156,161,190,165,172,165,184,168,184,149,169,172,172,178,215,180,165,178,178,182,164,184,187,189,190 in order.

This shows that for the function f(x), the pair of limits that would verify the existence of a vertical asymptote at x = –1 is expressed as:

[tex]\lim_{x \to -1^+} a_n = \lim_{x \to -1^-} a_n =f(c)[/tex]

For the limit of a function to be continuous at a point x = a, the left hand limit of the function must be equal to the right hand limit.

Mathematically, the expression below must be true

[tex]\lim_{x \to a^+} a_n = \lim_{x \to a^-} a_n =f(c)[/tex]

This shows that for the function f(x), the pair of limits that would verify the existence of a vertical asymptote at x = –1 is expressed as:

[tex]\lim_{x \to -1^+} a_n = \lim_{x \to -1^-} a_n =f(c)[/tex]

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Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

p(H and <3)= [tex]\frac{1}{2}[/tex]×[tex]\frac{2}{6}[/tex]

                   = [tex]\frac{1}{6}[/tex]

Answer:

[tex]y=\frac{2}{3}x+4[/tex]

Step-by-step explanation:

Calculate the slope by using rise over run to get 2/3x

The Y Intercept is 4

Answer:

y=4x-3

Step-by-step explanation:

Using y - intercept form:

y=mx+b

Slope goes up by 4 squares and to the right by 2 squares. This means the slope is 4. The y intercept is -3, thus b is -3.

Answer:

18.8%

Step-by-step explanation:

For calculating this, focus on one part of the table :

There are 32 students who do not like sandwiches, and 6 of them do not like pies. Take this a proportion :

Students who don't like sandwiches also don't like pie is the 2 nd box on 2 nd line

Probability

Option D

Answer:

a²+1/a² = 7

Step-by-step explanation:

Given, a = (3+√5)/2

We have to find the value of a² + 1/a².

1/a = 1/((3+√5)/2) = 2/(3+√5)

By taking conjugate,

2/(3+√5) = 2/(3+√5) × (3-√5)/(3-√5)

= 2(3-√5) / (3+√5)(3-√5)

By using algebraic identity,

(a - b)(a + b) = a² - b²

(3+√5)(3-√5) = (3)² - (√5)²

= 9 - 5

= 4

2(3-√5) / (3+√5)(3-√5) = 2(3-√5) / 4

So, 1/a = (3-√5)/2

Now, a² = [(3+√5)/2]²

= (3+√5)²/4

By using algebraic identity,

(a + b)² = a² + 2ab + b²

(3+√5)² = (3)² + 2(3)(√5) + (√5)²

= 9 + 6√5 + 5

= 14 + 6√5

a² = (14+6√5)/4

= 2(7+3√5)/4

a² = (7+3√5)/2

Now, 1/a² = [(3-√5)/2]²

= (3-√5)²/4

By using algebraic identity,

(a - b)² = a² - 2ab + b²

(3-√5)² = (3)² - 2(3)(√5) + (√5)²

= 9 - 6√5 + 5

= 14 - 6√5

1/a² = (14-6√5)/4

1/a² = (7-3√5)/2

a²+1/a² = (7+3√5)/2 + (7-3√5)/2

= 7/2 + 3√5/2 + 7/2 - 3√5/2

= 7/2 + 7/2

= 7

Therefore, a²+1/a² = 7

Answer:

6 and 11

Step-by-step explanation:

n1 = n + 5

ns^2 = 3 + 3nb

6^2 = 3 + 3(11)

36 = 3 + 33

11 = 6 + 5

The standard deviation of the amount paid for monthly water usage is $35.25

From the summary statistics, we have:

Standard deviation, σ = 2350

Rate = $0.015

The standard deviation of the amount is calculated using:

σ = Standard deviation * rate

This gives

σ = 2350 * $0.015

Evaluate

σ = $35.25

Hence, the standard deviation of the amount paid for monthly water usage is $35.25

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Answer:

63,000 milligrams

Step-by-step explanation:

there are 1,000 milligrams in one gram. So, 63 x 1,000 = 63,000

Answer:

I think it's 55

Step-by-step explanation:

10C3 + 5C3

The value of cos x⁰ from the information given is; g/h.

According to the task content;

The value of cos x° from the information contained in the task content is required.

From conventional Trigonometry;

It follows that tan x = sin x/cos x.

On this note, it follows that;

cos x⁰ = sin x⁰/tan x⁰.

cos x⁰ = 6/h ÷ 6/g

cos x⁰ = g/h

Ultimately, the value of Cos x⁰ by evaluation is g/h.

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Answer:

cos x° = g divided by h

Step-by-step explanation:

Answer: Max. Max has a 49% chance of getting a 1 or 2 when Josie only has a 33% chance of getting a green block

............................................................................

Answer:

fraction :4

Step-by-step explanation:

Answer:

60^2/5

Step-by-step explanation:

2^2/5 × 5^2/5

=(12×5)^2/5

=60^2/5

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textsf{12}}^ \mathsf{^ {\dfrac{2}{5}}}\ \huge\boxed{\times}\ \huge\textsf{5}^\mathsf{^ \dfrac{2}{5}}[/tex]

[tex]\huge\boxed{=}\huge\textsf{ 2.70192 }\huge\boxed{\times}\huge\textsf{ 1.903654}[/tex]

[tex]\huge\boxed{= }\huge\textsf{ 60}^\mathsf{\dfrac{2}{5}}[/tex]

[tex]\huge\boxed{\approx}\huge\textsf{ 5.143521}[/tex]

[tex]\huge\text{Therefore, the answer is: \boxed{\textsf{60}^\mathsf{^\dfrac{2}{5}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

7

Step-by-step explanation:

the range is the difference between the highest and lowest value in a data set.

13 is the highest in the distribution

6 is the lowest in the distribution

13-6=7

Give brainliest, please!

Hope this helps :)

Answer:

17

Step-by-step explanation:

f(x) = 2x+7

Let x =5

f(5) = 2*5 +7

     = 10+7

    = 17

Answer:

-1

2

4

Step-by-step explanation:

You have to replace x with each number that is given, follow the order of operations, and then you have the correct y value.

Answer:

See below ~

Step-by-step explanation:

Question 12

Question 17

Part A

Part B

Using it's concept, it is found that the average rate of change of the function over the interval [4,13] is given by:

[tex]\frac{4}{9}[/tex]

It is given by the change in the output divided by the change in input.

In this problem, we have points (4,8) and (13,12), hence the rate of change is given by:

r = (12 - 8)/(13 - 4) = 4/9.

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Answer:

B

Step-by-step explanation:

4/13

Answer:

y ≥ 1

Step-by-step explanation:

The graph of an inequality is illustrated, with a solid horizontal line passing through point (0, -1) and shading above the line.

It indicates that the line equation is:

For various x values, y=-1.

Also, because the darkened region is above the line, i.e. towards the origin, it must pass the 0-test.

As a result, the inequality is:

y≥-1

Answer:

[tex]y\geq -1[/tex]

Step-by-step explanation:

Hope this helps

The equation that represents the directrix of y² = 12x is x = -3

The parabola is given as:

y² = 12x

The general equation of a parabola is

(y-y₀)² = 4a(x-x₀)

Where the equation of the directrix is x = x₀ - a

By comparing (y-y₀)² = 4a(x-x₀) and y² = 12x, we have:

4a = 12 and x-x₀ = x

Solve for a in 4a = 12

a = 3

Solve for x₀ in x-x₀ = x

x₀ = 0

Substitute a = 3 and x₀ = 0 in x = x₀ - a

x = 0 - 3

Evaluate

x = -3

Hence, the equation that represents the directrix is x = -3

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Answer:

12 ft

Step-by-step explanation:

Tim Height: Tim Shadow
5ft              : 2ft

Tree Height: Tree Shadow
30ft              : ?ft

Using this knowledge, we can compare Tim's Height to the Tree's Height. The tree's height is 6 times more than Tim (5x6=30). We can find the shadow of the tree if we multiple tim's shadow by 6.

Therefore, 2ft x 6 = 12ft

The Tree's Shadow is 12ft.

Answer:

Step-by-step explanation:

Draw a straight line.

Then draw 2 lines of equal length from the 2 ends of the line at angles of 120 degrees  going up and apart.

Then draw the fourth line joining the ends of these 2 lines.

The 2 angles formed will equal 60 degrees.

The quadrilateral formed is a trapezoid.

Answer:

D

Step-by-step explanation:

13x16=208

208/3= 69 reapeated.

Answer:

The set of points equidistant from a given point (the center). Radius : A segment with endpoints at the center and on the circle.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is 10,000,000 because u have to do 10x10x10x10x10x10x10

So basically I did the most easiest way possible with is multiply 1 and 1 and then add the zero and I got 10 so if u add the zeros up 6 more times then we get 10 million or 10,000,000.