Consider function g.

g(x)={(6,-8<=(-2)<-2 ),(0,-2<=(-2)<4),(-4,4<=(-2)<10):}

What are the values of the function when x = -2 and when x = 4?

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

The equivalent expression of 9q^ 2 - 2/3(3q - 7) + 5q^2 is 14q^ 2 - 2q - 14/3

The expression is given as:

9q^ 2 - 2/3(3q - 7) + 5q^2

Open the bracket

9q^ 2 - 2q - 14/3 + 5q^2

Evaluate the like terms

14q^ 2 - 2q - 14/3

Hence, the equivalent expression of 9q^ 2 - 2/3(3q - 7) + 5q^2 is 14q^ 2 - 2q - 14/3

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Answer:

The height of the ladder is 6.9 meter

Explanation:

Given:

As opposite and hypotenuse given, use sine rule:

[tex]\rightarrow \sf sin(x) = \dfrac{opposite}{hypotenuse}[/tex]

[tex]\rightarrow \sf sin(60) = \dfrac{6}{h}[/tex]

[tex]\rightarrow \sf h = \dfrac{6}{sin(60)} = 4\sqrt{3} = 6.928 \ meters \quad \approx \ 6.9 \ meters \ \ (one \ decimal \ place)[/tex]

Answer:

Step-by-step explanation:

Part A

Neighborhood A :

2, 2, 2, 4, 4, 5, 5, 5, 5

mean = [tex]\frac{2+2+2+4+4+5+5+5+5}{9}[/tex] = [tex]\frac{34}{9}[/tex] ≈ 3.8  

median = 4

mode = 5

range = 3

[tex]Q_{3}[/tex] - [tex]Q_{1}[/tex] = 5 - 2 = 3

===================

Part B.

Neighborhood B :

1, 1, 2, 2, 3, 4, 5, 5, 12

mean = ( 1 + 1 + 2 + 2 + 3 + 4 + 5 + 5 + 12 ) ÷ 9 = [tex]\frac{35}{9}[/tex] ≈ 3.9

median = 3

mode = 1, 2, 5

range = 11

[tex]Q_{3}[/tex] - [tex]Q_{1}[/tex] = 5 - 1.5 = 3.5

Outlier = 12

Answer: B.

Step-by-step explanation:

   See attached. We examine the equation and decide which situation, or problem, models it correctly.

The airplane reaches its maximum height of 81 feet in 12 seconds.

If y = [tex]x^{2}[/tex], it means that the second derivate is 2 which is positive, then there is a minimum turning point.

If y = - [tex]x^{2}[/tex], it means that the second derivative will be -2 which is negative, then there is a maximum turning point.

Analysis:

h(t) = -[tex](t - 12)^{2}[/tex] + 81

By expanding,

h(t) = -([tex]t^{2}[/tex] - 24t + 144) +81

h(t) = -[tex]t^{2}[/tex] + 24t - 144 + 81

h(t) = -[tex]t^{2}[/tex] + 24t - 63

at turning point d/dt(h(t)) = 0

d/dt (h(t)) = -2t +24

-2t +24 = 0

if we differentiate again, second derivative is -2 which is negative, so it is a maximum point.

2t = 24

t  = 12 seconds

h(t) at t = 12

h(t) = [tex]-(12)^{2}[/tex] + 24(12) - 63 = 81 feet

In conclusion, the maximum height of the airplane after 12 seconds is 81 feet.

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The probability that none of the prizes is a $10 gift certificate is; 7/99

The expected number of $20 gift certificates drawn is 2.083

This is a question of picking objects from a mixture without replacement. The modelling distribution is the hypergeometric distribution, given by the formula:

P(a) = C(A,a) * C(B,b)/C(A+B,a+b)

Where;

a = number of good objects picked

b = number of bad objects picked.

A = number of good objects in the given batch.

B = number of bad objects in the given batch.

a + b = total number of objects picked without replacement.

A + B = total number of objects in the batch.

A) In this question;

A = 4 ($10, good)

B = 3 + 5 = 8 ($20, $50, "bad")

a = 0, b = 5

a + b = 5

Thus;

P(a = 0) = C(4, 0) × C(8, 5)/C(12, 5)

P(a = 0) = 1 × 56/792

P(a = 0) = 7/99

B) $20 is the "good" prize.

Thus;

A = 5

B = 3 + 4 = 7

a + b = 5 (total number of prizes drawn)

Thus;

E[$20] = (5/(5 + 3 + 4)*5)

E[$20] = (5/12)*5

E[$20] = 25/12

E[$20] = 2.083

Complete Question is;

The door prizes at a dance are four $10 gift certificates, five $20 gift certificates, and three $50 gift certificates. The prize envelopes are mixed together in a bag, and five prizes are drawn at random.

What is the probability that none of the prizes is a $10 gift certificate?

What is the expected number of $20 gift certificates drawn?

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The total purchase price of the dictionary and the software package is  $61.47.

The total purchase price is the sum of the dictionary, software package and taxes.

Total cost of  the dictionary and the software package = $27.65 + $29.80 = $57.45

Total cost after the taxes = ( 1 + 0.055 + 0.015) x $57.45 = $61.47

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Answer:

375 plates were sold

Step-by-step explanation:

$2400 (profit) - $150 (advertising) = $6 (profit per plate $8 cost - $2 expense) times x

2400 - 150 = 6x

Simplify the left side: 2400 - 150 = 2250

2250 = 6x

Divide both sides by 6

2250/6 = 375

If ɑ and β are the roots of x² + bx + c = 0, then we can write

x² + bx + c = (x - ɑ) (x - β)

Expanding the right side gives

x² + bx + c = x² - (ɑ + β) x + ɑβ

so that ɑ + β = -b and ɑβ = c.

Recall that for all real numbers m and n,

(m + n)² = m² + 2mn + n²

a) It follows that

(i) ɑ² + β² = (ɑ + β)² - 2ɑβ = (-b)² + c = b² + c

(ii) (ɑ - β)² = ɑ² - 2ɑβ + β² = b² + c - 2c = b² - c

b) I assume you mean to find the quadratic whose roots are ɑ² + β² and (ɑ - β)² (and not (ɑ - 3)²). The simplest quadratic of this form is

(x - (ɑ² + β²)) (x - (ɑ - β)²)

Using the results from part (a), this becomes

(x - (b² + c)) (x - (b² - c))

and expanding, we get

x² - (b² + c + b² - c) x + (b² + c) (b² - c)

= x² - 2b² x + b⁴ - c²

Answer:

reason 1.) This is the original expression

reason 2.) you subtract 4 from both sides

reason 3.) you divide both sides by 2 to get x=5

Answer:

c

cuz it is

first of all 4,3 + 0,0 = 4,3

2,1+0,0 = 2,1

and which is the answer

The range of the exponential function will be y ≥ 250,0003. Then the correct option is B.

The domain means all the possible values of x and the range means all the possible values of y.

The Population Of Center City Is Modeled By Exponential Function F, Where X Is The Number Of Years After The Year 2015.

The graph is given below.

We know that the exponential function is given as

y = abˣ

For x = 0, y will be 250,000

250,000 = a

For x = 40, y will be 400,000

400,000 = 250,000b⁴⁰

           b = 1.0118

Then we have

y = 250,000 (1.0118)ˣ

Then the range of the exponential function will be y ≥ 250,0003.

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Answer:

the solution  is (1,-4)

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

[tex]\text{Given that,}~ (x_1,y_1) = (-2,4)~ \text{and}~ \text{slope,}~ m = -\dfrac 32\\ \\\text{Equation of line,}~\\\\~~~~~~~y -y_1 = m(x-x_1)\\\\\implies y -4 =-\dfrac 32(x+2)\\\\\implies y-4 =-\dfrac 32x - 3\\\\\implies y = -\dfrac 32x -3 +4\\\\\implies y = -\dfrac 32x +1[/tex]

The current equation of the perpendicular line;

 ⇒ is the slope-intercept form: [tex]y= mx + b[/tex]

Now for the point-slope form, we need a point on the line and the slope of the line:

⇒ we have

Since this is the point-slope form: [tex](y-y_1)=m(x-x_1)[/tex]

 ⇒ where the (x₁,y₁) is the point on the line and m is the slope

    [tex]= > Equation: (y-4)=-\frac{3}{2}(x+2)[/tex]

To convert the equation to slope-intercept form:

  ⇒ must isolate 'y' to one side and everything to the other side

      [tex]y= -\frac{3}{2}(x+2)+4\\ y=-\frac{3}{2} x-3+4\\y=-\frac{3}{2}x+1[/tex]

Answer: [tex]y = -\frac{3}{2}x+1[/tex]

Hope that helps!

El volumen es una cantidad escalar tridimensional. El volumen de la pecera con un diámetro de 50 cm y una altura de 30 cm es 58,904.863 cm³.

Un volumen es un número escalar que expresa la cantidad de espacio tridimensional encerrado por una superficie cerrada.

El volumen de la pecera con un diámetro de 50 cm y una altura de 30 cm será,

Volumen del cilindro = (π/4)×diámetro ²×altura

                                = (π/4)×(50cm)²×30cm

                                = 58,904.863cm³

Por lo tanto, el volumen de la pecera con un diámetro de 50 cm y una altura de 30 cm es 58,904.863 cm³.

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Answer: number 1 and number 2 and 4 and 5

Step-by-step explanation:

Answer:

0.125 times larger

Step-by-step explanation:

given the scale factor of 2 solids is k , then the volume  factor = k³

here k = 0.5 , so

volume factor = (0.5)³ = 0.125

Answer:

D.

Step-by-step explanation:

0.45*5=2.25

0.25*9=2.25

2.25*2=4.50

Hope this helps!

If not, I am sorry.

The boat suspended by wire ropes AB and AD, AC is 4 units high.

An equation is an expression that shows the relationship between two or more variables and numbers.

The gradient of AB is 0.8, hence:

AC / BC = 0.8

Since BC = 5, therefore:

AC / 5 = 0.8

AC = 4

The boat suspended by wire ropes AB and AD, AC is 4 units high.

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Answer:

16 feet

Step-by-step explanation:

her first try is 2 and you multiply by 2 every time so her first would be 2 which we would multiply to get 4 which we would multiply again to get 8 which we would multiply AGAIN to get the final answer of 16

[1] t ≥ 45

   Since Isabel exercises more ("no less") than 45 minutes a day, we will use greater than or equal to.

-> because being equal is not less, hence still "no less"

[2] f ≥ 45

   Because the vehicle's fuel is "at least" that means it can also be equal too, hence the user of greater than or equal to.

Answer:

P(5 ≤ X ≤ 8)  = a  rectangle  with a width of 3  and height of .15   = 3(.15)  = .45

P( 4 ≤ X ≤ 5)  =  a triangle  with a base of 1  and a height of (0.15 -0.05) = .10

So....this area  =   (1/2)(1)(.10)  = .05

And  another rectangle with a width of 1 and height of .05  = (1) (.05) = .05

So

Adding these areas

P( 4 ≤ X ≤ 8 )  =  .45 + .05 + .05   =  .55

Step-by-step explanation:

Hoped this helped!

Answer: 36

Step-by-step explanation:

[tex]g(2)=2^{2}=4\\g(3)=3^{2}=9\\g(2) \cdot g(3)=4 \cdot 9=\boxed{36}[/tex]

Using it's concept, it is found that the range of the function [tex]f(x) = 9^x[/tex] is given by:

all real numbers greater than 0.

It is the set that contains all possible output values for the function.

In this problem, the function is:

[tex]f(x) = 9^x[/tex]

For exponential functions without vertical shifts, as is the case in this problem, the range is given by:

all real numbers greater than 0.

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Answer:

C. x = ±4

Explanation:

Given two equation's:

Solve them simultaneously:

 y       =       y

3x² + 15 = 5x² - 17

5x² - 3x² = 15 + 17

2x² = 32

x² = 16

x = ±√16

x = ±4

Answer:

56

Step-by-step explanation:because 12345

Answer:

14

29  as a fraction

Step-by-step explanation:

Based on the given conditions, formulate:

14=19+14+6）

2 Calculate

14

9+14+6

Calculate

14

23+6

Calculate the sum or difference

14

29

X

Calculate the sum or difference

14

29

Alternative forms

~ 0.482759, ~ 48.275862%,

4.827586 × 10

Hope it help :)

Answer:

  B.  180° about the origin

Step-by-step explanation:

You are given a figure and its image, and asked to determine the angle of rotation. All of the answer choices indicate the center of rotation is the origin.

__

You have two clues that the rotation is 180° about the origin:

__

To find the angle of rotation, you can look at the angle formed by a point, the center of rotation, and the image of the original point. Here, the angle UOU' is a straight angle, so the angle of rotation about O is 180°--the measure of that angle. (It can be convenient to use points close to the center of rotation, but any corresponding points on preimage and image will do.)