Find the limit. Use a graphing utilily to verify your result. (Hint: Treat the expression as a fraction whose denominator Is 1, and rationalize the numerator: If an answer does not exist, enter DNE.
Lim (6x + √36x^2 - x)
x → -[infinity]

The given probability distribution "a teacher monitored the number of people texting during class each day and calculated the corresponding probability distribution." is a type of discrete probability distribution.

The probability distribution is used to describe the probability of each outcome in a series of possible outcomes. It is a mathematical representation of the outcomes of an experiment.

The teacher likely used a discrete probability distribution to calculate the probability of a certain number of people texting during class each day.

A discrete probability distribution is used to analyze data where the outcome is counted in whole numbers, such as the number of people texting in a given class period.

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Answer:

7

Step-by-step explanation:

A(-5,−2) , B(5,−6)

Equation of line AB⟹

(5-6), (-5-2) = 3+3 = 6+1= 7

the area of her entire bedroom is 176 feet².

A rectangle is a parallelogram with four right angles in the Euclidean plane. It can also be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equivalent. A square is a rectangle with four equal edges.

The size of a section on a surface is determined by its area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.

Area of first rectangle = length * breadth= 10*8=80 feet²

Area of second rectangle = length * breadth= 12*8 = 96 feet²

Total area of bedroom= 80+96= 176 feet²

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The probability of drawing four red balls in succession, with replacement, is 0.04 or 4%.

Since we are replacing the ball after each draw, the probability of drawing a red ball remains the same for each draw. The probability of drawing a red ball on any given draw is:

P(Red) = Number of Red Balls / Total Number of Balls

P(Red) = 6 / (8 + 6)

P(Red) = 0.4286

So, the probability of drawing four red balls in a row is the product of the probability of drawing a red ball four times in a row:

P(4 Red Balls) = P(Red) * P(Red) * P(Red) * P(Red)

P(4 Red Balls) = 0.4286 * 0.4286 * 0.4286 * 0.4286

P(4 Red Balls) = 0.04 or 4%

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Answer:

90 degrees then decreace that then turn that into a fraction

Step-by-step explanation:

The time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0.

The current of the given LR-series circuit can be determined using the formula I = (E/R) * (1 - e^-Rt/L).The current i(t) if i(0) = 0 in the LR-series circuit is given by i(t) = 0.125A. The current as t → [infinity] is given by lim t→[infinity] i(t) = 0.How to solve this?The formula for the current in the LR-series circuit is given by:Where E is the electromotive force, R is the resistance, L is the inductance, t is time and I is the current.I = (E/R) * (1 - e^-Rt/L)Given E = 20V, R = 40Ω, L = 0.1H, and i(0) = 0Substitute these values in the above formula.I = (20/40) * (1 - e^-40t/0.1)I = 0.5(1 - e^-400t)I = 0.5 - 0.5e^-400tSo the current is i(t) = 0.5 - 0.5e^-400t.Limit of t as t → [infinity] means that when the time is allowed to run infinitely, then the current will become constant. Hence, when the time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0. Answer: The current is i(t) = 0.5 - 0.5e^-400t. Limit of t as t → [infinity] means that when the time is allowed to run infinitely, then the current will become constant. Hence, when the time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0.

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1. The breakeven in units equals 31 units.

2. The dollar amount to breakeven is

The variable cost per unit includes the cost of the sweatshirt ($16.50) and the additional charge for shipping and plastic wrap ($0.50), so the total variable cost per unit is:

= $16.50 + $0.50

= $17.00

The contribution margin per unit is:

= 22.00 - $17.00

= $5.00

The fixed costs include the one-time charges of art ($45), screen and set-up ($60), and advertising ($50), so the total fixed costs are:

= $45 + $60 + $50

= $155

Using the breakeven formula, we can calculate the number of units required to break even:

= Fixed costs / Contribution margin per unit

= $155 / $5.00

= 31 units

To calculate the breakeven in dollars, we need to multiply the breakeven in units by the selling price per unit:

The breakeven in dollars equals to:

= Breakeven in units x Selling price per unit

= 31 x $22.00

= $682.00

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The lengths of LV and OE are 15cm, and the lengths of LD and EV are 3√7 cm and 9/√7 cm, respectively.

Since LOVE is a kite, LV and OE are perpendicular bisectors of each other. Let the length of LD be x, and the length of EV be y. Then, we can use the Pythagorean theorem and the fact that the diagonals bisect each other to set up two equations:

x² + (LV/2)² = DV²/4

y² + (OE/2)² = LE²/4

Simplifying each equation and substituting the given values, we get:

x² + (LV/2)² = 81/4

y² + (OE/2)² = 225/4

We also know that the diagonals bisect each other, so we can set up another equation:

LV/2 + OE/2 = LO = VE

Substituting the given value for LE, we get:

LV/2 + OE/2 = 15

Solving this equation for one of the variables, we get:

LV = 30 - OE

Substituting this expression into the first equation above, we get:

x² + ((30 - OE)/2)² = 81/4

Simplifying and rearranging, we get:

OE² - 60OE + 675 = 0

Using the quadratic formula, we get:

OE = (60 ± √(3600 - 2700)) / 2

OE = 15 or 45

If OE = 15, then LV = 30 - 15 = 15, and we can solve for x and y:

x² + 7.5² = 81/4

y² + 7.5² = 225/4

Solving these equations, we get:

x = 3√7

y = 9/√7

If OE = 45, then LV = 30 - 45 = -15, which is impossible for a length. Therefore, the solution is:

LV = OE = 15

x = 3√7

y = 9/√7

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Complete question:

LOVE is a kite. LV and OE are diagonals. The segments DV = 9cm and LE = 15cm are given. Find the lengths of the other segments of the diagonals, DV, OE, and LV.

Answer:

X / 19 = 6 / 4.5        both person and pile have same ratio of shadow

X = 6 / 4.5 * 19 = 25.3 ft

13/12 will be long the next airplane model. This will be because her next model is to be 1/4 as long as the first.

Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be entire. When we cut a piece of cake in real life from the entire cake, the part represents the per cent of the cake. The word "fraction" is derived from Roman. "Fractus" means "broken" in Latin. The fraction was expressed verbally in earlier times. It was afterwards presented in numerical form.

Given,

The length of her first model is in the fraction [tex]4\frac{1}{3}[/tex]

As her next model has to be 1/4 as long as the first model

Therefore,

Length of her new or next model

1/4 of [tex]4\frac{1}{3}[/tex]

so, 1/4 * 13 / 3

13/12

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Answer:

yes it is right now you can write it

No, the given value of h=2 is not a solution of the equation 1/3h=6.

Answer:

the area of triangle OAP is 12 square units.

Step-by-step explanation:

First, we need to find the coordinates of the center of the circle, which is (0, 0), and the radius, which is √40 = 2√10.

Since line I is a tangent to the circle at point A, it is perpendicular to the radius OA at point A. Therefore, OA is perpendicular to line I and forms a right angle with it.

We can find the equation of line I using the point-slope form:

slope of radius OA = (0 - 6) / (0 - 2) = -3

slope of line I = 1 / 3 (because it is perpendicular to OA)

equation of line I: y - 6 = (1/3)(x - 2)

simplifying, we get: y = (1/3)x + 4

To find the x-coordinate of point P, we need to solve for x when y = 0:

0 = (1/3)x + 4

x = -12

Therefore, point P has coordinates (-12, 0).

Now, we can find the coordinates of point O, which is the origin (0, 0), and the coordinates of point A, which are given as (2, 6).

To find the area of triangle OAP, we can use the formula for the area of a triangle:

Area = (1/2) x base x height

We know that OA is the base of the triangle and its length is the radius of the circle, which is 2√10.

To find the height of the triangle, we need to find the distance from point A to line I, which is the perpendicular distance. We can use the formula for the distance between a point and a line:

distance = |ax + by + c| / √(a² + b²)

where a, b, and c are the coefficients of the equation of the line, and x and y are the coordinates of the point.

In this case, the equation of line I is y = (1/3)x + 4, so a = -1, b = 3, and c = -12.

Substituting the values, we get:

distance = |(-1)(2) + (3)(6) - 12| / √((-1)² + 3²)

distance = |6| / √10

distance = 3√10 / 5

Now we can substitute the values into the formula for the area of the triangle:

Area = (1/2) x base x height

Area = (1/2) x 2√10 x (3√10 / 5)

Area = 6/5 x 10

Area = 12

Therefore, the area of triangle OAP is 12 square units.

Answer:

224

Step-by-step explanation:

392 ÷ 7 = 56

56 *4 = 224

hope this helps

Answer:

Step-by-step explanation:

the second blank is wrongt

Answer: y=12

Step-by-step explanation: can't simplify

Answer: 23

Step-by-step explanation:

Vertical angles are congruent (equal) so you first make the equations for angle A and B equal to each other and solve for x.

x + 15 = 5x - 17

32 = 4x

x = 8

Plug the x value (8) back into either equation to find the measure of angle B.

x + 15

8 + 15 = 23

The possible expression that can be a rule for the number sequence is:[tex]$a_n = 4n + 1$[/tex],

As an illustration, the expression x + y is one where x and y are words with an addition operator in between. There are two types of expressions in mathematics: numerical expressions, which only comprise numbers, and algebraic expressions, which also include variables.

One possible expression that can be a rule for the number sequence is:

[tex]$a_n = 4n + 1$[/tex], where n is the position of the term in the sequence.

Using this expression, we can find the values of the first few terms as follows:

[tex]$a_1 = 4(1) + 1 = 5$[/tex]

[tex]$a_2 = 4(2) + 1 = 9$[/tex]

[tex]$a_3 = 4(3) + 1 = 13$[/tex]

[tex]$a_4 = 4(4) + 1 = 17$[/tex]

[tex]$a_5 = 4(5) + 1 = 21$[/tex]

Thus, possible expression that can be a rule for the number sequence is:[tex]$a_n = 4n + 1$[/tex],

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Answer:

5n, where n is equal to 0, 1, 2, 3, 4

Step-by-step explanation:

5, 9, 13, 17, 21,

Answer:For random variable X~N(3,0.75), what is the probability that X takes on a value within two standard deviations on either side of the mean?

Step-by-step explanation:

The coordinates of your position If we start at the origin, we are moving only along the x-axis  of  a distance of 7 units in positive direction and then only in the negative y-axis direction and  z-coordinate is zero are (7,-6,0).

The origin is the point in space that has a position of (0, 0, 0), which represents the point where the x, y, and z axes intersect.

The first step is to move 7 units in the positive x direction. The positive x direction is the direction in which x values increase. Therefore, we move to the right along the x-axis to the point (7, 0). This means that we have moved 7 units along the x-axis, and our position is now (7, 0, 0).

The second step is to move downward a distance of 6 units. Since we are not moving in the x direction, we are only changing our position along the y-axis. Moving downward in the y direction means decreasing our y-coordinate. Therefore, we move 6 units downward from our current position to the point (7, -6, 0).

Therefore, the coordinates of our position are (7, -6, 0)

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Another strategy is to start by pressing a square in the middle of the grid, and then pressing the squares adjacent to it. This should help you turn off the squares in a cross pattern.

In mathematics, a sequence is an ordered list of elements, typically numbers, which may be finite or infinite. Each element in the sequence is called a term. For example, the sequence {1, 2, 3, 4, 5} is a finite sequence of integers with five terms. Sequences can be represented in several ways, such as listing out the terms, using a formula to generate the terms, or using recursive rules. For example, the sequence of even numbers can be generated using the formula 2n, where n is a positive integer. So, the first five terms of the sequence are 2, 4, 6, 8, 10. Sequences are used in many areas of mathematics, including number theory, calculus, and statistics. They are also used in real-world applications, such as modeling population growth or predicting stock prices.

Here,

One common strategy is to start by pressing one of the corner squares, and then pressing the squares adjacent to it. Then, move to the adjacent corner square and repeat the process. This should help you turn off the squares in one diagonal line.

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Answer:

24 cm (to nearest cm)

Step-by-step explanation:

XLV = extra large tin volume (cm³)

LV = large tin volume (cm³)

XLR = extre large tin radius (cm)

LR = large tin radius (cm) = 20

XLV = 1.75 × LV

Since the tins are geometrically similar cylinders, we can infer that the volumes and radii of the 2 tins are related;

We know the relationship between the volume of the two tins, i.e. the XL tin is 75% greater in volume than the L tin;

This means the volumetric scale factor or multiplier is ×1.75;

Subsequently, we know:

XLV = 1.75 × LV

Similarly, there is a relationship between the radii of the tins;

The relationship is, however, slightly different;

[tex]XLR = (\sqrt[3]{1.75}) \times LR[/tex]

We need to take the cube root of the volumetric scale factor, reason being, the radius is a linear dimension unlike volume;

Easy way to figure this is radius is in cm, volume is in cm³;

So:

XLR = 1.205... × LR

XLR = 1.205... × 20

XLR = 24.101... --> 24 cm (to nearest cm)

The probability that wrist watch chosen is a defective watch is 1 / 10

Total number of watches n(S)=500

Number of watches defective n(A)=50

P(A)= n(A) / n(S)

​

⇒P(A)= 50 / 500

​

Probability of watches to be defective = 1 / 10 or  50 / 500

Probability is a branch of mathematics that deals with the study of the likelihood or chance of an event occurring. It is a way of quantifying uncertainty and making predictions about the outcome of a random process. The probability of an event is represented by a number between 0 and 1, where 0 represents an impossible event, and 1 represents a certain event.

Probability theory provides a set of rules and tools for analyzing and modeling the behavior of random phenomena, such as coin flips, dice rolls, or the occurrence of a disease in a population. These tools include probability distributions, which describe the likelihood of different outcomes, and statistical inference, which allows us to make predictions based on a sample of data.​

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The required ratio of  is (a + c) : c 11:8.

Given that a:b=1:4 and b:c=3:2.

We can simplify the ratio b:c by multiplying both sides by 4 to get b:c=12:8=3:2.

To find the ratio (a+c):c, we need to express a and c in terms of b. From the first ratio, we have [tex]a=\frac14 b$[/tex]. From the second ratio, we have [tex]c=\frac{2}{3}b$[/tex]. Substituting these values into the expression (a+c):c, we get:

[tex]$$(a+c):c = \left(\frac{1}{4}b + \frac{2}{3}b\right):\frac{2}{3}b$$[/tex]

Simplifying the expression inside the parentheses, we get:

[tex]$\frac{1}{4}b + \frac{2}{3}b = \frac{3b}{12} + \frac{8b}{12} = \frac{11b}{12}$$[/tex]

Therefore, the ratio [tex]$(a+c):c$[/tex] is:

[tex]$(a+c):c = \frac{11b}{12}:\frac{2}{3}b = 11:8$$[/tex]

Hence, the required ratio is 11:8$.

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The correct option among the four options that are given in the question is option C. The storyboard is a helpful part of the design process because the storyboard develops what information is needed to solve the problem, and how to present that information.

What is a storyboard?

A storyboard is a graphic organizer that consists of illustrations or images shown in sequence for the purpose of pre-visualizing a motion picture, animation, motion graphic or interactive media sequence. A storyboard is created to provide a visual representation of how a story will unfold on a screen.Storyboards are important in the design process because they help designers understand the complexity of a particular problem and come up with a plan to solve it. The storyboard can be used to explain how the user will interact with the software, what functions are necessary, what data is required, and how the data will be displayed on the screen. Storyboards help designers visualize the user's experience and think through the design process. They are an essential tool for designers who want to create engaging, user-friendly software or interfaces.

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The value οf x fοr the expressiοn must be simplified is 12,32,48.

Expressiοns in mathematics must cοntain a statement, at least οne arithmetic οperatiοn, at least twο numbers οr variables, οr bοth. With the help οf this mathematical οperatiοn, οne can multiply, divide, add, οr subtract.

Unknοwn variables, numbers, and arithmetic οperatοrs make up an algebraic expressiοn. There are nο symbοlic representatiοns οf equality οr inequality in it.

Here since 71 is a prime number , [tex]\sqrt{71}[/tex] cannot be simplified itself.

Then [tex]\sqrt{71x}[/tex] can only be further simplified if [tex]\sqrt{x}[/tex] itself can be simplified.

Here , amοng the given chοices,

=>12 = 4*3 [ 4 is perfect square] , sο it  can be simplified.

=> 32 = 16*2 [16 is perfect square] , sο it can be simplified.

=> 48 = 16*3 [ 16 is perfect square] , sο it can be simplified.

Hence the value οf x fοr the expressiοn must be simplified is 12,32,48.

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To find the next two terms of the sequence, we need to first find the common difference between consecutive terms:

52 - 44 = 8

64 - 52 = 12

80 - 64 = 16

We notice that the common difference is increasing by 4 for each term. Therefore, the next two terms of the sequence are:

80 + 20 = 100

100 + 24 = 124

To determine the nth term of the quadratic sequence, we can use the formula:

an = a1 + (n-1)d + bn^2

where a1 is the first term, d is the common difference, b is the coefficient of n^2, and n is the term number.

Using the first four terms of the sequence, we can form a system of equations:

44 = a1 + b

52 = a1 + d + b

64 = a1 + 2d + b

80 = a1 + 3d + b

Solving for a1 and b, we get:

a1 = 20

b = 24

Substituting these values into the formula for an, we get:

an = 20 + (n-1)4 + 24n^2

an = 24n^2 + 4n - 4

To find the 30th term of the sequence, we simply substitute n = 30 into the formula we just derived:

a30 = 24(30)^2 + 4(30) - 4

a30 = 21,596

To prove that the quadratic sequence will always have even terms, we notice that the first term is even (44 = 2 x 22), and the common difference is even (8 = 2 x 4). Therefore, every term of the sequence can be expressed as an even number plus an even multiple of n^2, which is always even. Hence, the quadratic sequence will always have even terms.

Step-by-step explanation:

Sequence is 44;52;64;80;.....44;52;64;80;.....

General formula is Tn=2n2+2n+40