Assume that the random variable X is normally distributed, with mean p = 100 and standard deviation o = 15. Compute the
probability P(X > 112).

Answer:

588 kilómetros

Step-by-step explanation:

La función con la que estamos trabajando según la pregunta es;

F (x) = 6x ^ 2 -12

Ahora, la pregunta que simplemente nos hace es encontrar el valor de F (x) dado que x = 10

Entonces, lo simple que hacemos aquí es hacer una sustitución de x = 10 Eso sería;

F (10) = 6 (10) ^ 2 - 12 = 600-12 = 588

Answer:

−67b + 6 ≤ 9b + 43

Group like terms

That's

- 67b - 9b ≤ 43 - 6

Simplify

- 76b ≤ 37

Divide both sides by - 76

Hope this helps you

Answer:

a cone with a base radius of 17 units

Step-by-step explanation:

The computation of three-dimensional shape is shown below:-

Data provided

Perimeter of Triangle = 58 units

One non equal side = 24 units

We will assume two equal side = x units

x + x + 24 = 58

2 x = 58 - 24

2 x = 34

[tex]x = \frac{34}{2}[/tex]

x = 17

As we can see that the triangle is rotated about line k

This will give in a cone as it is a dimensional shape of three

So, the shape which is new will be of cone having radius 17 units

slant height 24

height k units

Answer:

A

Step-by-step explanation:

Answer:

Yes, because each x-value corresponds to one y value.

Step-by-step explanation:

If you look at the table, you notice that there is one output (y) for every input (x). This means that it is a function. It would NOT be a function if you had two outputs for an input. For example, there are two x values that are 6. For one coordinate pair, the table says (6,9) and (6,8). Since there are two values for the same input- it wouldn't be a function. In this case, there is an input of 4 and 5 with the same output. That is okay! Even though they have the same y value, those inputs still only have ONE output.

Answer:

s = 8 degrees

Step-by-step explanation:

12s + 42 + 42 = 180

12s + 84 = 180

12s = 96

s = 8 degrees

Answer:

a. 16; b. aₙ = 4ⁿ⁻¹; c. predation and carrying capacity will limit the population

Step-by-step explanation:

a. The first female had 4 pups.

If each of them had 4 pups, there would be 4 × 4 = 4² = 16 pups.

b. 1st generation                        =     1 pup

2nd generation = 4 ×  1 pup      =    4 pups

3rd generation  = 4 ×  4 pups    =  16 pups

4th generation  = 4 × 16 pups    = 64 pups

5th generation  = 4 × 64 pups = 256 pups

The sequence is           1,   4, 16, 64, 256, …

We can also write it as 4⁰, 4¹, 4²,  4³,   4⁴, …

Note that the exponent is one less than the number of the generation.

Thus, the general formula for the nth term, aₙ, is

aₙ = 4ⁿ⁻¹, where

n = the number of the generation

a = the number of pups in that generation.

c. a₂₅ = 4²⁵⁻¹ = 4²⁴ ≈ 281 000 000 000 000 or 281 trillion

The population would not reach that number because there would not be enough food for all those pups. Pups would die of starvation until their numbers equalled the carrying capacity of the ecosystem and would level off at that point.

There would also be increased predation by coyotes, bobcats, etc. This would also keep the population growth in check,

Answer:

-28.

Step-by-step explanation:

(x^2 + 3) / (x + 6)

x = -9

[(-9)^2 + 3] / (-9 + 6)

= (81 + 3) / (-3)

= 84 / (-3)

= -28

Hope this helps!

Answer:  the value of the expression is 80

Step-by-step explanation:

[tex]x^2 +3/ x+6[/tex]

(-9)² + 3 / (-9 + 6) .  PEMDAS: figure  parentheses and exponents  first

81 + 3/-3    division   3/-3  = –1

81 + (–1) .adding a negative is the same as subtracting

81 –1

80

Answer:  see below

Step-by-step explanation:

I used a coordinate graph and placed the Ticket Booth at the origin (0, 0)

Then I chose a distance of 4 (you can choose any distance) and placed the three events equidistant from the origin by using the x- and y- axis to easily determine a distance of 4 from the origin.

(0 - 4, 0) = (-4, 0)

(0 + 4, 0) = (4, 0)

(0, 0 + 4) = (0, 4)

If the booths are placed first you would need to find the equation of a circle that contains all three points and place the booth at the center.

You do this by creating a system of three equations inputting the x,y coordinates of each booth and solving for h, k, r.

Equation of a circle is: (x - h)² + (y - k)² = r²

Answer:

None

Step-by-step explanation:

You wrote:

"Determine what type of quadrilateral ABCD is, given the following points. A(0,0) B(5,0) C(0,4) D(5,4) Parallelogram, Rectangle, Rhombus, or Square"

According to what you wrote, you don't have any of the listed quadrilaterals.

ABCD (in that precise order) is not a simple polygon according to the coordinates of the points since there is an internal intersection of sides.

ABDC, though, is a rectangle.

The quadrilateral with points A(0,0), B(5,0), C(0,4) and D(5,4) is a rectangle, option B is correct.

To find the type of quadrilateral find the length of four sides:

For A(0,0) and B(5,0)

AB=√(5-0)²+(0-0)²

AB=5 units

For  B(5,0) and D(5,4)

BD=√(5-5)²+(4-0)²

BD=√16

BD=4 units

For C(0,4) and D(5,4):

BD=√(5-0)²+(4-4)²

=5 units

For A(0,0) and C(0,4):

AC=√(0-0)²+(4-0)²

= 4 units.

In the quadrilateral the opposite sides are equal, so it is a rectangle.

Hence, the quadrilateral is a rectangle. Option B is correct.

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Complete question:

Determine what type of quadrilateral ABCD is, given the following points. A(0,0) B(5,0) C(0,4) D(5,4)

(A) Parallelogram

(B) Rectangle

(C) Rhombus
(D)Square

Answer:

x = 125°

Step-by-step explanation:

The given polygon is a hexagon with 6 sides.

The sum of the interior angles for any given polygon = (n - 2)180, where n is the number of sides of the polygon.

Therefore:

[tex] x + 117 + 124 + 102 + 145 + 107 = (6 - 2)180 [/tex]

[tex] x + 595 = (4)180 [/tex]

[tex] x + 595 = 720 [/tex]

Subtract both sides by 595 to solve for x:

[tex] x + 595 - 595 = 720 - 595 [/tex]

[tex] x = 125 [/tex]

x = 125°

Answer:

86

Step-by-step explanation:

We can set the first digit as (10x+y)

We can interchange it to be (10y+x)

X is the second digit and Y is the first.

1) (10x+y) +(10y+x) =154

2) 11x+11y=154

3) 11(x+y) =154

4) x+y=14

5) x+x+2=14

6) 2x=12

7) x=6

8) y=6+2=8 , so y =8

Answer:

B. 6sqrt(2).

Step-by-step explanation:

Since the two legs of the right triangle are congruent, this is a 45-45-90 triangle. That means that the hypotenuse will measure xsqrt(2) units, and each leg will measure x units.

In this case, x = 6.

So, the hypotenuse is B. 6sqrt(2).

Hope this helps!

Answer:

Graph (B)

Step-by-step explanation:

For x < 3,

An arrow starting with a hollow circle at x = 3 and heading towards 0 will represent the given inequality on a number line.

Similarly, x ≥ 5,

An arrow starting with a dark circle at x = 5 and heading towards 12 will represent the given inequality on a number line.

When we combine these inequalities on a number line, Graph (B) will be the answer.

Answer:

Choice D - 8cm and 9cm.

Step-by-step explanation:

The other sides are not greater than 13.

A: 5 + 8 = 13

B: 6 + 7 = 13

C: 7 + 2 = 9

However, D is greater than 13 and is the correct answer.

D: 8 + 8 = 16.

Option d: 8 cm and 9 cm.

There is a theorem in mathematics stating:

" The sum of length of two sides of any triangle is greater than the rest third side"

According to that theorem, first three given options cant form the sides of the given triangle whose one side is 13 cm.

The 4th option has 8 cm and 9 cm for which we have:

8 + 9 > 13

Thus this option follows the theorem.

Hence fourth option is correct.

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Answer:

30%

Step-by-step explanation:

Total population=15,000

kantipur=9000

gorkhapatra= 7500

Both magazine=40%

n(k intersection g)=40% of 15,000

=0.4*15,000

=6,000

n(k) =9000

n(g)=7500

n(A union B)= n(k) + n(g) -n(k intersection g)

=9000+7500-6000

=10,500

Population who do no read= Total population - n(A union B)

=15000-10500

=4500

Percentage population who do not read both magazine

=4,500/15,000 * 100

=0.3 * 100

=30%

Answer:

1. Cosine

2. x = 49°

3. Sine

4. y = 41°

Step-by-step explanation:

1. The trig function that will be used to solve for x is cosine.

2. Determination of angle x

x° =..?

Adjacent = 13

Hypothenus = 20

Cos x = Adjacent /Hypothenus

Cos x = 13/20

Take the inverse of Cos

x = Cos¯¹ (13/20)

x = 49°

3. The trig function that will be used to solve for y is sine.

4. Determination of angle y.

y° =..?

Opposite = 13

Hypothenus = 20

Sine y = Opposite /Hypothenus

Sine y = 13/20

Take the inverse of Sine

y = Sine¯¹ (13/20)

y = 41°

Answer:

(4,7.5)

Step-by-step explanation:

Reflect (-4,7.5) at the y-axis

Answer:

a) point (2, 1) is when the ball is on it's way down at 2 seconds

b) vertex (1, 2) is the highest the ball goes, which is 2 at 1 second.

c) y-intercept (0, 1) at time zero the ball is starting at a height of 1.

d) Points (0, 1) and (2, 1) are the points at which the ball starts and when it is in the same position from the ground as when it started, which is 1.

e) zero (x-int) is when the ball hits the ground at 2.5 seconds.

Step-by-step explanation:

Answer:

See below

step by step explanation

A. (2 , 1 ) is point on the parabola . It represents that the height of the ball after 2 second have passed.

b. The vertex is at ( 1 , 2 ) . It represent that the maximum height of the ball which is 2 units to at t = 1 second

c. The y - intercept is ( 0 , 1 ) . It represent that the initial height of ball at t = 0 second is 1 unit.

d. Point ( 0 , 1 ) and ( 2 , 1 )

This point represent the set of point having equal height at two different time. It represents how long before the ball reaches the same height from the starting point.

e. The zero or x - intercept is ( 2.5 , 0 )

It represent the time taken by ball before it reaches the ground.

Hope this helps...

Best regards!!

Answer:

Half angle Identity for cosine:

[tex]$\cos \left(\frac{\theta}{2} \right)=\pm \sqrt{\frac{1+\cos(\theta)}{2} } $[/tex]

[tex]\text{Note that it is} \pm \text{because we don't know which Quadrant the half-angle is, }[/tex][tex]\text{the information of}\cos(\theta) \text{is not enough to conclude the angle}[/tex]

[tex]$\frac{\pi}{8} \text{ is a Quadrant I angle, therefore, positive}$[/tex]

[tex]$\cos \left(\frac{\pi}{8} \right)=\sqrt{\frac{1+\cos(\frac{\pi}{4} )}{2} } $[/tex]

The equation is true.

Answer:

(4,0)

Step-by-step explanation:

The zeros of the quadratic functions are where it crosses the x axis

It crosses at x=-2 and x=4

( -2,0) and (4,0)

Answer:

[tex]\boxed{(4,0)}[/tex]

Step-by-step explanation:

A zero of a quadratic function is where the parabola touches a point on the x-axis.

The parabola touches two points on the x-axis:

(4, 0) and (-2, 0)

A zero of the quadratic function is (4, 0).

Answer:

1.  20 tins of milk

2.  Weight of the Carton = 8,4kg ot 8400g

Step-by-step explanation:

Given

Volume of a Tin = 77cm³

Weight of a tin = 5000g

Volume of Empty Carton = 1540cm³

Weight of Empty Carton = 5000g

Calculating the number of tins of milk

To do this, we have to make use of the given volumes;

And this is done as follows;

[tex]Number = \frac{Volume\ of\ Empty\ Carton}{Volume\ of\ a\ Tin}[/tex]

Substitute  77cm³ for Volume of a Tin and 1540cm³ for Volume of an Empty Carton

[tex]Number = \frac{1540cm^3}{77cm^3}[/tex]

[tex]Number = 20[/tex]

Hence, 20 tins of milk will filled the empty carton

Calculating the weight of the Carton after filled with tins of milk

This is calculated as thus;

Total Weight = Weight of Empty Carton + Weight of Tins of Milk

Substitute 5000g for Weight of Empty Carton

Total Weight = 5000g + Weight of Tins of Milk

_________________________________________

Calculating Weight of Tins of Milk

Since 20 tins of milk will fill the empty carton, the

Weight of Tins of Milk = 20 * Weight of 1 Tin of Milk

Weight of Tins of Milk = 20 * 170g

Weight of Tins of Milk = 3400g

_________________________________________

Substitute 3400g for Weight of Tins of Milk

[tex]Total\ Weight = 5000g + 3400g[/tex]

[tex]Total\ Weight = 8400g[/tex]

In Kilograms:

[tex]Total\ Weight = 8.4kg[/tex]

Answer:

Step-by-step explanation:

A term, loosely defined, is a product of numbers and variables. Terms are separated from one another with a + or a - sign. So we have 2 terms here.

The degree of the polynomial, because it is just in terms of x and no other variable, is the highest degree'd term.  Our highest degree of x is 3, so this is a third degree polynomial.

It is classified by its number of terms:

1 term is a monomial, 2 terms is a binomial, 3 is a trinomial, and anything higher is just called a "polynomial". This has 2 terms so it is a binomial.

The answer is:

Work/explanation:

Here's how we classify polynomials based on the number of terms:

monomial - has only one term

binomial - has two terms

trinomial - has three terms

polynomial - has four terms or more

As for degrees, those are the highest exponents the polynomial.

Now, [tex]\sf{14x^3+x^2}[/tex] has 2 terms so it's a binomial; the highest exponent is 3.

Answer:

5

Step-by-step explanation:

The initial value is when x=0

When x=0, y =5

The initial value is 5

Answer:

no

Step-by-step explanation:

its not divisible by 10

you can also see that it ends with a 6

sorry if thats wrong

Answer:

no b/c the last digit does not end with a ten

Answer:

60.75

Step-by-step explanation:

sinA    sinB

------- = -----

a           b

sin(79)/9 = sinB/8

inverse sin B = 0.87

B = 60.75

Answer:

A, B, A

Step-by-step explanation:

(3)

Given

- 2x² + 10x + 12 ← factor out - 2 from each term

= - 2(x² - 5x - 6) ← factor the quadratic

Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (- 5)

The factors are - 6 and + 1, since

- 6 × 1 = - 6 and - 6 + 1 = - 5, thus

x² - 5x - 6 = (x - 6)(x + 1) and

- 2x² + 10x + 12 = - 2(x - 6)(x + 1) → A

(4)

[tex]x^{4}[/tex] - 81 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b), thus

[tex]x^{4}[/tex] - 81

= (x² )² - 9²

=(x² - 9)(x² + 9) ← note that x² - 9 is also a difference of squares

= (x - 3)(x + 3)(x² + 9) ← in factored form

x² - 3 is not a factor → B

(5)

Given

5[tex]x^{4}[/tex] - 320 ← factor out 5 from each term

= 5([tex]x^{4}[/tex] - 64) ← difference of squares

= 5(x² - 8)(x² + 8) → A

Answer:

Randomization allows a sample or small groups with similar characteristics to determine a probability or to hypothesize an event, that is why this type of samples is important in an experiment, that is, to carry it out in a random way.

Step-by-step explanation:

For example;

If a crop at a certain time of year, for example in summer, is affected by a certain fungus, to know if it is really the time of year that affects this problem, random samples of the same crop with the same characteristics and put it to the test at another time of the year to see if the weather is really a risk factor in the spread of this fungus.

Answer:

Step-by-step explanation:

The given set of data is 83, 71, 62, 86, 90, 95, 61, 60, 87, 72, 95, 74, 82, 54, 99, 62, 78, 76, 84, 92.

Now the stem - leaf plot will be,

5  4

6  0   1   2   2

7   1   2  4   6    8

8 2   3  4   6    7

9  0   2  5   5   9

Since range of the data = Highest term of the data - Lowest term of the data

                                       = 99 - 54

                                       = 45

Therefore, range of the data set is 45.

The range of the data is 45.

As we know that

Since range of the data = Highest term of the data - Lowest term of the data

= 99 - 54

= 45

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Answer:

The maximum size of the smaller jars is 6 liters

Step-by-step explanation:

Container 1=174 liters of oil

Container 2=258 liters of oil

Same pours the entire content of container one and container 2 into the same number of smaller jars

The maximum size of the smaller jar can be found by finding the highest common factor of 174 and 258

Factors of 174=1,2,3,6,29

Factors of 258=1,2,3,6,43

Common factors of 174 and 258=1,2,3 and 6

Highest common factor=6

Therefore,

The maximum size of the smaller jars is 6 liters