An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation h(x) = -x^2+10x+7.5 where x is the number of feet away from the sprinkler head (along the ground) the spray is.

The irrigation system is positioned____ feet above the ground to start.
The spray reaches a maximum height of ____feet at a horizontal distance of feet away from the sprinkler head.
The spray reaches all the way to the ground at about_____ feet away​

Answer:

Both give remainder 0 for the polynomial

Step-by-step explanation:

p(-2) = (-2)² - (-2) - 6

= 6 - 6 = 0

p(3) = (3)² - 3 - 6

= 9 - 9 = 0

Answer:

The volume is maximum when the height is 3 cm.

Step-by-step explanation:

let the side of the removed potion is x.

length of the box = 18 - 2 x

width of the box = 18 - 2 x

height = x

Volume of box

V = Length x width x height

[tex]V = (18 - 2 x)^2 \times x\\\\V = x(324 + 4x^2 - 72 x)\\\\V = 4 x^3 - 72 x^2 + 324 x \\\\\frac{dV}{dx} = 12 x^2 - 144 x + 324 \\\\So,\\\\ \frac{dV}{dx} =0\\\\x^2 - 12 x + 27 = 0 \\\\x^2 -9 x - 3 x + 27 =0\\\\x (x - 9) - 3 (x -9) = 0\\\\x = 3, 9[/tex]

Now

[tex]\frac{d^2V}{dx^2}=24 x - 144 \\\\Put x = 3 \\\\\frac{d^2V}{dx^2}=24\times 3 - 144 = - 72\\\\Put x = 9\\\\\frac{d^2V}{dx^2}=24\times 9 - 144 = 72\\[/tex]

So, the volume is maximum when x = 3 .

Answer:

-2x³ - 14x² + 7x - 4

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

(3x³ - 2x² + 4x - 8) - (5x³ + 12x² - 3x - 4)

Step 2: Simplify

Answer:

Y = 2/3X + 4/3

Step-by-step explanation:

(1,2) (4,4)

M = 2/3

Y = 2/3X + b

4 = 8/3 + b

12 = 8 + 3b

4 = 3b

B = 4/3

Y = 2/3X + 4/3

Answer:

1 ans A second phi okay yed

Answer:

this would look like

0.5x+x=165

1.5x=165

x=110

Hope This Helps!!!

Answer:

£2120.27

Step-by-step explanation:

A = P (1 + r100)

A = 2000 (1+ 0.03/365)^365(2)

A = 2000 ( 1.00008)^730

A = 2000 (1.060)

A = £2120.27

Answer:

Values of x

Step-by-step explanation:

The domain of a function is the set of all possible inputs for the function while the co-domain is the set of all possible outputs of the function.

In other words, domain is the set of x-values that you can put into any given equation while co-domain is the sex of f(x)-values that you get from substituting the values of x.

Hope it's clear

Answer:

0.15866

Step-by-step explanation:

6-7/1

=-1

p(x>-1)=1-p(x<1)

=0.15866

Answer:

840 mm

Step-by-step explanation:

multiply by 10

Answer:

840 millimetres

Step-by-step explanation:

To convert cm to mm, multiply the value in cm by 10

84cm x 10 = 840 mm

Hope this helps! <3

Answer:

Outlier therefore could only be values below  - 12.75

or could only be values above + 121.125

Step-by-step explanation:

0, 4, 6, 14, 17

inner quartile range of 0 - 17 is 1/2 of 17 subtracted from the higher number = 17 - 1/2 of 8.5 =  8.5 - 4.25 = 4.25 - 4.25 x 3

= 4.25 to 12.75 for inner quartile

inner quartile range is 12.75-4.25 = 8.5

We then 1.5 x 8.5 to show the outlier

= 12.75 meaning there is no outlier if is below.

Lower quartile fences  = 4.25 - 1.5 = 2.75

or -1.5 x 8.5 (the range) =   -12.75

Upper quartile fence = 12.75 + 1.5 = 14.25 x 8.5 =   121.125  this would be an outlier if it is 12.75 higher than 121.125 or 12.75 lower than 5.50.

Outlier therefore could only be values below  - 12.75

or could only be values above + 121.125

An observation is considered an outlier if it exceeds a distance of 1.5 times the interquartile range (IQR) below the lower quartile or above the upper quartile. The values of the lower quartile - 1.5 x IQR and upper quartile + 1.5 x IQR are known as the inner fences.

An observation is an outlier if it falls more than above the upper quartile or more than below the lower quartile. The minimum value is so there are no outliers in the low end of the distribution. The maximum value is so there are no outliers in the high end of the distribution.

Answer

$0.1346

Explanation:

Find probability of each card and the value of each card and then add them together.

Probability of getting a heart = 13/52

Price of one heart =$0.30

Pay for one heart = 13/52×0.30=$0.075

Probability of getting a queen =4/52

Price of one queen =$0.55

Pay for one queen =4/52×$0.55=$0.0423

Probability of getting a queen of hearts =1/52

Price of one queen =$0.90

Pay for one queen =1/52×$0.90=$0.0173

Therefore the pay for one draw= $0.075+$0.0423+$0.0173=$0.1346

Answer:

Atleast 4 women

Step-by-step explanation:

Ratio of

Women to men = 2 : 7

Number of women needed to maintain the ratio if there are 14 men on the roster :

The minimum number of women required :

(2 : 7) * number of men in roster

(2 / 7) * 14

2 * 2 = 4 women

Atleast 4 women are required to main the ratio

Answer:

1) a)  accepting the new drug is better based on its effectiveness when in reality the drug ain't better than the drug in current use because of its side effects

b) Accepting and using the current drug in use when it is not as effective as the new drug

c) Type 1 error

2) a) rejecting the vitamin supplement based on not knowing the harmful side effects

b) Accepting the Vitamin supplement based on just health benefits it portrays without comparison with other supplement.

c) Type II error

3) Increase the significance level  ( A )

Step-by-step explanation:

1)

a) To make a type 1 error in this situation is accepting the new drug is better and prescribing it to the millions of people based only on its effectiveness when in reality the drug ain't better than the drug in current use because of its side effects

b) A type II error in context is :Accepting and using the current drug in use when it is not as effective as the new drug

c)  Type I error

2)

a) Type 1 error is rejecting the vitamin supplement based on not knowing the harmful side effects

b) Accepting the Vitamin supplement based on just health benefits it portrays without comparison with other supplement.

c) Type II error

3) If committing a type 1 error is much worse

Increase the significance level

Answer:

2n+2

_____

9 2n

Answer:

= ∑ 6*n*x^n-1

Radius of convergence = 1

Step-by-step explanation:

f(x) = 6(1-x)^-2

Maclaurin series can be expressed using the formula

f(x) =  f(0) + f '(0)x + f ''(0)/ 2!  (x)^2 + f '''(0)/3! (x)^3 + f (4)(0) 4! x4 + .

attached below is the detailed solution

Radius of convergence = 1

The Maclaurin series for f(x) = 6 / (1 - x )^2  = ∑ 6*n*x^n-1  ( boundary ; ∞ and n = 1 )

Answer:

the total square footage = 194

1.88 x 194 = 364.72

Step-by-step explanation:

Area for triangle ends.

A = [tex]\frac{2.5 (8)}{2}[/tex]   (Times two, because there are two ends.)

Base of prism = 8 x 10 = 80

Sides of prism = 2(10 x 4.7 ) = 94  (What's the 2?  There's two of them)

Add all together : 10 + 10 + 80 + 94 = 194

1.88 x 194 = 364.72

Answer:

[tex]\frac{29}{35}[/tex] ft (29/35 ft)

Step-by-step explanation:

Perimeter: [tex]2w+2l[/tex]

[tex]2(\frac{1}{5})+2(\frac{3}{14})=\frac{2}{5} +\frac{6}{14}[/tex]

Since [tex]\frac{6}{14} = \frac{3}{7}[/tex], the LCD would be 35

New equation: [tex]\frac{14}{35} +\frac{15}{35} =\frac{29}{35}[/tex]

[tex]\frac{29}{35}[/tex]

Hope this helped! Please mark brainliest :)

Answer:

$2550

Step-by-step explanation:

Calculation to determine the amount of retained earnings at the beginning of Year 2

Using this formula

Beginning Retained Earnings + Revenue − Expenses − Dividends = Ending Retained Earnings

Let plug in the formula

Beginning Retained Earnings + $3,200 − $1,700 − $1,100 = $2950

Beginning Retained Earnings= $2,950-$400

Beginning Retained Earnings = $2,550

Therefore the amount of retained earnings at the beginning of Year 2 is $2550

Answer:

y = [ 4 ]

Step-by-step explanation:

5y - 10 = 10

     +10  +10

5y = 20

/5     /5

y = 4

hope this helps ! ^^

Answer:

[tex]5y-10=10[/tex]

[tex]Add ~10[/tex]

[tex]5y=10+10[/tex]

[tex]5y=20[/tex]

[tex]divide ~by ~5[/tex]

[tex]y=4[/tex]

[tex]ANSWER: y=4[/tex]

-----------------------------

HOPE IT HELPS

HAVE A GREAT DAY!!

Answer:

a=2, b=3,x=6

Step-by-step explanation:

We are given that

We have to find the value of the missing letters in the sum of numbers.

From given sum

1+a+b=x   ....(1)

b+b+b=9  .....(2)

a+a=4       ......(3)

From equation (2) we get

[tex]3b=9[/tex]

[tex]\implies b=3[/tex]

From equation (3) we get

[tex]2a=4[/tex]

[tex]a=4/2[/tex]

[tex]a=2[/tex]

Now, substitute the values in equation (1) we get

[tex]1+2+3=x[/tex]

[tex]x=6[/tex]

Therefore,

231+32+233=496

Answer:

[tex]\displaystyle y' = 20x^3 + 6x^2 + 70x + 9[/tex]

General Formulas and Concepts:

Pre-Algebra

Algebra I

Calculus

Derivatives

Derivative Notation

Derivative Property [Multiplied Constant]:                                                              [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]:                                                            [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Basic Power Rule:

Derivative Rule [Product Rule]:                                                                                [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = (x^3 + 7x - 1)(5x + 2)[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

Answer:

100

Step-by-step explanation:

I assume you mean [tex]\frac{5}{12}[/tex] of the students in Year 9.

Basically, first you need to work out 1/12 of the students, which is just 240 divided by 12, equals 20.

So, we know 1/12 of 240 is 20, therefore, in order to work out 5/12, we must do 20 x 5, which is 100.

Answer:

(4, 2 )

Step-by-step explanation:

Given the 2 equations

3x + y = 14 → (1)

7x - 4y = 20 → (2)

Rearrange (1) making y the subject by subtracting 3x from both sides

y = 14 - 3x → (3)

Substitute y = 14 - 3x into (2)

7x - 4(14 - 3x) = 20 ← distribute parenthesis and simplify left side

7x - 56 + 12x = 20

19x - 56 = 20 ( add 56 to both sides )

19x = 76 ( divide both sides by 19 )

x = 4

Substitute x = 4 into (3) for corresponding value of y

y = 14 - 3(4) = 14 - 12 = 2

solution is (4, 2 )

Answer:

[tex]3x + y = 14 \\ y = 14 - 3x \\ substitute \: y \: into \: equation \: 2\\ 7x - 4(14 - 3x) = 20 \\ 7x - 56 + 12x = 20 \\ 19x = 76 \\ x = \frac{76}{19} =4 \\ y = 14 - 3( 4 ) = 2 \\ [/tex]

Answer:

Given Two equations :-

[tex]3x {}^{2} - 2 {y}^{2} = 57 .\: .\: .\: . \:(i) \\ - 2 {x}^{2} + 3 {y}^{2} = -23.\: .\: .\: . \:(ii)[/tex]

[tex](3x {}^{2} - 2 {y}^{2} = 57 ) \times 2 .\: .\: .\: . \:(i) \\ ( - 2 {x}^{2} + 3{y}^{2} = - 23) \times 3.\: .\: .\: . \:(ii)[/tex]

[tex]6x {}^{2} - 4 {y}^{2} =114 .\: .\: .\: . \:(i) \\ - 6 {x}^{2} + 9 {y}^{2} = - 69.\: .\: .\: . \:(ii)[/tex]

[tex]0 + 5 {y}^{2} = 45 \\ 5y {}^{2} = 45 [/tex]

[tex] {y}^{2} = 9[/tex]

[tex]y = + - 3[/tex]

3x²- 2×9 = 57

3x² - 18 = 57

3x² = 57 + 18

3x²= 75

x² = 25

x = ± 5

Answer:

The slope of diagonal AB is 0 and its equation is [tex]y=-2[/tex].

Step-by-step explanation:

Horizontal lines have zero slope. Since diagonal AB represents a horizontal line (same y-value regardless of x-value), the slope of diagonal AB is 0.

Horizontal lines can be expressed as [tex]y=n[/tex] where [tex]n[/tex] is some real number. In this case, diagonal AB sits on a line with only y-values of -2, and therefore the equation of the line the diagonal is on is [tex]\boxed{y=-2}[/tex].

Answer: A

Step-by-step explanation:

The main parent functions are x, and x raised to the power of something (examples: [tex]x^2, x^3, x^4[/tex], etc)

Answer:

The correct answer is:

(a) 0.0884

(b) 0.0190

(c) 0.9596

(d) 0.2921

Step-by-step explanation:

(a)

= [tex]P(1.26<Z<2.16)[/tex]

= [tex]P(Z<2.16)-P(Z<1.26)[/tex]

= [tex]0.9846-0.8962[/tex]

= [tex]0.0884[/tex]

(b)

= [tex]P(2.05<Z<3.05)[/tex]

= [tex]P(Z<3.05)-P(Z<2.05)[/tex]

= [tex]0.9989-0.9798[/tex]

= [tex]0.0190[/tex]

(c)

= [tex]P(-2.05<Z<2.05)[/tex]

= [tex]P(Z<2.05)-P(Z<-2.05)[/tex]

= [tex]0.9798-0.0202[/tex]

= [tex]0.9596[/tex]

(d)

= [tex]P(Z>0.55)[/tex]

= [tex]1-P(Z<0.55)[/tex]

= [tex]1-0.7088[/tex]

= [tex]0.2912[/tex]