what number and what percent describe the probability of certain event ? what number and what percent describe the probability of an impossible event

Factors (1) x² - 11x + 28 = (x-4)(x-7), (2) 2x² + 8x + 6 = 2(x+1)(x+3), (3) k² - 25 = (k+5)(k-5), (4) a² - 9a + 20 = (a-5)(a-4), (5) 7x² - 11x - 6 = (7x+2)(x-3) , (6) 14x² - 52x + 30 = 2(7x-3)(x-5), (7) 6n³ - 8n² + 3n - 4 = (2n-1)(3n²-2n+4), (8) 15y³ - 3v² + 20v - 4 = (5y-1)(3y²+1)(4-v)

Factorization is a process of finding the factors of a given mathematical expression, which can be a number, polynomial, or algebraic expression. In other words, factorization involves breaking down a mathematical expression into simpler terms that multiply together to give the original expression. For example, the factors of the expression x^2 - 4 are (x + 2)(x - 2).

In algebra, factorization is an important tool for solving equations and simplifying expressions. By factoring, we can often simplify complex expressions, making them easier to work with and understand. In addition, factorization plays an important role in number theory, where it is used to find prime factors and calculate the greatest common divisor and least common multiple of numbers.

(1) x² - 11x + 28 = (x-4)(x-7)

(2) 2x² + 8x + 6 = 2(x+1)(x+3)

(3) k² - 25 = (k+5)(k-5)

(4) a² - 9a + 20 = (a-5)(a-4)

(5) 7x² - 11x - 6 = (7x+2)(x-3)

(6) 14x² - 52x + 30 = 2(7x-3)(x-5)

(7) 6n³ - 8n² + 3n - 4 = (2n-1)(3n²-2n+4)

(8) 15y³ - 3v² + 20v - 4 = (5y-1)(3y²+1)(4-v)

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The vertices of the triangle after reflection is

D)N′(−5, 2), M′(−8, 1), O′(−7, 3).

What is triangle?

A triangle is a form of polygon with three sides; the intersection of the two longest sides is known as the triangle's vertex. There is an angle created between two sides. One of the crucial elements of geometry is this

Remember that the general rule to reflect over a vertical line in the form

if  x = a then,

=> (x , y) -> (-x-2a , y)

For x = 5, we'll have that the general rule is:

=> (x , y)  -> (-x-10 , y).

Now the triangle vertices are,

N(-5,2) => (-(-5)-10,2) => (5-10 , 2) => N'(-5,2)

M(-2,1) => (-(-2)-10,1) => (2-10,1) => M' (-8,1)

O(-3,3) => (-(-3)-10,3) => (3-10,3) => O'(-7,3)

Hence the vertices of the triangle after reflection is D)N′(−5, 2), M′(−8, 1), O′(−7, 3).

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Answer:

Probability of George picking black pants and a green shirt is 2/13

Probability of George picking a green shirt is 6/7

Probability of George not choosing a blue shirt 5/7

Answer:

The Correct answers are

A

C

D

E

Answer:

Correct Answers:

A 3/4=6/8

C 2/3=8/12

D 8/8=5/5

E 2/5=4/10

Step-by-step explanation:

Answer:

Every day, 33% of locusts are added to the locust population

Answer: 96 slices

Step-by-step explanation:

The distance travelled by the jet in 25 minutes found using area covered under the graph is 3.7 miles.

What is area?

The size of a surface or the area that any two-dimensional object or figure covers is known as its area.

Area of triangle = [tex]\frac{bh}{2}[/tex]

Area of rectangle=l x w

The area covered under graph= area of triangle+ area of rectangle

                                                   = [tex]\frac{bh}{2}[/tex] + l x w

Dimension of triangle:

base(time on x-axis)=5 seconds

height(speed on y-axis)= 600 miles per hour

                                      =600÷3600 miles per seconds

                                       =0.167 miles per seconds

Dimensions of rectangle:

length(time on x-axis):25-5 =20 seconds

width(speed on y-axis)= 600 miles per hour

                                      =600÷3600 miles per seconds

                                       =0.167 miles per seconds

Distance = The area covered under graph

              = area of triangle+ area of rectangle

               = [tex]\frac{bh}{2}[/tex] + l x w

               =[tex]\frac{5(0.167)}{2}[/tex] + 20(0.167)

               =0.4175 + 3.34

                =3.7575

Distance ≈3.7 miles

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Answer:

Please leave more information regarding the question thank you

Answer:

3.142 in 2 decimal is 3.100

Step-by-step explanation:

When we come to diameter of 8cm I don't know

a. 15, 16, 17 : The triangle is an acute triangle

b. 20, 18, 7 : The triangle is an obtuse triangle

c. 17, 144, 145 : The triangle is a right triangle

d. 24, 32, 40 : The triangle is a right triangle

From the question, we are to classify the given triangles as obtuse, acute or right triangles

To classify the triangles, we will consider the longest side of the triangles

a.  15, 16, 17

Is 17² = 15² + 16² ?

17² = 289

15² + 16² = 225 + 256 = 481

NO,

17² < 15² + 16²

Thus,

The triangle is an acute triangle

b.  20, 18, 7

Is 20² = 18² + 7² ?

20² = 400

18² + 7² = 324 + 49 = 373

NO,

20² > 18² + 7²

Thus,

The triangle is an obtuse triangle

a.  17, 144, 145

Is 145² = 144² + 17² ?

145² = 21025

144² + 17² = 20736 + 289 = 21025

YES,

Thus,

The triangle is a right triangle

a.  24, 32, 40

Is 40² = 32² + 24² ?

40² = 1600

32² + 24² = 1024 + 576 = 1600

YES

Hence,

The triangle is a right triangle

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Answer:

The common difference is 2.

Answer:

The common difference of the arithmetic sequence 14, 16, 18 is **2**.

In any arithmetic sequence, each term is equal to the previous term plus the common difference. So, the second term is equal to the first term plus the common difference. In this case, the second term, 16, is 2 more than the first term, 14. Therefore, the common difference is 2.

We can also find the common difference by subtracting any two consecutive terms in the sequence. For example, we can subtract the second term from the third term to get 18 - 16 = 2.

The common difference of an arithmetic sequence is always constant. This means that the difference between any two consecutive terms in the sequence will always be the same. In this case, the difference between any two consecutive terms is 2.

Step-by-step explanation:

We can say with 95% confidence that the population variance σ2 lies within the interval [155.25, 570.06].

To construct a 95% confidence interval for the population variance σ2, we can use the chi-square distribution.

First, we need to calculate the chi-square values for the upper and lower limits of the confidence interval. We use the formula:

chi-square upper = (n-1)*s^2 / χ^2(α/2, n-1)

chi-square lower = (n-1)*s^2 / χ^2(1-α/2, n-1)

where n is the sample size, s is the sample standard deviation, α is the level of significance (0.05 for 95% confidence interval), and χ^2 is the chi-square distribution function.

Plugging in the values, we get:

chi-square upper = (25-1)*14^2 / χ^2(0.025, 24) = 43.98

chi-square lower = (25-1)*14^2 / χ^2(0.975, 24) = 15.14

Next, we can use these chi-square values to calculate the confidence interval for σ2:

confidence interval = [(n-1)*s^2 / chi-square upper, (n-1)*s^2 / chi-square lower]

Plugging in the values, we get:

confidence interval = [(25-1)*14^2 / 43.98, (25-1)*14^2 / 15.14]

confidence interval = [155.25, 570.06]

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8 is the value of x in parallel lines.

With an example, what is a parallel line?

Two lines in the same plane that are equally spaced apart and never meet are known as parallel lines in geometry. They can be either vertical or horizontal.

                      Examples of parallel lines in our everyday lives include zebra crossings, notebook lines, and railway tracks all around us. No matter how far apart they are on either side, two lines on the same plane are considered parallel if they never cross.

given

      m ║n

 8x - 10 + 126 = 180°

  8x + 116 = 180°

  8x  = 180° - 116

    8x = 64

      x = 64/8

       x = 8

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Answer:

2j - c

Step-by-step explanation:

(a) Volume of the solid generated by revolving the region bounded by the graph is 12.422 cubic units.

(b)

(i) The work done in stretching the spring from its natural length to a length of 10 in. is 54 lb.-in.

(ii) The work done in stretching the spring from a length of 7 in. to a length of 9 in. is approximately 13.5 lb.-in.

(a) To find the volume of the solid generated by revolving the region bounded by the graph[tex]x^2=y-2[/tex] and 2y-x-2=0 for 0≤x≤1 about y=3, we can use the method of cylindrical shells:

First, we need to find the limits of integration for the radius of the shells. Since we are revolving around y=3, the distance between y=3 and the curve x^2=y-2 will give us the radius of the shell.

Solving for y in [tex]x^2=y-2[/tex], we get[tex]y=x^2+2.[/tex] Substituting this into 2y-x-2=0, we get [tex]x=2y-2y^2-2.[/tex] So the limits of integration for the radius will be from [tex]3-(x^2+2) to 3-(2y-2y^2-2).[/tex]

Next, we need to find the height of the shells. This is simply the length of the interval of integration for x, which is 0 to 1.

So the volume of the solid is given by the integral:

[tex]V = \int (3-(x^2+2)) - (3-(2y-2y^2-2)) dx[/tex] from x=0 to x=1

Simplifying and evaluating the integral, we get:

V ≈ 12.422 cubic units.

Therefore, the volume of the solid generated by revolving the region bounded by the graph [tex]x^2=y-2[/tex] and [tex]2y-x-2=0[/tex] for 0≤x≤1 about y=3 is approximately 12.422 cubic units.

(b) (i) The work done in stretching the spring from its natural length of 6 in. to a length of 10 in. can be found using the formula:

W =[tex](1/2)k(d2^2 - d1^2)[/tex]

where k is the spring constant, d1 is the initial length, and d2 is the final length.

Given that the force required to stretch the spring from its natural length of 6 in. to a length of 8 in. is 9 lb., we can find the spring constant as follows:

k = F/(d2 - d1) = 9/(8-6) = 4.5 lb/in

So the work done in stretching the spring from its natural length of 6 in. to a length of 10 in. is:

W = [tex](1/2)(4.5)(10^2 - 6^2)[/tex]= 54 lb.-in.

Therefore, the work done in stretching the spring from its natural length to a length of 10 in. is 54 lb.-in.

(ii) To find the work done in stretching the spring from a length of 7 in. to a length of 9 in., we can use the same formula:

W =[tex](1/2)k(d2^2 - d1^2)[/tex]

Using the same spring constant of 4.5 lb/in, the work done is:

W = [tex](1/2)(4.5)(9^2 - 7^2)[/tex]≈ 13.5 lb.-in.

Therefore, the work done in stretching the spring from a length of 7 in. to a length of 9 in. is approximately 13.5 lb.-in.

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The result cos²(α) = -2 is not possible, as the square of cosine must be between 0 and 1. It appears there might be an error in the given information. Please double-check the values and try again.

Given that cos(2α) = -5 and that it terminates in quadrant I, we need to find the exact value of sin(α).

First, let's recall the Pythagorean identity: sin²(α) + cos²(α) = 1.

Since cos(2α) = -5, we need to find the value of cos(α). In order to do this, we'll use the double-angle formula for cosine: cos(2α) = 2cos²(α) - 1.

Now, we can plug in the given value of cos(2α) and solve for cos(α):
-5 = 2cos²(α) - 1
-4 = 2cos²(α)
cos²(α) = -2

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The standard errors of the proportion for sample sizes of 40, 80, and 120 are 0.0733, 0.0518, and 0.0422, respectively,

How to calculate the standard error of the proportion?

To calculate the standard error of the proportion for a population with a proportion equal to 0.32 and sample sizes of 40, 80, and 120, we can use the formula:

Standard Error (SE) = √[(p * (1 - p)) / n]

where p is the proportion (0.32), and n is the sample size.

For a sample size of 40:
SE = √[(0.32 * (1 - 0.32)) / 40]
SE ≈ 0.0733 (rounded to 4 decimal places)

For a sample size of 80:
SE = √[(0.32 * (1 - 0.32)) / 80]
SE ≈ 0.0518 (rounded to 4 decimal places)

For a sample size of 120:
SE = √[(0.32 * (1 - 0.32)) / 120]
SE ≈ 0.0422 (rounded to 4 decimal places)

So, for a population with a proportion equal to 0.32, the standard errors of the proportion for sample sizes of 40, 80, and 120 are approximately 0.0733, 0.0518, and 0.0422, respectively, when rounded to 4 decimal places.

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The vertex form of the given quadratic equation is.

y = -5(x + 6)² - 356

To complete squares we need to use the perfect square trinomial:

(a + b)² = a² + 2ab +b²

Here we can rewrite our quadratic as follows:

y = -5x² - 60x - 176

y = -5*( x² + 12x) - 176

y = -5*( x² + 2*6x) - 176

Now we can add and subtract 6² = 36 then we will get:

y = -5*( x² + 2*6x + 36 - 36) - 176

y = -5*( (x + 6)² - 36) - 176

y = -5(x + 6)² - 356

Which means that the vertex is at (-6, -356)

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The double integral of x² 2y over the given region (bounded by y = x, y = x³, and x > 0) is 2/35.

To solve this double integral, we need to integrate the function x² 2y over the given region in the xy-plane.

The region is bounded by the curves y = x and y = x³, and the line x = 0.

First, we need to determine the limits of integration. Since x > 0,

we can integrate from x = 0 to x = 1.

For each value of x in this range, the lower bound of y is given by y = x, and the upper bound is given by y = x³.

Therefore, we need to integrate with respect to y from y = x to y = x³ for each value of x in the range [0, 1].

So, the double integral can be written as:

∫(0 to 1) ∫(x to x³) x² 2y dy dx

Integrating with respect to y first, we get:

Therefore, the double integral of x² 2y over the given region is 2/35.

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Hence,0.72 rather than to increase the radius to meet their requirements.

A cone is a three-dimensional geometric form with a plane base and a smooth tapering vertex. A cone is made up of a collection of line segments, half-lines, its  lines that connect the apex of the common point at to every point on a base that is in a flat  other than the apex. 

A measurement of three-dimensional space is volume. It is frequently expressed quantitatively using  US-standard units ,SI-derived units, as well as several imperial  Volume and the notion of length are connected.

Let the new radius x and the old radius as r. The formed volume was 175 cubic cm, and the new container height is 5 cm,

V = [tex]\frac{1}{3}\pi r^2h[/tex], where V is the volume, r is the radius, and h is the height, is the formula for a cone volume.

We can construct an equation using the previous volume:

175 =    [tex]\frac{1}{3}\pi r^2h[/tex]

the height is same for new and old container , so,:

175 =[tex]\frac{1}{3}\pi r^2*5[/tex]

175 = [tex]\frac{5}{3}\pi r^2[/tex]

By multiplying both sides by (5/3)

[tex]r^2 = \frac{175*3}{5*\pi}[/tex] ≈ 22.3 use [tex]\pi[/tex]=3.14

When both sides are square root

r ≈ 4.72

Therefore, the old container  radius is 4.72 cm.

now,We subtract the old radius from the new radius for  determine how much the radius must increase to s the new container:

x - r ≈ 4 - 4.72 ≈ -0.72

Because the new radius is lower than the old radius, the outcome is negative.

We would need to reduce the radius by roughly 0.72 cm rather than expand it to satisfy the needs of the new container.

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Let's use variables to represent the number of child and adult tickets sold on Wednesday.

Let c be the number of child tickets sold, and let a be the number of adult tickets sold.

We know that the price of a child ticket is $5.60, and the price of an adult ticket is $9.40.

From the problem statement, we know that 177 tickets were sold in total, so:

c + a = 177

We also know that the total revenue from ticket sales was $1352.20, so:

5.60c + 9.40a = 1352.20

Now we have a system of two equations with two variables. We can solve for a by using the first equation to express c in terms of a, and then substituting into the second equation:

c + a = 177 --> c = 177 - a

5.60c + 9.40a = 1352.20

Substituting c = 177 - a into the second equation, we get:

5.60(177 - a) + 9.40a = 1352.20

Expanding and simplifying:

992.20 - 5.60a + 9.40a = 1352.20

3.80a = 360

a = 95

Therefore, 95 adult tickets were sold on Wednesday.

Its bugging out but I got 95 tickets I would add explanation if it didn't act out.

X=Adult tickets

Y=Child tickets

X+Y=117

Y=117-X

9.40X+5.60Y=1352.20

9.40X+5.60(117-X)=1352.20

9.40X+991.20-5.60x=1352.20

3.80X=361

X=95

Answer:

f(1) = 15

f(n) = f(n-1) x n

Step-by-step explanation:

The sequence in recursive form is:

f(1) = 15

f(n) = f(n-1) x n

Using this recursive formula, we can find the value of any term in the sequence by calculating the value of the previous term and multiplying it by the index of the current term.

For example, to find the value of f(2), we would use the formula:

f(2) = f(1) x 2

f(2) = 15 x 2

f(2) = 30

Similarly, to find the value of f(3), we would use the formula:

f(3) = f(2) x 3

f(3) = 30 x 3

f(3) = 90

And to find the value of f(4), we would use the formula:

f(4) = f(3) x 4

f(4) = 90 x 4

f(4) = 360

We can continue using this formula to find the values of any term in the sequence.

The charge on the capacitor at time t is given by q(t) = -21292.5e^(-0.00878t) + 21292.5e^(-314.53t) + 626000 coulombs.

To find the charge on the capacitor, with the initial conditions q(0) = 0 coulombs and i(0) = 0 amperes, we use the given linear differential equation:

L d^2q/dt^2 + R dq/dt + 1/C q = E(t)

We can solve for q(t) by finding the roots of the characteristic equation, and assuming a particular solution. Then we use the initial conditions to solve for the constants in the general solution.

The solution to the differential equation is:

q(t) = -21292.5e^(-0.00878t) + 21292.5e^(-314.53t) + 626000

Therefore, the charge on the capacitor at time t is given by q(t) = -21292.5e^(-0.00878t) + 21292.5e^(-314.53t) + 626000 coulombs.

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The, a z-score of -0.65 is not unusual

To calculate the z-score, we use the formula:

[tex]z =\frac{ (x - μ)}{σ}[/tex]

where x is the individual score, μ is the mean, and σ is the standard deviation.

Plugging in the values given, we get:

[tex]z= \frac{71-73}{3.1}[/tex]
z = -0.65

Rounding to 2 decimal places, the z-score is -0.65.

To determine if this score is unusual or not, we need to compare it to the normal distribution. A z-score of -0.65 means that the individual's score is 0.65 standard deviations below the mean.

According to the empirical rule, about 68% of the data falls within 1 standard deviation of the mean. Therefore, a z-score of -0.65 is not unusual and falls within the normal range of scores.

So, the answer is B. Not Unusual.

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The measure of arc FE is 27degrees,angle m<B is 112degrees, <GHJ = <GIJ = 73⁰ , m<S = 90 degrees in the given circles

The sum of angle in the triangle DEF is 180 degrees

mFE = <D

Recall that <D+<E+<F = 180⁰

<D+63+90 = 180

<D = 180-153

<D = 27 degrees

Hence the measure of arc FE is 27degrees

6) For this circle geometry, we will use the theorem

The sum of Opposite side of a cyclic quadrilateral is 180 degrees.

A + C = 180

m<A + 101 = 180

m<A = 180-101

m<A = 79degrees

Similarly

B + D = 180

m<B + 68 = 180

m<B = 180-68

m<B = 112degrees

7) The sum of angle in a circle is 360, hence;

arcGJ+68+31+115 = 36p

arcGJ = 360 - 214

arcGJ = 146⁰

Since the angle at the centre is twice angle at the circumference, then;

<GHJ = 1/2 arcGJ

<GHJ = 1/2(146)

<GHJ = 73⁰

<GHJ = <GIJ = 73⁰ (angle in the same segment of the circle are equal)

8) Recall that the sum of Opposite side of a cyclic quadrilateral is 180 degrees.

P + R = 180

57 + <R = 180

m<R = 180-57

m<R = 123degrees

Similarly, m<Q+m<S = 180⁰

Since the triangle in a semi circle is a right angled triangle, hence m<Q = 90 degrees (triangle PQR is a right angled triangle)

m<S = 180 - 90

m<S = 90 degrees

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True: A Chorochromatic map is a type of cartographic map that represents features depending on how they are distributed across the surface in terms of quality.`

We have,

The art and science of cartography involves visually depicting a geographic location, typically on a flat surface like a map or chart. It could include superimposing a region's depiction with non-geographical distinctions like political, cultural, or other ones.

Making and utilizing maps is the theory and application of cartography. Cartography, which combines science, aesthetics, and method, is based on the idea that reality may be described in ways that effectively convey spatial information. The same basic components are included on most maps: the main body, the legend, the title, the scale and orientation indications, the inset map, and the source notes.

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complete question:

a cartographic map style that symbolizes features based on the qualitative surface distribution of a mapped feature is called a chorochromatic map.

A) Length A = 5 ft and width B= 4 ft

B) Volume of the water though = 88 [tex]ft^3[/tex]

What is volume?

The space taken up by any three-dimensional solid constitutes a volume, to put it simply. A cube, cuboid, cone, cylinder, or sphere can be one of these solids. Cubic units are used to measure the volume of solids. The volume will be given in cubic metres, for instance, if the dimensions are given in metres.

Here consider the prism plane figure the dotted lines are equal to the width,

Then width B= 8-4 = 4 ft

Length A = 8-3 = 5 ft

B) Now volume of rectangular prism = lwh cubic unit.

Volume of big prism = 8*2*3=48 [tex]ft^3[/tex]

Volume of small prism = 5*4*2 = 40 [tex]ft^3[/tex]

Then Total volume = 48+40 = 88  [tex]ft^3[/tex]

Hence in the rectangular prisms,

A) Length A = 5 ft and width B= 4 ft

B) Volume of the water though = 88 [tex]ft^3[/tex]

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Answer:

If you're asking if its possible, yes it is