What is the slope of this line?
A. 2
B. -1/2
C. 1/2
D. -2

The vertical lines (whiskers) extend from the box to the minimum value (20) and the maximum value (55).

That's how you create a box-and-whisker plot for the given set of values.

To create a box-and-whisker plot for the given set of values: 20, 23, 25, 36, 37, 38, 39, 50, 52, 55, you need to follow these steps:

Step 1: Sort the data in ascending order:

20, 23, 25, 36, 37, 38, 39, 50, 52, 55

Step 2: Find the median (middle value):

Since we have 10 data points, the median is the average of the two middle values. In this case, the two middle values are 37 and 38. So, the median is (37 + 38) / 2 = 37.5.

Step 3: Determine the lower quartile (Q1):

The lower quartile is the median of the lower half of the data set. In our case, the lower half is:

20, 23, 25, 36, 37

Since we have an odd number of values, the lower quartile Q1 is the median of this subset. The median of this subset is 25.

Step 4: Determine the upper quartile (Q3):

The upper quartile is the median of the upper half of the data set. In our case, the upper half is:

38, 39, 50, 52, 55

Again, since we have an odd number of values, the upper quartile Q3 is the median of this subset. The median of this subset is 50.

Step 5: Find the minimum and maximum values:

The minimum value from the sorted list is 20, and the maximum value is 55.

Step 6: Plot the box-and-whisker plot:

Now that we have all the necessary values, we can create the box-and-whisker plot:

|           |

-----|-----------|-----

20  |   |       |

|---|-------|

|           |

25  |           |

|-----------|

37  |           |

|-----------|

|           |

50  |           |

|---|-------|

|   |       |

55  |           |

|           |

In the plot:

The line in the middle represents the median (37.5).

The box represents the interquartile range (IQR), which spans from the lower quartile (Q1 = 25) to the upper quartile (Q3 = 50).

The vertical lines (whiskers) extend from the box to the minimum value (20) and the maximum value (55).

That's how you create a box-and-whisker plot for the given set of values.

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Answer:

9/10 or 0.9

Step-by-step explanation:

Slope of a line passing through two points (x1, y1) and (x2, y2) is given by
Slope m = rise/run

where
rise = y2 - y1
run = x2 - x1

Given points (- 6, - 5) and (4, 4),

rise = 4 - (-5) = 4 + 5 = 9

run = 4 - ( - 6) = 4 + 6 = 10

Slope = rise/run = 9/10 or 0.9

Step-by-step explanation:

5 % decrease means 95 %  (.95)  remain

Year 1

   800 * .95

   year 2  800 * .95  * .95

       .

       .

        year 5 = 800(.95)^5 = 619 deer after year 5

Answer: 628

Step-by-step explanation:

2πr^2+2πrh

2(3.14)(5)^2+2(3.14)(5)(15)

2(3.14)(25)+2(3.14)(75)

2(78.5)+2(235.5)

157+471

628

assume the point (10,20) belongs to the graph of f of x what point belongs to the graph of y equals f (x )minus 5 ​

In this problem we have a transformation with the dollowing rule

(x,y) ------> (x,y-5)

so

(10,20) --------> (10, 20-5)

(10,20) --------> (10, 15)

therefore

The answer is

(10, 15)

a. the probabilities for X = 3, X = 4, and X = 5. The PMF of X can be plotted as a bar graph, with X on the x-axis and P(X) on the y-axis. b. Var[X] = E[X^2] - (E[X])^2

(a) To find the PMF (Probability Mass Function) of X, we need to consider all possible outcomes when two dice are tossed. There are 36 possible outcomes, each of which has a probability of 1/36. The absolute difference in the number of dots facing up can be 0, 1, 2, 3, 4, 5. We can calculate the probabilities of these outcomes as follows:

When the absolute difference is 0, the numbers on both dice are the same, so there are 6 possible outcomes: (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6). The probability of each outcome is 1/36. Therefore, P(X = 0) = 6/36 = 1/6.

When the absolute difference is 1, the numbers on the dice differ by 1, so there are 10 possible outcomes: (1,2), (2,1), (2,3), (3,2), (3,4), (4,3), (4,5), (5,4), (5,6), and (6,5). The probability of each outcome is 1/36. Therefore, P(X = 1) = 10/36 = 5/18.

When the absolute difference is 2, the numbers on the dice differ by 2, so there are 8 possible outcomes: (1,3), (3,1), (2,4), (4,2), (3,5), (5,3), (4,6), and (6,4). The probability of each outcome is 1/36. Therefore, P(X = 2) = 8/36 = 2/9.

Similarly, we can find the probabilities for X = 3, X = 4, and X = 5. The PMF of X can be plotted as a bar graph, with X on the x-axis and P(X) on the y-axis.

(b) To find the probability that X ≤ 2, we need to add the probabilities of X = 0, X = 1, and X = 2. Therefore, P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2) = 1/6 + 5/18 + 2/9 = 11/18.

(c) To find the expected value E[X], we can use the formula E[X] = ∑x P(X = x). Using the PMF values calculated in part (a), we get:

E[X] = 0(1/6) + 1(5/18) + 2(2/9) + 3(1/6) + 4(1/18) + 5(1/36)

= 35/12

To find the variance Var[X], we can use the formula Var[X] = E[X^2] - (E[X])^2, where E[X^2] = ∑x (x^2) P(X = x). Using the PMF values calculated in part (a), we get:

E[X^2] = 0^2(1/6) + 1^2(5/18) + 2^2(2/9) + 3^2(1/6) + 4^2(1/18) + 5^2(1/36)

= 161/18

Therefore, Var[X] = E[X^2] - (E[X])^2

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The coordinates of the circumcenter of the triangle ΔABC is; ( 4 , -1 )

The circumcenter of a triangle is the point of intersection of the perpendicular bisectors of the triangle, therefore;

The coordinates of the centers of the sides of the triangle are; ((1+7)/2, (1 + (-3))/2)

((1+7)/2, (1 + (-3))/2) = (4, -1)

The equation of the side AB is; y - 1 = ((1 - (-3))/(1 - 7))·(x - 1) = (-2/3)·(x - 1)

y = (-2/3)·(x - 1) + 1

y = (-2/3)·(x - 1) + 1

The equation of the perpendicular bisector of AB is; y - (-1) = (3/2)·(x - 4)

y + 1 = (3/2)·(x - 4)

y = (3/2)·(x - 4) - 1 = 3·x/2 - 7

y = 3·x/2 - 7

The middle of the side AB is; ((1 + 1)/2, (1 + (-3))/2) = (0, -1)

The side AB is vertical, therefore, the slope of the perpendicular line to AB is 0, and the equation of the perpendicular bisector to AB therefore is; y = -1

The x-coordinates of the circumcenter can therefore be found as follows;

-1 = 3·x/2 - 7

3·x/2 - 7 = -1

3·x/2 = -1 + 7 = 6

x = (2/3) × 6 = 4

x = 4

The y-coordinate of the circumcenter is; y = -1

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The average answer time for the entire day on Monday was 15.9 seconds.

For the average answer time for the entire day on Monday, we need to calculate the total time spent answering calls and divide by the total number of calls answered.

Let's first calculate the total time spent answering calls:

- For the 500 calls before noon, the total time spent answering calls is: 500 x 16 = 8,000 seconds

- For the 350 calls from noon to 6pm, the total time spent answering calls is: 350 x 14 = 4,900 seconds

- For the 150 calls on Monday night, the total time spent answering calls is: 150 x 20 = 3,000 seconds

So the total time spent answering calls on Monday is:

8,000 + 4,900 + 3,000 = 15,900 seconds

Now, let's calculate the total number of calls answered:

500 + 350 + 150 = 1,000 calls

Finally, we can calculate the average answer time for the entire day on Monday:

Average answer time = Total time spent answering calls / Total number of calls answered

= 15,900 / 1,000

= 15.9 seconds

Therefore, the average answer time for the entire day on Monday was 15.9 seconds.

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Answer:

-24

Step-by-step explanation:

Hi!

I can help you, no worries!

Your answer is y = -4/5x - 3

To solve this is much easier than you think. To "solve for y" we just have to get y on one side of the equal sign all by itself. We can see that it's "1 + y" on the left instead of just the y.

To get y by itself, we just subtract "1" from both sides.

1 + y = -4/5x - 2

-1                     -1

     y = -4/5x - 3

If you don't know why we have to subtract from both sides, think of it like this (it's how I like to think of it).

Each side of the equal sign is a twin. They are equal to eachother. If you change something about one twin, such as changing their hair color (or adding a number to one side of the equal sign), you have to do it to both in order for them to be the same. Right?

Hope this helps! Have a great day! :D

Answer:

Step-by-step explanation:

no graph was shown

P = 2l + 2w

Subtract both sides by 2w

P - 2w = 2l

Divide both sides by 2

(P - 2w) / 2 = l

In our problem,

w = 7 in

P = 42 in

Let's plug our values into the formula above.

(42 in - 2(7 in) / 2 = l

(42 in - 14 in) / 2 = l

28 / 2 = l

14 in = length

The maximum speed of the sprinter during the race is estimated to be approximately 12.72 meters per second.

To calculate the maximum speed of the sprinter during the race, we need to determine the average speed over the entire distance. The formula for average speed is distance divided by time. In this case, the distance covered by the sprinter is 200 meters, and the time taken to cover this distance is 20.32 seconds.

Average Speed = Distance / Time

Average Speed = 200 meters / 20.32 seconds

Average Speed ≈ 9.84 meters per second

So, the average speed of the sprinter during the race is approximately 9.84 meters per second.

However, to find the maximum speed, we need to consider that sprinters often accelerate during a race. The sprinter's time splits of 0-5-20.32 indicate that it took the sprinter 5 seconds to cover the initial 0 meters. This suggests that the sprinter was accelerating during this period.

To estimate the maximum speed, we can calculate the average speed for the remaining 195 meters (200 meters - 5 meters).

Average Speed = Distance / Time

Average Speed = 195 meters / (20.32 seconds - 5 seconds)

Average Speed ≈ 195 meters / 15.32 seconds

Average Speed ≈ 12.72 meters per second

Therefore, the maximum speed of the sprinter during the race is estimated to be approximately 12.72 meters per second. It's important to note that this is an estimate based on the given information, and actual maximum speeds achieved by athletes can vary based on various factors such as training, technique, and race conditions.

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Answer:

10m/7n

Step-by-step explanation:

distribute the

7n-7m=3m

7n=

A linear equation in​ slope-intercept form that models the description is c = 1.50m + 8.50.

Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Assuming the variable c represent the total cost and the variable m to represent the number of movie rentals, a linear equation in​ slope-intercept form that models the scenario is given by:

c = 1.50m + 8.50.

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Step-by-step explanation:

The shape of a parabola is determined by its focus and directrix. In this problem, the focus is 30 ft above the ground, so the directrix is 30 ft below the ground. Since the ground is the x-axis, the directrix is a horizontal line with equation y = -30.

The base of the satellite dish should be positioned on the axis of symmetry of the parabola, which passes through the focus and is perpendicular to the directrix. Since the directrix is a horizontal line, the axis of symmetry is a vertical line passing through the focus. Therefore, the base of the satellite dish should be positioned directly below the focus, which is (0, 30).

The equation of a parabola with vertex at the origin, opening upwards or downwards, and axis of symmetry along the y-axis is given by the equation y = a x^2, where a is a constant. In this problem, the parabola opens upwards and its vertex is (0, 30), so the equation of the parabola is of the form y = a x^2 + 30.

To determine the value of a, we need to use the fact that the directrix is y = -30. The distance from a point (x, y) on the parabola to the directrix is given by |y - (-30)| = |y + 30|. The distance from the same point to the focus (0, 30) is given by the distance formula:

sqrt(x^2 + (y - 30)^2)

Since the point lies on the parabola, we can substitute y = ax^2 + 30 into this expression and simplify:

sqrt(x^2 + (a x^2)^2) = sqrt(1 + a^2) x^2

Now we can set the two expressions for the distances equal to each other and solve for a:

|ax^2 + 30 + 30| = sqrt(1 + a^2) x^2

|ax^2 + 60| = sqrt(1 + a^2) x^2

a^2 x^4 + 120 a x^2 + 3600 = x^4 + a^2 x^4

(a^2 - 1) x^4 + 120 a x^2 + 3600 = 0

This is a quartic equation in x^2. We can solve for x^2 using the quadratic formula:

x^2 = (-120 a ± sqrt(120^2 a^2 - 4 (a^2 - 1) 3600)) / 2(a^2 - 1)

x^2 = (-60 a ± sqrt(3600 a^2 + 14400)) / (a^2 - 1)

For the base of the satellite dish to be positioned on the ground, we need x^2 to be non-negative, which means the discriminant of the quadratic formula must be non-negative:

3600 a^2 + 14400 ≥ 0

a^2 ≥ -4

Since a is a positive constant that determines the shape of the parabola, we can take the positive square root of both sides and obtain a ≥ 0. Therefore, the equation of the satellite is:

y = a x^2 + 30, where a is a non-negative constant.

None of the provided equations match the answer obtained.

Para escolher o pote de miçangas que permitirá fazer uma quantidade exata de pulseiras sem sobrar nenhuma miçanga no pote, precisamos encontrar um número que seja divisível por 16 em cada um dos valores apresentados nos potes.

Analisando as opções apresentadas no quadro, podemos ver que apenas a quantidade de miçangas no pote B é divisível por 16, já que 16 x 9 = 144. Portanto, Ana deve escolher o pote B com 144 miçangas para confeccionar as pulseiras de seus amigos. Dessa forma, ela poderá fazer 9 pulseiras utilizando todas as miçangas disponíveis no pote. As outras opções apresentam quantidades de miçangas que não são divisíveis por 16, o que resultaria em sobras de miçangas no processo de confecção das pulseiras.

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Answer:

Answer:

1543.59

Step-by-step explanation:

See image below for equation!

PLZZZ give me brainliest!

The probability that x is between 40 and 50 will be 0.5.

From the information, the continuous random variable x is uniformly distributed on the interval [35, 45].

The probability that x is between 40 and 50 will be:

(45 - 40)/(45 - 35)

= 5/10

= 0.5

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All values of x in the interval [0, 2] that satisfy the equation are \(\frac{\pi }{2} ,3\frac{\pi }{2}\).

A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality. A well-formed formula consisting of two expressions linked by an equals sign is considered to be an equation in English, but the word's cognates in other languages may have slightly different definitions. For instance, an équation is defined as having one or more variables in French.

The first step in resolving a variable equation is to identify the values of the variables that lead to the equality being true. The variables that must be changed in order to solve the equation are referred to as the unknowns, and the values of the unknowns that satisfy the equality are referred to as the equation's solutions.

Calculations:

16cos(x +8sin(2x)=0

Divide by 8

2cos(x)+sin(2x)=0

Identity:

sin(2x)=2sin(x)cos(x)

2cos(x)+2sin(x)cos(x)=0

Factor:

2cos(x)(1+sin(x))=0

2cos(x)=0

cos(x)=0=x=\(\frac{\pi }{2}\),3\(\frac{\pi }{2}\)

(1+sin(x))=0

sin(x)=−1=x=3\(\frac{\pi }{2}\)

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The percentage increase in the price of a gallon of gas is 80.84 %.

Given,

Jason bought a gallon of gas in 1992 = $1.20

He bought a gallon of gas yesterday = $2.17

Using the formula for the percentage increase in the price,

= ( New Price - Old Price) / Old Price × 100

= ( 2.17 - 1.20) / 1.20 × 100

= 80.84%

Therefore, the percentage increase in the price of a gallon of gas from 1992 to yesterday is 80.84 %.

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Answer:

1. f(–9) = -66 , g( 1 ) = 27  (Please double-check your given options, there must have been a typographical error for Option C for g( 1 ) = 29). g( 1 ) is supposed to be 27.

2. Option A: f(–9) = 25, g(–1) = 21

Step-by-step explanation:

1.Find the value of f(–9) and g(1) if f(x) = 8x + 6 and g(x) = 9x + 20x−2

f(x) = 8x + 6

f(–9) = 8(-9) + 6 = -66

g(x) = 9x + 20x − 2

g( 1 ) = 9( 1 ) + 20( 1 ) − 2 = 27

None of the given choices were correct (unless there's a typo error for Option C — it's supposed to be g( 1 ) = 27 instead of 29?) because the correct answers are: f(–9) = -66 and g( 1 ) = 27

2.  f(–9) and g(–1) if f(x) = –3x – 2 and g(x) = 3x³ – 24x

f(x) = –3x – 2

f(–9) = –3(–9) – 2 = 25

g(x) = 3x³ – 24x

g(–1) = 3(–1)³ – 24(–1) = 21

Therefore, the correct answer is Option A: f(–9) = 25, g(–1) = 21

On a postsynaptic membrane, the opening of K+ ion channel induces an IPSP (Inhibitory Postsynaptic Potential).

The potential changes in a neuron after the receptor and ion channel activation is called synaptic potential. This potential can be either an Excitatory Postsynaptic Potential (EPSP) or an Inhibitory Postsynaptic Potential (IPSP).EPSP is a depolarizing potential that results from the opening of the Na+ ion channel. It causes a change in the potential of the neuron towards threshold level that may trigger an action potential.Ion channels and pumps in a postsynaptic neuron regulate the internal potential of the cell. In a typical postsynaptic cell, the resting potential (Vrest) is -70 mV, the threshold value is -55 mV, the reversal potential for Cl- ion (Ec) is -63 mV, the reversal potential for K+ ion (Ex) is -90 mV, and the reversal potential for Na+ ion (ENa) is 60 mV.The opening of Cl- ion channel leads to an inward flow of negative ions and thus results in hyperpolarization. The opening of K+ ion channel leads to an outward flow of K+ ions, and the membrane potential becomes more negative. Thus, it also results in hyperpolarization. The opening of a Na+ ion channel leads to inward flow of Na+ ions, which makes the cell more positive, and it is depolarization. Therefore, the opening of K+ ion channel leads to an IPSP, and it hyperpolarizes the neuron.

The postsynaptic potential can be either an Excitatory Postsynaptic Potential (EPSP) or an Inhibitory Postsynaptic Potential (IPSP). The opening of the K+ ion channel leads to an outward flow of K+ ions, which makes the cell more negative and hyperpolarizes it, leading to IPSP.

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Magnification of a convex mirror is 0.67 times for objects 3.8 m from the mirror .the focal length is negative, this means that the mirror is a diverging mirror (convex mirror). Therefore, the focal length of this mirror is 2.4 meters.

To find the focal length of a convex mirror, we can use the mirror formula:

1/f = 1/v + 1/u

where f is the focal length, v is the image distance, and u is the object distance.

In this case, we know that the magnification (M) of the mirror is 0.67, and the object distance (u) is 3.8 m. We also know that for a convex mirror, the image is always virtual and upright, so the image distance (v) is negative.

The magnification formula is:

M = -v/u

Substituting the values we have:

0.67 = -v/3.8

v = -2.546 m

Now we can use the mirror formula to find the focal length:

1/f = 1/-2.546 + 1/3.8

1/f = -0.416

f = -2.4 m

Since the focal length is negative, this means that the mirror is a diverging mirror (convex mirror). Therefore, the focal length of this mirror is 2.4 meters.

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Answer: 27

Step-by-step explanation:

If 2 scoops of ice cream cost $6, then 1 scoop of ice cream costs $6/2 = $3.

So, 9 scoops of ice cream would cost 9 x $3 = $27.

Answer:

27$

Step-by-step explanation:

If two wcoops of ice crewm cost 6$ them one scoop would cost 3$ because 6/2 =3. If one scoop costs 3$ then 9 scoops would cost 9x3 so 27$

Step-by-step explanation:

\( \large\underline{\sf{Solution-}}\)

Given function is

\(\rm \longmapsto\:f = \bigg(x, \: \dfrac{ {x}^{2} }{ {x}^{2} + 1} \bigg) : x \: \in \: R\)

To find the range of the function f, Let assume that

\(\rm \longmapsto\:y = \dfrac{ {x}^{2} }{ {x}^{2} + 1} \)

\(\rm \longmapsto\: {yx}^{2} + y = {x}^{2} \)

\(\rm \longmapsto\: {yx}^{2} - {x}^{2} = - y\)

\(\rm \longmapsto\: - {x}^{2} (1 - y) = - y\)

\(\rm \longmapsto\: {x}^{2} (1 - y) = y\)

\(\rm \longmapsto\: {x}^{2} = \dfrac{y}{1 - y} \)

\(\rm\implies \:x = \sqrt{\dfrac{y}{1 - y} } \)

For x to be defined,

\(\rm \longmapsto\:y \geqslant 0 \: \: and \: \: 1 - y > 0\)

\(\rm \longmapsto\:y \geqslant 0 \: \: and \: \: - y > - 1\)

\(\rm \longmapsto\:y \geqslant 0 \: \: and \: \: y < 1\)

\(\bf\implies \:y \: \in \: [0, \: 1)\)

Hence,

\(\bf\implies \:Range \: of \: f \: \in \: [0, \: 1)\)

The radius of the circle is 13.

To find the radius of the circle with the center at the origin and passing through the point (-12, 5), we can use the distance formula.

The distance formula between two points (x1, y1) and (x2, y2) is given by:

Distance = √[(x2 - x1)² + (y2 - y1)²]

In this case, the center of the circle is at the origin (0, 0), and the given point is (-12, 5). Plugging these values into the distance formula, we get:

Distance = √[(-12 - 0)² + (5 - 0)²]

= √[(-12)² + 5²]

= √[144 + 25]

= √169

= 13

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The measure of arc BC is 720 times the measure of angle BAC.

Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).

To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:

AB * BC = AC * CE

16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)

Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:

Area = π * r^2

289 = π * r^2

r^2 = 289 / π

r = √(289 / π)

Now, we can substitute the known values into the equation for the product of the segments:

16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8

To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.

mBC = 0.5 * m(arc BC)

To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:

arc BC = (mBC / 0.5) * 360

arc BC = 720 * mBC

Therefore, the length of the arc BC equals 720 times the length of the angle BAC.

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