Standard deviation of two sets:

The rocket reaches its maximum height at 1.25 second(s) after launch

The maximum height reached by the object is 32 feet.

The function is given as

h(t) = -16t² + 40t + 7

Differentiate the above function

So, we have the following representation

h'(t) = -32t + 40

Set to 0

-32t + 40 = 0

So, we have

32t = 40

Divide by 32

t = 1.25

Hence, the time is 1.25 seconds

In (a), we have

t = 1.25

Substitute t = 1.25 in h(t) = -16t² + 40t + 7

h(1.25) = -16(1.25)² + 40(1.25) + 7

Evaluate

h(1.25) = 32

Hence, the maximum height is 32 feet

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The range for this situation is {125, 150, ... 250}.

The range of a function includes all the possible output (y) values when the x value is substituted with a number.

The daily cost of hiring a lawn service = y

The number of hours mowing = x hours

Fixed cost per day = $100

Variable cost per hour = $25

Maximum hours of work per day = 6 hours

Minimum hour of work per day = 1 hour

y = 100 + 25x

y = 100 + 25(6)

y = 250

y = $250

For 5 hours, y = $225 (100 + 25(5)

For 4 hours, y = $200 (100 + 25(4)

For 3 hours, y = $175 (100 + 25(3)

For 2 hours, y = $150 (100 + 25(2)

For 1 hour, y = $125 (100 + 25(1)

Thus, the daily cost of hiring a lawn service ranges from  {125, 150, ... 250}.

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Answer:

[tex](3,0)[/tex]

Step-by-step explanation:

The ordered pair that satisfies both inequalities will lie in the region that is shaded by both inequalities.

x=3.5 and y=2.5

First, combine the equations in such a way that you can eliminate a variable. Then solve for the variable. Insert this value into one of the original equations and solve for the unknown variable.

See details:

Answer:

you cannot factor it anymore

therefore, there is no solution

Answer:

inequality form: -4≤x<5

Answer:

x = - 4

Step-by-step explanation:

6x + 2 = 2x - 14 ( subtract 2x from both sides )

4x + 2 = - 14 ( subtract 2 from both sides )

4x = - 16 ( divide both sides by 4 )

x = - 4

We move all terms to the left:

We get rid of the parentheses.

We add all the numbers and all the variables.

We move all terms containing x to the left hand side, all other terms to the right hand side

Answer:

38°

128°

Step-by-step explanation:

Complementary angles have measures that add to 90°.

Supplementary angles have measures that add to 180°.

comp: 90 - 52 = 38

sup: 180 - 52 = 128

Answer:

y = 7 + 2√2, y = 7 - 2√2

Step-by-step explanation:

We need to solve for y to find the solutions of the quadratic equation:

3(y-7)^2 = 24

(y-7)^2 = 8

y-7 = ±√8 = ±√(4*2) = ±2√2

y = 7 + 2√2

y = 7 - 2√2

2√2 is the simplified radical form because 4 is the highest factor of 8 that is a perfect square.

The roots of the radical expression is given as 8, not defined, 10

What is radical expression?

a radical expression is defined as any expression containing a radical (√) symbol. Many people mistakenly call this a 'square root' symbol, and many times it is used to determine the square root of a number.

Given,

1. √64

we know 8 multiplied by 8 gives 64

√64 =8

2. ⁴√ -1

not defined

3. ³√1000

We know 10 multiplied by 10 =100

and 100 multiplied by 10 =1000

root of ³√1000 = 10

The radical form or number is

1. (⁴√ 1)⁷=1

2. ³ √-64=8i

3. (2⁹)¹/³=8

4. (11²)¹/² =11

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Answer:

n= 9,10,11,12,13

Step-by-step explanation:

Change the denominator to 16 so it can be common with n

1/2

1x8/2x8

8/16

3/4

3x4/4x4

14/16

Now we look at the numerators and see the new ones are 8 and 14 so all the numbers in between 8 and 14 are 9,10,11, 12, and 13

Hopes this helps please mark brainliest

The possible values of n are 9, 10, and 11.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

1/2 < n/16 < 3/4

Now,

Take 1/2 < n/16

1/2 < n/16

16/2 < n

8 < n ____(1)

Take n/16 < 3/4

n/16 < 3/4

n < 3/4 x 16

n < 12 ______(2)

From (1) and (2) we get,

8 < n < 12

This means,

The possible values of n are 9, 10, and 11.

Thus,

n values are 9, 10, and 11.

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Answer:

3.75%

Step-by-step explanation:

800+3.75%=830

The inequality that describes the relationship between the maximum amount Herman wants to spend and the total golf costs for the season is 450 + 18x ≤ 1000.

Herman can play for a maximum of 30 rounds, which will cost $990 in total.

Herman decides to take up golf. His golf club membership will cost $450 for the season, and he will be charged $18 for each round of golf that he plays. Herman has decided not to spend more than $1000 on golf for the season.

Let the number of rounds of golf Herman plays be represented by the variable "x". We can write the inequality as given below.

450 + 18x ≤ 1000

We can further simplify and solve this inequality.

18x ≤ 1000 - 450

18x ≤ 550

x ≤ 30.56

Hence, the maximum number of rounds of golf is 30. The total cost is calculated below.

C = $450 + $18*30

C = $450 + $540

C = $990

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Inverse of the given function y= 4x² +12x + 9 is given by x=(1/2) (√y -3).

Restricted domain is required to make function one -one so that its inverse exist.

Domain of the inverse function is y ≥ 0.

As given in the question,

Given function is equal to :

y = 4x² +12x + 9

Inverse of the function exist if and only if it is one to one.

x₁ ≠ x₂

⇒2x₁ +3  ≠ 2x₂ + 3

⇒f(x₁) ≠ f(x₂)

It is one -one. Inverse exist.

y = (2x +3)²

⇒ 2x + 3 = √y

⇒x = (1/2) ( √y -3)

Restricted domain of the inverse of the function is y ≥0.

Therefore, Inverse of the given function y = 4x² +12x + 9 is given by

x = (1/2) (√y -3)

Restricted domain is required to make function one -one so that its inverse exist.

Domain of the inverse function is y ≥ 0.

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Answer: B

Step-by-step explanation:

B

After factoring the given expression [tex]12y^2-17y-5[/tex], we get (4y+1)(3y-5).

The breakdown of a thing into a product of other objects, or factors, which when multiplied together provide the original, is known as factorization or factoring in mathematics. Factorization can be done using middle term splitting method in which the middle term of the expression is broken down to factor.

Factoring the given expression by splitting the middle term -17y to -3y and 20y as product of 12 and 5 is 60 and also the product of 3 and 20 is 60.

[tex]12y^2-17y-5=12y^2+3y-20y-5\\=3y(4y+1)-5(4y+1)\\[/tex]

Now, factoring out [tex](4y+1)[/tex],

[tex]=(4y+1)(3y-5)[/tex]

Therefore, After factoring the given expression, we get [tex](4y+1)(3y-5)[/tex].

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Answer:

[tex]-\frac{3}{\sqrt{7} } .[/tex]

Step-by-step explanation:

1) tanΘ=sinΘ/cosΘ;

[tex]2) \ cos \theta=^+_-\sqrt{1-sin^2 \theta}; \ = > \ cos \theta=^+_-\frac{\sqrt{7}}{4};[/tex]

3) if according to the initial condition Θ is in II-quadrant, then the cosΘ<0!

[tex]cos \theta=-\frac{\sqrt{7}}{4} ;[/tex]

4) finally,

[tex]tan \theta=\frac{sin \theta}{cos \theta}=-\frac{3}{\sqrt{7}}.[/tex]

Answer:

I c Phil and the way u are u 3AM u are u and tahsin will u be happy so we will be crazy for a different time to kick in hamtramck tomorrow so we will have

This statement is false about metric system.

What is metric system?

matric systemare a group of two or more Lewis structure that represents a single polyatomic species.

Resonance is the ability of system to moves it's pi electron to the system .

Resonance structure are more significant beacuse they provide a much more realistic views of the shape of a molecule.

Each individua matric system is average into a resonance which is both true shape of the molecule .

Thus this statement is false about memetrictric system.

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Answer:

Step-by-step explanation:

The volume of premium antifreeze to be used is 60 gallons.

The volume of water to be used is 120 gallons

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Let the volume of 60% pure antifreeze be used to make 20% pure antifreeze.

= x gallons  

The volume of 20% pure antifreeze = 180 gallons

For 60% pure antifreeze:

C₁ = 60% , V₁ = x gallons

For 20% pure antifreeze :

C₂ = 20% , V₂ = 180  gallons

Applying,

C₁V₁ = C₂V₂

60 × x = 20 × 180

x = 60 gallons

The volume of 60% pure antifreeze used = 60 gallons.

The volume of water to be used.

= 180 - 60 gallons

= 120 gallons

Thus,

The volume of premium antifreeze to be used is 60 gallons.

The volume of water to be used is 120 gallons

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The sides of ∠1 are FG and FE, the vertex of ∠HFG is F and the names of ∠EFH are ∠F and ∠2

The figure represents the given parameter

From the question, we have

Angle = ∠1

The sides of ∠1 are the sides that extend from the vertex of angle 1

These sides are FG and FE

From the question, we have

Angle = ∠HFG

In the above representation, the angle can be expressed as

Angle = ∠F

This represents the vertex

So, the vertex is F

From the question, we have

Angle = ∠EFH

In the above representation, the angle can be expressed as

Angle = ∠F

Also, we have

Angle = ∠2

So, the names are ∠F and ∠2

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In a case whereby Henry incorrectly said the rate 1/4 hour/ 1/12 acre can be written as the unit rate 1/48 hour per acre the correct unit rate is 3hours per acre, he made the mistake by multiplying directly.

Rate  can be described as thequantity, or degree of something measured per unit of something else, the concept that will be used is the concept of rate.

The given rate will be   1/4 hour per 1/12 acre

but the per that was added implies division,

Then te rate will now be  1/4 hour ÷ 1/12 acre , then we can express as product as :1/4 hour * 12 /1 acre

Then we can simplify as : 3hours per acre

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Answer:

Step-by-step explanation:

x=-11we know thatPoints A,B,C,and D are collinear and positioned in that ordersoAD=AB+BC+CD -----> by addition segment postulatewe haveAB=2x+30AD=x=32substitute the given values and solve for xx+32 = (2x+43)Group terms that contain the same variable2x-x=32-43x=-11

He should increase each dimension by 8 feet.

What is the area of a rectangle?

The area of the rectangle is the region enclosed by the perimeter of the rectangle and is equal to the product of length and width.

i.e. Area (A) = length(l) * width (w)

Given, a deck measurement is 12 feet by 10 feet

i.e. length (l) = 12 feet

width(w) = 10 feet

Area of deck (A) = 12*10 = 120 square feet

Let 'x' be the increased dimensions then,

new length = (12 + x) feet

new width = (10+x) feet

And, area of new dimensions = 3*120 = 360 square feet

So,  [tex](12 + x)*(10+x) = 360[/tex]

or, [tex]120+12x + 10x + x^{2} =360[/tex]

or, [tex]x^{2}+ 22x+120-360=0[/tex]

or, [tex]x^{2}+ 22x-240=0[/tex]

or, [tex]x^{2}+30x-8x-240=0[/tex]

or, [tex]x(x+30)-8(x+30)=0[/tex]

or, [tex](x+30)(x-8)=0[/tex]

Either, [tex](x+30)=0[/tex]            or, [tex](x-8)=0[/tex]

             [tex]x=-30[/tex]                        [tex]x=8[/tex] (Valid)

Hence, the increased dimension is 8 feet.

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Answer:

57°

Step-by-step explanation:

Vertical angels are congruent.  They have the same measurements.

Answer:

57

Step-by-step explanation:

<PQS and <RQN are vertical angles and thus are congruent by the Vertical Angles Theorem. If m<PQS = 57, then m<RQN = 57.

You could buy 1 box, 14 bags and 4 single marbles and you could buy 2 box, 4 bags and 14 single marbles.

What is fundamental operation?

The fundamental operations are expressed in an order. Generally, the order will be in the format of “DMAS” where “D” stands for “Division”, “M” stands for “Multiplication”, “A” stands for “Addition”, “S” stands for “Subtraction”. This order is considered and sequentially performed from left to right.

Given, 1 box contains 10 bags of marbles

1 bag contains 10 marbles

Hence, 1 box contains 10 × 10 = 100 marbles.

Total numbers of marbles = 254

First condition is,

you can buy one box of marble = 1× 100 = 100

4 single marbles,

To find the number of bags, let x be the number of bag and one box contains 10 marbles,

therefore, x bags contains 10x marbles.

According to question,

100 + 4 +10x =254

104 +10x = 254

10x = 254- 104

10x = 150

x = 150÷10

= 15

Similarly in case of second condition,

2 boxes = 100×2 = 200

4 bags = 10× 4 = 40

Single marbles =?

200 + 40 +? =254

the single marble = 14

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Answer:

[tex]g(x)=|-x+1|-2[/tex]

Step-by-step explanation:

When reflecting over the [tex]y[/tex] axis, [tex]f(x) \to f(-x)[/tex].

[tex]f(x)=|x+1|-2 \implies g(x)=|-x+1|-2[/tex]

The equation would be g(x) = |-x+1| -2 reflecting the function over the y-axis.

Reflection across the y-axis is defined as reflecting a point across they = x,  the x-coordinate, and y-coordinate places, the line y = -x is the coordinates (-x, y).

So reflected across the y-axis: f(x) → f(-x),

⇒ (x,y) → (-x , y)

The function is given in the question

f(x) = |x+1| -2

We know that the reflected across the y-axis: f(x) → f(-x),

⇒ (x,y) → (-x , y)

g(x) = f(-x)

g(x) = |-x+1| -2

Thus, the equation would be g(x) = |-x+1| -2 reflect the function over the y-axis.

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Answer:

3.2

Step-by-step explanation:

8(4-a)=2a

32-8a=2a

collect like terms

32=2a+8a

32=10a

divide both sides by 10

a=3.2

Your solution is correct