

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The length of the other diagonal is 11.25 cm.

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

In this question, we are given the following:

The area of a kite is 180. One of the diagonals is 16.

What is the length of the other diagonal?

The details of the solution are as follows:

We know that,

The area of a kite is the product of the diagonals divided by 2:

[tex]\text{A} = \dfrac{(\text{d}^1 \times \text{d}^2)}{2}[/tex]

You can substitute what we have:

[tex]180= \dfrac{(16 \times \text{d}^2)}{2}[/tex]

And solve.

[tex]180 = 16 \times \text{d}^2[/tex]

[tex]\text{d}^2=\dfrac{180}{16}[/tex]

[tex]\text{d}^2=\bold{11.25 \ cm}[/tex]

Therefore, the length of the other diagonal = 11.25 cm.

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Answer:

The values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Step-by-step explanation:

To find the values of b that satisfy the equation 3(2b + 3)² = 36, we can solve for b by following these steps:

1. Divide both sides of the equation by 3:

  (2b + 3)² = 12

2. Take the square root of both sides:

  √[(2b + 3)²] = √12

  Simplifying further:

  2b + 3 = ±√12

3. Subtract 3 from both sides:

  2b = ±√12 - 3

4. Divide both sides by 2:

  b = (±√12 - 3) / 2

  Simplifying further:

  b = (±√4 * √3 - 3) / 2

  b = (±2√3 - 3) / 2

Therefore, the values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

answer: 13/2 or 6 1/2

step-by-step explanation:

hihi so basically your problem is making a solvable equation so w variables and stuff

heres my explanation !

the difference of a number and 2 is b-2

twice the difference of a number and 2 would be 2(b-2)

number 9 = 9 (duh lol)
so

2(b-2) = 9

2b - 4 = 9

2b = 13

improper: b = 13/2
mixed: b = 6 1/2

Terri have to react 1.42 seconds before the volleyball hits the ground.

Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is:

[tex]\text{ax}^2 + \text{bx} + \text{c} = 0[/tex]

Given data:

The height can be modeled by a quadratic equation.

[tex]h(t)=-16t^2+v_0t+h_0[/tex]

Where h is the height and t is the time.

[tex]h(t)=-16t^2+19.5t+4.5[/tex]

[tex]-16t^2+19.5t+4.5=0[/tex]

[tex]a = -16, b = 19.5, c = 4.5[/tex]

It looks like a quadratic equation. we can solve it by quadratic formula.

[tex]\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

[tex]\rightarrow t=\dfrac{-19.5\pm\sqrt{(-19.5)^2-4\times(-16)(4.5)} }{2(-16)}[/tex]

[tex]\rightarrow t=\dfrac{-19.5\pm\sqrt{380.25+288} }{-32}[/tex]

[tex]\rightarrow t=\dfrac{-19.5\pm25.851 }{-32}[/tex]

[tex]\rightarrow t=\dfrac{-19.5-25.851 }{-32}, \ t=\dfrac{-19.5+25.851 }{-32}[/tex]

[tex]\rightarrow t=1.42, \ t=-0.20[/tex]

Time cannot be in negative. So neglect t = –0.235.

Hence, Terri have to react 1.42 seconds before the volleyball hits the ground.

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Using the physics concept of projectile motion and inputting the given values into the appropriate equation, we can determine the time it takes for the volleyball to hit the ground after being served

This question is a classic use of physics, more specifically, the concept of projectile motion. Here, the volleyball can be conceived as a projectile. When Patricia serves the ball upward, the ball will first ascend and then descend due to gravity.

Let's use the following equation which is a version of kinematic equations to solve this problem, adjusting for the fact that we're dealing with an initial height of 4.5 ft and an ending height of 0 ft (when the ball hits the ground). The equation y = yo + vot - 0.5gt² , where:

Setting y=0, yo=4.5 feet, vo=19.5 feet/second, and g=32.2 feet/second², and plug these values into the equation, we'll get a quadratic equation in the form of 0 = 4.5 + 19.5t - 16.1t². Solve that equation for t to find the time it takes for the ball to hit the ground.

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