in a large population, 63 % of the people have been vaccinated. if 4 people are randomly selected, what is the probability that at least one of them has been vaccinated? give your answer as a decimal (to at least 3 places) or fraction.

The quadratic equation to model the graph is y = x² - 6 · x + 14.

The picture presents us the graph of a parabola, whose algebraic expression is a quadratic equation. In accordance with fundamental theorem of algebra, a quadratic equation can be derived by knowing three distinct points on Cartesian plane.

If we know that (x, y) = (0, 14), (x, y) = (3, 5) and (x, y) = (6, 14), then the coefficients of the quadratic equation in standard form:

14 = c                                       (1)

5 = 9 · a + 3 · b + c                  (2)

14 = 36 · a + 6 · b + c              (3)

The solution of the system of linear equations is (a, b, c) = (1, - 6, 14). Hence, the quadratic equation to model the graph is y = x² - 6 · x + 14.

To learn more on quadratic equations: https://brainly.com/question/1863222

#SPJ1

Answer:

k = -4

Step-by-step explanation:

8 = 2k - 8 - 6k

Collect like terms

8 = -4k - 8

Add 4k to both sides (nice to have variable on left, constants on right)

8 + 4k = -8

Subtract 8 from both sides

4k = -16

Divide both sides by 4

k = -4

The solution to the expansion of each polynomial is;

1. (x + 9)(x² - 9x + 81) = x³ + 729

2. (y² - 7)(y⁴ - 7y² + 49) = y⁶ − 14y⁴ + 98y² - 343

3. (x² - 5)(x⁴ + 5x² + 25) = x⁶ - 125

4. (8x - 9y)(64x² + 72xy + 81y²) = 512x³ - 729y³

5. (10m - 11) (100m² + 110m + 121) = ​1000m³ - 1331

1) We want to expand the polynomial;

(x + 9)(x² - 9x + 81)

= x³ + 729

2) We want to expand the polynomial;

(y² - 7)(y⁴ - 7y² + 49)

Multiplying out gives;

y⁶ −7y⁴ + 49y² −7y⁴ + 49y² - 343

Combining like terms gives;

y⁶ − 14y⁴ + 98y² - 343

3) We want to expand the polynomial;

(x² - 5)(x⁴ + 5x² + 25)

Multiplying out gives;

x⁶ - 125

4) We want to expand the polynomial;

(8x - 9y)(64x² + 72xy + 81y²)

Multiplying out gives;

512x³ - 729y³

5) We want to expand the polynomial;

(10m - 11)(100m² + 110m + 121)

Multiplying out gives;

1000m³ - 1331

Read more about Expanding Polynomials at; https://brainly.com/question/24492376

#SPJ1

a. Total amount of fencing needed = perimeter of the rectangular area excluding one length of the side close to the river = F = l + 2w

b. F = 44 ft

c. The width (w) = 45 ft.

Perimeter of rectangle = 2(length + width)

a. Total amount of fencing needed = perimeter of the rectangular area excluding one length of the side close to the river = l + 2w

F = l + 2w

b. w = 12 ft

l = 20 ft

Amount of fencing needed, F = l + 2w = 20 + 2(12)

F = 44 ft

c. F = 120 ft

l = 30 ft

Substitute F = 120 and l = 30 into F = l + 2w to solve for w

120 = 30 + 2w

120 - 30 = 2w

90 = 2w

90/2 = w

w = 45

The width (w) = 45 ft.

Learn more about the perimeter of rectangle on:

https://brainly.com/question/24571594

#SPJ1

The slope of the line that passes through the points (-9, 0) and (−17,4) is -2

The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b). For instance, the slope and y-intercept of the equation y = 3x - 7 are 3 and 0, respectively.

The formula to calculate slope is -

m = x2 - x1 / y2 - y1

(-9, 0) and (−17,4)

m = -17 + 9 / 4 - 0

m = -8/4

m = -2

To learn more about the slope of the equation from give link

https://brainly.com/question/3493733

#SPJ9

[tex]\displaystyle\\Answer: \frac{400}{93}\approx4.3[/tex]

Step-by-step explanation:

[tex]\displaystyle\\4:0.93=\\\\\frac{4}{0.93 }=\\\\\frac{4}{\frac{93}{100} } \\\\\frac{4*100}{93} \\\\\frac{400}{93} \approx\\\\4.3[/tex]

Answer: −8n+3+n+11

Add the terms

−7n+3+11

Solution

−7n+14

Step-by-step explanation: hope this helps

The greatest possible value of A + B is 600000.

The smallest possible value of A + B is 600000.

The greatest possible value of A - B is 0.

It should be noted that from the information, A and B are integers.

A = 300,000 to the nearest 100,000

B = 300,000 to the nearest 10,000

Therefore, the greatest possible value of A + B will be:

= 300,000 + 300,000

= 600000.

The smallest possible value of A + B is also, 600000.

The greatest possible value of A - B will be:

= 300,000 - 300,000

= 0.

Learn more about numbers on:

brainly.com/question/24644930

#SPJ1

Answer:

g(-6) = -6

g(0) = 5

g(7) = 8

h(-6) = 10

h(0) = -1

h(7) = -4

Step-by-step explanation:

g(x) = (1/3) f(x)

g(-6) = (1/3)(-18) = -6

g(0) = (1/3)(15) = 5

g(7) = (1/3) (24) = 8

h(x) = -g (x) + 4

h(-6) = -(-6) + 4 = 10

h(0) = -(5) + 4 = -1

h(7) = -(8) + 4 = -4

I hope this helps!

Answer:

$45

Step-by-step explanation:

100% = $75

100% - 40% = 60% (discounted price)

60% = 0.6

0.6 x 75 = 45

60% = $45 (discounted price)

According to the given statement the teenagers went to the zoo = 300

First order equations include linear equations. In the coordinate system, the linear equations have been defined for lines. A linear equation throughout one variable is one in which there is a homogeneous variable having degree 1 (i.e., only one variable). many  variables have present in a linear equation.

6a+4c+5t = 5300......................(equation)

a+c+t = 1200

3c-8t = 0

So,

Putting the value a= 1/6

6a+4c+5t = 5300

0.333c+0.167t = 316.667

3c-8t = 0

solving for the value of t:

6a+4c+5t = 5300

3c-8t = 0

1.056t = 316.667

So,

t = 316.66666667/1.05555556

= 300

According to the given statement the teenagers went to the zoo = 300.

To know more about Linear equations visit:

https://brainly.com/question/11897796

#SPJ4

Answer: -6x+18

Step-by-step explanation:

-3(2x-6)=

-3*2x-(-3*6)=     ==> During distribution

-6x-(-18)=-6x+18    ==> After distribution property

Answer: she could buy 10 cookies.

Step-by-step explanation:

In order to figure out how many cookies she can buy just do 20÷2.

Answer:

-1

Step-by-step explanation:

Tn = a+(n-1)d (general formula)

Tn = 8-n (given formula)

T9 =8-9

T9=-1

the area covered by the light of the lighthouse is given by: A = πx²

All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

Area of a circle having r as radius = πr²

Given: The revolving light beam that extends to the pier.

Let the distance to the pier x.

Typically, the rotating beam rotates 360 degrees.

Therefore, Its motion is circular.

The mathematical formula for the area that the light covers is: A = πx²

Hence, the area covered by the light of the lighthouse is given by: A = πx²

To learn more about circles, refer to the link: https://brainly.com/question/24375372

#SPJ4

Answer:

The answer would be six batches of cookies.

Answer:

6 batches

Step-by-step explanation:

so 28 people including you

24 cookies per batch

5 cookies each

24 cookies in each batch, if you round that up it would be 30 and 30 x 5 = 150, so instead of rounding the amount of cookies, add 1 more to the amount you multiply 24 by

then it would be 24 x 6 = 144

now divide that by 28

144/28= 5 1/6

it would take 6 (7 if everyone gets whole numbers of cookies because It would be a fraction if not 7) batches to make sure everyone gets cookies

double check:

24 times 6 =  cookies

144/28= 5 1/6

Answer: 3x+25

Step-by-step explanation: Fraction 3/1 is the same as 3. Using PEMDAS we multiply the numbers in the parenthesis 3x+3x9-2, 3x+27-2, Answer=3x+25

Using the weighted mean, the coordinates of P are given as follows:

The weighted mean is given by the sum of all elements in a data-set multiplied by it's weight, divided by the sum of the weights.

In this problem, we have these following points:

Applying the weighted mean, the coordinates of P are given as follows:

In which xA and yA are the coordinates x and y of point A, and xB and yB are the coordinates x and y of point B.

More can be learned about the weighted mean at https://brainly.com/question/24398353

#SPJ1

Answer:

2 1/3 :)

Step-by-step explanation:

86 and 39

Step-by-step explanation:

let A is the first letter and B is the second number

A+B=125

A-B=47

2A=172

A=86

A+B=125

86+B=125

B=125-86

B=39

Answer:

7.8

-7.9

-17.40

1. 5.6

-2. 17.18

-5. 7.12

.8 15.22

Step-by-step explanation:

Answer:

∉

Step-by-step explanation:

10 is not a member of the set {6, 8, 13, 14} and ∉ is used to represent "not a member of"

Answer:

B ( if you talking about Mathematics enhancement )

Step-by-step explanation:

First one make the statement true but ( 6, 8, 13 ,14 ) didn't related to 10 According to a pattern

Answer:

see explanation

Step-by-step explanation:

f(x) × g(x)

= 3x(4x - 1) ← distribute parenthesis by 3x

= 12x² - 3x

when x =  1 , then

= 12(1)² - 3(1) = 12(1) - 3 = 12 - 3 = 9

The degree of the polynomial formed is 6.

The degree of a polynomial is the highest degree of the variables present with non-zero coefficients.

For example the polynomial has three 7x³y²+9xy+4 terms. The first term has a degree of 5 (the sum of the powers 2 and 3), the second term has a degree of 1, and the last term has a degree of 0. Therefore, the polynomial has a degree of 5, which is the highest degree of any term.

Now the given functions are:

[tex]f(x)=x^3[/tex] ,g(x)=3x²-1 and h(x)=2x

Now we have to find (f ° g° h)(x). Let us first find (g°h)(x).

(g°h)(x) is equal to g[h(x)]

=g[2x+5]

=3(2x+5)²-1

=3(4x²+20x+25)-1

=12x²+60x+74

Now we find (f ° g° h)(x)

(f ° g° h)(x)=f[g(2x+5)]

f[g(2x+5)]=f(12x²+60x+74)

f(12x²+60x+74)=(12x²+60x+74)³

Now we have to simplify the expression:

(12x²+60x+74)³

=[tex]1728x^6+25920x^5+161568x^4+535680x^3+996336x^2+985680x+405224[/tex]

The largest degree of the variable x in the polynomial is 6.

hence the degree of [f o go h](x) is 6.

To learn more about degree of a function or polynomial visit:

https://brainly.com/question/2284746

#SPJ9

Step-by-step explanation:

5/8 = y/3

(5/8) times 3 = 15/8

y=15/8

or

y = 1 and 7 over 8

or y = 1.875

Answer: 1:8

Step-by-step explanation:

13 tables

104 chairs

Ratio: 13:104

divide both sides by 13

13:104 = 1:8

the time taken by Rita to travel 1875 miles is 4.5 days, by unitary method.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Given:

To find: Time taken to travel 1875 miles.

Finding:

By unitary method,

Time taken to travel 1250 miles = 3 days

Time taken to travel 1 mile = [tex]\frac{3}{1250}[/tex] days

Time taken to travel 1875 miles = [tex]\frac{3}{1250}(1875) = 4.5[/tex] days

Hence, the time taken by Rita to travel 1875 miles is 4.5 days, by unitary method.

To learn more about unitary method, refer to the link: https://brainly.com/question/24587372

#SPJ4

Answer:

Step-by-step explanation:

Answer:

0.153 or 15.3%

Step-by-step explanation:

Subtract save percentage last season from save percentage this season:

0.738 - 0.585 = 0.153

Convert the decimal answer to a percent

0.153 x 100% = 15.3%