Find the slope of the line that contains the points:
(-6, 3) and (-4, 5).
1
-1
-5
-1/5

The probability that Joe and Mathew would have to purchase no books on this visit to the bookstore is given as 0.125.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

We are to find the probability where p(x) = 0 and p(y) = 0

This is where we would have

from the table,  p(x) = 0 is 0.5

p(y) = 0 is 0.25

0.25 x 0.5 = 0.125

Hence the probability that no books would be bought is 0.125.

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Answer:  love

Step-by-step explanation:  love

The equation → x - 4/5 - x + 1/6 = 1/3 will have infinitely many solutions.

A equation in mathematics is a mathematical statement depicting that the values of two mathematical expressions are equal. Some examples representing equations are -

y = 5x + 4

2x + 3y = 5x + 8π

cos(ny) = sin(πx)

Given is the following equation -

x - 4/5 - x + 1/6 = 1/3

We have -

x - 4/5 - x + 1/6 = 1/3

x - x - 4/5 + 1/6 = 1/3

- 4/5 + 1/6 = 1/3

Now, [x] will cancel out for ever possible value of [x], therefore, it will have infinitely many solutions

Therefore, the equation → x - 4/5 - x + 1/6 = 1/3 will have infinitely many solutions

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The length and width of a rectangle that maximises the enclosed area are 800 yards. The maximum area is 640,000 square yards.

In the given question we have to find the maximum area of the rectangular area.

Liana has 3200 yards of fencing to enclose a rectangle.

As we know that the perimeter of rectangle

P= 2(l+b)

Let length of the rectangle is x yards and width is y yards.

So the equation should be

2(x+y) = 3200

Divide by 2 on both side we get

x+y = 1600................(1)

From the area of rectangle is

A = xy

From the equation the value of y is 1600-x.

Now putting the value of y

A = x(1600-x)

A = 1600x-x^2

On differentiating

dA/dx = 1600-2x

Putting dA/dx=0

1600-2x=0

Subtract 1600 on both side we get

-2x= -1600

Divide by -2 on both side we get

x = 800 yards

Now putting the value of x in the y=1600-x

y=1600-800

y=800 yards

So the maximum area is

A= 800*800

A= 640,000 square yards

Hence, the length and width of a rectangle that maximises the enclosed area are 800 yards. 640,000 square yards is the maximum area.

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Answer:

[tex] - 3 \leqslant w < 1[/tex]

Step-by-step explanation:

as shown in picture attached

Answer:

Step-by-step explanation:

Given:

Binomial: x² + 10x

To Find:

Solution:

To find the constant we would compare the binomial with (a + b)² i.e. a² + 2ab + b² as it is the formula for perfect square.

By comparing we get:

a² = x²

2ab = 10x

b² = constant (To find out)

From this we can make out:

a = x

[tex] \therefore[/tex]

[tex] \rm \implies 2 \times x \times b = 10x \\ \\ \rm \implies b = \frac{10x}{2x} \\ \\ \rm \implies b = 5 \\ \\ \therefore \\ \\ \rm \implies {b}^{2} = 25[/tex]

So, constant that should be added to the binomial so that it becomes a perfect square trinomial is [tex] \boxed{\rm 25} [/tex].

Perfect square trinomial is x² + 10x + 25

Factorisation of the trinomial:

[tex] \rm \implies {x}^{2} + 10x + 25 \\ \\ \rm \implies {x}^{2} + 10x + {5}^{2} \\ \\ \rm \implies {x}^{2} + 5x + 5x + {5}^{2} \\ \\ \rm \implies x(x + 5) + 5(x + 5) \\ \\ \rm \implies (x + 5)(x + 5) \\ \\ \rm \implies {(x + 5)}^{2} [/tex]

The total number of times the dice will land on 1 or on 5 is 153.

What is probability?

All of the probabilities will add up to 1. This gives us the equation.

P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1

P(1) + 0.17 + 0.08 + 0.16 + 0.14 + 0.1 = 1

P(1) + 0.65 = 1

P(1) = 1 - 0.66

P(1) = 0.35

We now need to find the probability of 1 or 5.

P( 1 or 5) = P(1) + P(5)

= 0.35 + 0.16

= 0.51

We now use the predicting outcomes formula

Expected = P( 1 or 5) * No. of times

= 0.51 * 300

= 153

Hence, the total number of times the dice will land on 1 or on 5 is 153.

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Answer:

Step-by-step explanation:

187

Using a proportional relationship, it is found that:

A. The slope of the line is of 4.

B. The slope is the same over both segments.

A proportional relationship is modeled as follows:

y = kx.

Hence a proportional relationship is a special case of a linear function, with slope represented by the constant of proportionality of k and intercept of 0.

For the presented case, the two variables x and y are direct proportional, and thus the output variable y is obtained as the multiplication of the input variable x by the constant of proportionality k.

In this problem, the relationship has two points presented as follows:

(3, 12) and (4, 16).

Hence the slope, which is the constant of the relation, is given as follows:

k = 12/3 = 16/4 = 4.

Given two points, the slope is given by the change in y divided by the change in x. Hence, over each segment, the slopes are given as follows:

Which are the same slopes.

The problem is given by the image at the end of the answer.

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Answer:

Step-by-step explanation:

the answer is 86

hope it helps!

(-_-)

Answer:

Step-by-step explanation:

2x + 3 = 4x - 5

4x - 5 = 2x + 3

Step 1 : Add 5 on both sides.

4x = 2x + 3 + 5

4x = 2x + 8

Step 2 : Subtract 2x on both sides.

4x - 2x = 8

2x = 8

Step 3 : Divide 2 on both sides.

x = 8/2

x = 4

Hence proved.

Answer:

Collect like terms

3+5=4x-2x

(note that when - crosses a line it turns to +

8=2x

8/2=2x/2

x=4

The altitude of the original pyramid is about 75.11 units

Given that,

Let h stand in for the original pyramid's height. The cut-off top then stands at a height of (h -22). The square of the scale factor for height is the scale factor for area, therefore we get :

Altitude of Pyramid means The slant height of a regular pyramid is its lateral face's height. Slant height in a non-rectangular pyramid is not specified. When determining the height (or altitude) of a regular, right pyramid, the vertex (the top) is used as the point perpendicular to the base. The base will intersect at this position.

(Height ratio)^2 = 1/2

((h -22)/h) ^ 2 = 1/2

(h-22) / h = 1/[tex]\sqrt{2}[/tex]

h-22 = h /[tex]\sqrt{2}[/tex]

h = 75.11 units

Consequently, the original pyramid's altitude is around 75.11 units.

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Answer:

Triangular prism

Step-by-step explanation:

If you were to fold all the creases and glue it together you would get a tent shape which is a triangular prism

Answer:the quadratic function in f(x)= a(x-h)^2+k is f(x) = - (x - 2)² + 2.I think this is false";}

Step-by-step explanation:

A. Applying the trigonometric ratio, the length of pole = 29.6 ft.

B. 23.1 ft.

C. Length of wire 1 = 45.1 feet.

The trigonometric ratios are:

Part A: Apply the trigonometric ratio, tan ∅ = opp/adj, to find the length of the pole

∅ = 41°

Opp. = length of pole

Adj. = 34 ft

Substitute

tan 41 = length of pole/34

Length of pole = (tan 41)(34) = 29.6 ft.

Part B:

Let the distance between the base of the pole and wire 2 be represented as x. Therefore, apply tan ∅ = opp/adj.

∅ = 38

Opp. = x

Adj. = 29.6 ft

Therefore:

tan 38 = x/29.6

x = (tan 38)(29.6)

x = 23.1 ft.

Part C: Use the Pythagorean theorem to find the length of wire 1.

Length of wire 1 = √34² + 29.6²)

= 45.1 feet.

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The graph of the given functions is (see in attachments).

From the question, we have

g(x) = 0.44√3.2x−4.1

Graph:

A graph is an organized visual representation of any data in mathematics. The relationship between the variable quantities is depicted on the graph. In a graph theory, the set of items that are somehow connected to one another is represented by a graph. The vertices or nodes of the objects are essentially mathematical notions, and the edges between the nodes represent the relationships between the nodes. In mathematics and statistics, there are various types of graphs that are used to visually display data. The study of points and lines is known as graph theory. It is a branch of mathematics that focuses on the investigation of graphs. The mathematical truth is shown visually in this picture. Relationships are studied using graph theory.

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1.because sample is random and (130)

(0.923) and (130)(0.077) are both at least 10.

This means the normal model is a good fit for the sampling distribution.

Consider the provided information.

130 randomly selected flights and find that

120 of the flights arrived on time.

n=130

The on-time arrival performance was 91.9%

p=0.923 and q=1-0.923=0.077

np = 130 x 0.923

np = 120 ≥ 10

nq = 130 × 0.077

nq = 10 = 10

Hence, Yes, because sample is random and

(130)(0.923) and (130)(0.077) are both at least 10. This means the normal model is a good fit for the sampling distribution.

2.because sample is random and (130)

(0.919) and (130)(0.081) are both at least 10.

This means the normal model is a good fit for the sampling distribution.

Consider the provided information.

130 randomly selected flights and find that

120 of the flights arrived on time.

n=130

The on-time arrival performance was 91.9%

p=0.919 and q=1-0.919=0.081

np = 130 x 0.919

np = 119.5 ≥ 10

nq = 130 × 0.081

nq = 10.5 ≥ 10

Hence, Yes, because sample is random and

(130)(0.919) and (130)(0.081) are both at least 10. This means the normal model is a good fit for the sampling distribution.

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The value of the function g(x) when x = -2 is 6

The definition of the function is given as

g(x)=x to the power of 2 minus x

Rewrite the above function properly

So, we have the following representation

g(x) = x² - x

To find the function g(-2), we set the value of x in the equation g(x) = x² - x to -2

This is represented by

Calculate g(x), when x = -2

Substitute -2 for x in the equation g(x) = x² - x

So, we have the following equation

g(-2) = (-2)² - (-2)

Evaluate the exponents

This gives

g(-2) = 4 - (-2)

Evaluate the sum

g(-2) = 6

Hence, the value of the function is 6

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Arturo can select the days on which to have pizza in 70 ways using combination rule if he chooses any four of the next eight days.

What is combination?

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

In combinations, one can select the items in any order.

Number of combination of a objects chosen from n objects

                                  ⁿCₐ = [tex]\frac{n!}{a! (n-a)!}[/tex]

According to the given question:

To select 4 days out of the next 8 days, use combination rule

ⁿCₐ = [tex]\frac{n!}{a! (n-a)!}[/tex]

⁸C₄ = [tex]\frac{8!}{4! (8-4)!}[/tex]

⁸C₄ = (8x7x6x5x4x3x2x1)/(4x3x2x1)(4x3x2x1)

⁸C₄ = (8x7x6x5)/(4x3x2x1)

⁸C₄ = 70

Therefore there are 70 ways Arturo can select the 4 days out of 8 to have pizza for dinner.

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Answer:

A. $760

Step-by-step explanation:

Price: $8

Amount of goods; 95

revenue = price x total units

$8 x 95 = $760 revenue

The vertex of the curve will be at (-2, -4) and the axis of symmetry is at -2

From the graph, the roots of the equation are -4 and 0, therefore, (x + 4) is a factor and x is also a a factor.

The equation of the curve is the product of the factors of the curve which is y = x(x + 4)

y =  + 4x

The x coordinate of the vertex =

will be illustrated as:

-b/2a = axis of symmetry

a and b is the coefficient of x

so a = 1, b = 4

x coordinate of vertex = -4/2 = -2

Then, substitute x = -2 into y =   + 4x to find the y-coordinate of the vertex

y = (-2)² + 4(-2)

y = 4 -8

y = -4

vertex  = (-2, -4)

The axis of symmetry is -b/2a which is -2

Therefore, the vertex is at (-2, -4).

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8.77 ft/sec  is the tip of her shadow moving with a speed of 6 ft/sec .

What is speed, for instance?

Let H = the height of the pole.

h = the height of the woman.

x = the length of the woman's shadow.

s = the distance from the pole to the woman.

By similar triangles,  H/h = (s + x)/x  or  Hx = h(s + x).

Differentiating, H dx/dt = h(ds/dt + dx/dt)

19 dx/dt = 6(6 + dx/dt) = 36 + 6 dx/dt

13 dx/dt = 36

dx/dt = 36/13 ft/sec = 2.77 ft/sec for how fast her shadow is lengthening.

The speed of the tip of her shadow would be this speed added to her traveling speed: 2.77 + 6 = 8.77 ft/sec.

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The equation of the line passing through

(1) point (-6, -3) and m = -1 is y = -x -9  .

(2) point (-7 , 6) and m = 0 is  y = 6 ,

(3) point (-2 , 11) and m = 4/3 is y = (4/3)x + 41/3  .

the graph of the line is shown below .

In the question ,

point on the line and slope of the line is given

So , equation will be

Part(1)

(-6, -3), m = -1

(y -(-3)) = -1(x -(-6))

y + 3 = -1(x + 6)

y + 3 = -x - 6

y = -x -6 -3

y = -x -9

the equation is y = -x -9  .

Part(2)

(-7, 6), m = 0

(y - 6) = 0(x -(-7))

y - 6 = 0(x + 7)

y - 6 = 0

y = 6

the equation is y = 6

Part(3)

(-2, 11), m=4/3

(y - 11) = (4/3)(x -(-2))

y - 11 = (4/3)x + 8/3

y = (4/3)x + 8/3 + 11

y = (4/3)x + 41/3

the equation is y = (4/3)x + 41/3

the graph of all the three equations are shown below .

Therefore , The equation of the line passing through

(1) point (-6, -3) and m = -1 is y = -x -9  .

(2) point (-7 , 6) and m = 0 is  y = 6 ,

(3) point (-2 , 11) and m = 4/3 is y = (4/3)x + 41/3  .

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Answer:

Step-by-step explanation:

a) 100cm 1m so, 320/100=3.2m, 1200/100=12m

b) 3.2+3.2+12+12= 6.4+24=30.4

c) 3*12=36m squared

d) 3.2*12= 3*12+0.2*12=36+2.4=38.4m squared

e) My estimate in d) was reasonable

f) This is because 36 and 38.4 are really close to each other they only have a difference of 2.4 and that is because instead of multiplying the estimate with 3 and a 0.2 I just multiplied it with a 3. 0.2*12=2.4 so the difference is reasonable.

The equation to find the original cost of hat is

44.80 = (x + 35) - (x+35)× 10/3

In the given question we have,

Ms. emlyn buys a hat and gloves with coupon for 30% off her entire purchase.

discount on total purchase = 30%

cost of gloves before discount = $35

let the cost of hat be $x before discount . The bill paid by Ms emlyn after discount but without tax = $44.80

total cost ( hat+gloves) before discount= $(x+35)

Now, after sum up all information we get,

$(x+35) - 30%discount on $(x+35) = $44.80

=> x+35 - (x+35)100/30 = 44.80

=> x+35 - (x+35)10/3= 44.80

which is required equation for original cost of hat.

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The coordinates of the image of vertex after a reflection of r x-axias (x,y) is (x, -y).

To get the coordinates of a point reflected on the x - axis, some important rules be considered here:

1. The x - coordinate of the reflected point is the same as the x - coordinate of the original point.

2. The y - coordinate of reflected point has opposite sign of y-coordinate of original point.

Example:

(1,9) when reflected on the x - axis it will be (1,-9).

Therefore the  coordinates of the image of vertex after a reflection of r x-axias (x,y) is (x, -y).

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Answer:

Step-by-step explanation:

Move 6a to the other side

Subtract 7a and 6a

use inverse operations. So add 3 on both sides

Answer:

a = 6

Step-by-step explanation:

The given equation is,

→ 7a - 3 = 3 + 6a

Now the value of a will be,

→ 7a - 3 = 3 + 6a

→ 7a - 6a = 3 + 3

→ a = 3 + 3

→ [ a = 6 ]

Hence, the value of a is 6.

The probability that both Rachel and Robert are in the picture is 3/16.

The terms probability and possibility are interchangeable. It is a mathematical branch concerned with the occurrence of a random event. The value is between 0 and 1. In mathematics, the probability was introduced to predict the likelihood of events occurring.

Given that

Rachel and Robert both begin at the same point

Rachel completes a lap every 90 seconds.

Robert completes a lap every 80 seconds.

The photographer captures 1/4th of the track, centered on the starting line.

As a result, the photo captures 1/8th of the track on either side of the starting line.

The photographer captures it between 10 and 11 minutes, or 600 and 660 seconds.

Let us calculate the time interval between 600 and 660 seconds during which Rachel and Robert will be running in the quarter-length region of the track centered on the starting line. Specifically, 1/8th of the track length on each side of the starting line.

Robert will complete 1/8th of a lap in 10 seconds. So, between 630 and 650 seconds, Robert will be in the area of the ground captured by the photographer.

Rachel finishes one lap in 90 seconds. As a result, Rachel will take the starting line at the 630th second (after 7 laps).

Rachel will complete 1/8th of a lap in 90/8 seconds. So, Rachel will be in the area of the ground captured by the photographer from (630 - 90/80) seconds to (630 + 90/80) seconds.

i.e., for a duration of 90/80 seconds out of the 60 seconds both of them are in the frame captured by the photographer.

Required probability = {time window in which both Rachel and Robert are in the favorable zone}/{time window in which the photographer captures the picture}

= {90/8}/60

= 3/16

Therefore the probability that both Rachel and Robert are in the picture is 3/16

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