A survey of Mr. Thorne’s class shows that 5 out of 8 students will buy lunch today. Based on this result, how many of the 720 students in the school will buy today?

Given:

The American marriage rate R,  x years after 1960 is defined by the function

[tex]R(x)=-0.0065x^2 +0.23x + 8.47[/tex]

To find:

The year in which the marriage rate is the highest.

Solution:

We have,

[tex]R(x)=-0.0065x^2 +0.23x + 8.47[/tex]

It is a quadratic function with negative leading coefficient. So, it is a downward parabola and vertex of downward parabola is maximum.

If a quadratic function is [tex]f(x)=ax^2+bx+c[/tex], then

[tex]Vertex=\left(\dfrac{-b}{2a},f(\dfrac{-b}{2a})\right)[/tex]

In the given function,

[tex]a=-0.0065,b=0.23,c=8.47[/tex]

Now, x-coordinate of vertex is

[tex]-\dfrac{b}{2a}=-\dfrac{0.23}{2(-0.0065)}[/tex]

[tex]-\dfrac{b}{2a}=-\dfrac{0.23}{-0.013}[/tex]

[tex]-\dfrac{b}{2a}\approx 17.69[/tex]

It means the marriage rate is highest after 17 years of 1960.

[tex]1960+17=1977[/tex]

Therefore, the marriage rate is highest in year 1977.

Answer:

Exponetial Growth

Answer:

The number of liters of the 45% acid solution = 10 liters

The number of liters of the 70% acid solution is = 40 liters

Step-by-step explanation:

How many liters each of a 45% acid solution and a 70% acid solution must be used to produce 50 liters of a 65% acid solution? (Round to two decimal places if necessary.)

Let x be the number of liters of the 45% acid solution

The number of liters of the 70% acid solution is y

x + y = 50

x = 50 - y

Also

How many liters each of a 45% acid solution and a 70% acid solution must be used to produce 50 liters of a 65% acid solution?

We have:

45% × x + 70% × y = 65% × 50

0.45x + 0.70y = 0.65 × 50

0.45x + 0.70y = 32.5

We substitute x = 50 - y in the equation

0.45(50 - y) + 0.70y = 32.5

= 22.5 - 0.45y + 0.70y = 32.5

= - 0.45y + 0.70y = 32.5 - 22.5

= 0.25y = 10

Divide both sides by 0.25

= y = 10/0.25

y = 40 liters

x = 50 - y

x = 50 - 40

x = 10 liters

Hence,

The number of liters of the 45% acid solution = 10 liters

The number of liters of the 70% acid solution is = 40 liters

Answer:

4x + 2 = 30

Step-by-step explanation:

To find the perimeter of a triangle, add up the length of all three sides of the triangle.

Here, the sides of the triangle are "x+6", "x+6", and "2x-10". When you add up all three sides of the triangle, it should be equal to the perimeter, 30. So:

(x+6) + (x+6) + (2x-10) = 30

We can simplify this equation:

(2 * (x+6)) + (2x-10) = 30

2x + 12 + 2x - 10 = 30

4x + 2 = 30

Answer D: 4x + 2 = 30

Answer:

around 15.3

Step-by-step explanation:

3^2 + 15^2=c^2

Answer:

Step-by-step explanation:

Formula:

a^2 + b^2 + c^2

3^2 + 15^2 + c^2 = To find hypotenuse

3 • 3 + 15 • 15 = -c^2

9 + 225 = -c^2

234 = c^2

square root of 234 = 15.2970585408

c = 15.2970585408

The roof is 15.2970585408

Answer:

D) (1,1)

Step-by-step explanation:

You can find the solution by plugging the x-value of each coordinate into the equation. It will be a solution if the y-value of the equation equals the y-value of the coordinate.

For example:

y = 3x -2

y = 3(1) - 2

y = 3-2

y = 1

1 = 1

(1, 1) are the coordinates that are on the given line.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given a equation y = 3x -2

To find which coordinates will satisfy the equation:

For coordinates (2, 0)

at x = 2, y should be zero

y = 3 * 2 -2

y = 4

Not satisfied

For coordinates(-3, 0)

at x = -3, y should be 0

y = 3 * -3 - 2

y = -9 -2

y = -11

Not satisfied

For coordinates(0, 2 )

at x = 0, y should be 2

y = 3*0 -2

y = -2

Not satisfied

For coordinates(1, 1)

at x = 1, y should be 1

Y = 3*1 - 2

y = 3 - 2

y = 1

satisfied

Therefore, (1, 1) are the coordinates that are on the given line.

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Answer:

-1/2

Step-by-step explanation:

y2-y1 over x2-x1

-2-4 over 10+2

which equals -6/12

which simplifies to -1/2

Answer:

-1/2

Step-by-step explanation:

Slope formula- m = y2 - y1

                                x2 - x1

x1,y1

-2, 4

x2,y2

10,-2                   -2 - 4

                           10 - (-2)  = -6/12 = -1/2                      

Answer:

There are sixteen 15-cent stamps and eight 20-cent stamps.

Step-by-step explanation:

Stamp collector has:

15c stamps

20c stamps

Total value is $4

x($0.15) + y($0.20) = $4.00

The # of 15c stamps is 8 - than 3 * the # of 20c stamps; 15c = 8 - 3c

x = 3y - 8

(3y-8)(0.15)+y(0.20) = $4.00

0.45)y-1.20+(0.20)y = 4.00

(0.65)y-1.20 = 4.00

(0.65)y = 5.20

y = 8

x = 3(8)-8 = 16

There are sixteen 15-cent stamps and eight 20-cent stamps.

Check:

16($0.15)+8($0.20) = $2.40+$1.60 = $4.00

Answer:

Tristan will need 32 feet of material for the perimeter of the garden.

Step-by-step explanation:

Given that

Area of square garden = A = 64 square feet

Perimeter = P = ?

We know that for calculation of perimeter, length of side of square is required which is not directly given in the question. The area will be used to calculate length of side and then length will be used to calculate the perimeter.

So,

[tex]Area = A = s^2[/tex]

s is for side

Putting the value of area

[tex]64 = a^2[/tex]

Taking square root on both sides

[tex]\sqrt{s^2} = \sqrt{64}\\s = 8\ feet[/tex]

The length of side is 8 feet.

Perimeter will be:

[tex]P = 4*s\\P = 4*8\\P = 32\ feet[/tex]

Hence,

Tristan will need 32 feet of material for the perimeter of the garden.

Answer:-3

Step-by-step explanation:

The minimum value of a function can be obtained from its derivative

The point on the x-axis that makes [tex]\overline{AC}[/tex] + [tex]\overline{BC}[/tex] minimum is the point [tex]\underline{(9, \, 0)}[/tex]

Reason:

Let (d, 0) represent the coordinate of the point, on the x-axis, we have;

[tex]\overline{AC}[/tex]² = (4 - d)² + (-5)²

[tex]\overline{AC}[/tex] = √((4 - d)² + (-5)²)

[tex]\overline{BC}[/tex]² = (12 - d)² + 3²

[tex]\overline{BC}[/tex] = √((12 - d)² + 3²)

[tex]\overline{AC}[/tex]² + [tex]\overline{BC}[/tex]² = L =  4² + (-5 - d)² + 12² + (3 - d)²

When [tex]\overline{AC}[/tex] + [tex]\overline{BC}[/tex] is minimum, we have;

[tex]\lim_{n \to \infty} a_n \dfrac{d}{dd} (\overline{AC} + \overline{BC}) = \dfrac{d}{dd} \left(\sqrt{ (4 - d)^2 + (-5)^2)} + \sqrt{ (12 - d)^2 + 3 ^2)} \right) = 0[/tex]

Which gives;

[tex]\dfrac{d}{dd} \left(\sqrt{ (4 - d)^2 + (-5)^2)} + \sqrt{ (12 - d)^2 + 3 ^2)} \right) = \dfrac{2 \cdot d - 24}{2 \cdot \sqrt{d^2-24 \cdot d + 153} } + \dfrac{2 \cdot d - 8}{2 \cdot \sqrt{d^2 - 8\cdot d + 41} }[/tex]

Therefore;

[tex]\dfrac{2 \cdot d - 24}{2 \cdot \sqrt{d^2-24 \cdot d + 153} } + \dfrac{2 \cdot d - 8}{2 \cdot \sqrt{d^2 - 8 \cdot d + 41} } = 0[/tex]

[tex]\dfrac{2 \cdot d - 24}{2 \cdot \sqrt{d^2-24 \cdot d + 153} } =- \dfrac{2 \cdot d - 8}{2 \cdot \sqrt{d^2 - 8 \cdot d + 41} }[/tex]

Squaring both sides and cross multiplying gives;

16·d² - 528·d + 3456 = 0

Which gives;

16·(d - 24)·(d - 9) = 0

Therefore, d = 24, and d = 9

The point (9, 0), is closer to the given points than the point (24, 0), therefore;

The point on the x-axis that makes [tex]\overline{AC}[/tex] + [tex]\overline{BC}[/tex] minimum is the point [tex]\underline{(9, \, 0)}[/tex]

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Answer:

(f+g)(2)=5

Step-by-step explanation:

Subsitute 2 in for x in both functions. Then add the answers of the functions together.

Answer:

c ≤ 6

Step-by-step explanation:

Lets make our equation!

2.5 per chore thats our slope

+3 she starts with 3 dollars

y = 2.50x +3

Substitute y for 17!

17 = 2.5x +3

Subtract 3!

14 = 2.5x

Divide both sides by 2.5!

x = 5.6

5.6 --> 6

x = 6

Turn it into an inequality!

c ≤ 6

Consider Brainliest! Hope I helped!

Answer:

(4, 1)

Step-by-step explanation:

Method elimination would be good for this system

2x - y = 7 ........ (1)

x + y = 5 ......... (2)

(1) + (2)

3x = 12 ⇒ x = 4

4 + y = 5 ⇒ y = 1

(4, 1)

Answer:

what are the answer

Step-by-step explanation:

Answer:

(3)¼×¾

Step-by-step explanation:

3⁴/⁴

hope its write

Answer:

[tex]\frac{13}{4}[/tex] · [tex]\frac{15}{4}[/tex]

Step-by-step explanation:

Focusing on the first fraction, in order to simplify it, you have to multiply the denominator by the whole number; 4 x 3 is 12. You add the product to the numerator, so 12 + 1 would be 13. Therefore, the first fraction simplified would be [tex]\frac{13}{4}[/tex].

We can apply the same procedure to the next fraction, so 3 x 4 is 12, and 12 + 3 is 15. [tex]\frac{15}{4}[/tex] would be your answer.

Hope this helps! :)

Answer:

1) C

2) O

3) P

4) T

5) I

6) C

7) P

8) S

9) A

10) L

11) T

12) E

13) L

Step-by-step explanation:

Answer:

x=9

Step-by-step explanation:

FE is 3x-7

since ΔABC≅ΔDEF the equivalent of FE is CB, or BC...which is 20

3x-7=20

3x=27

x=9

Answer:

2x + 5y = 36 in standard form

Step-by-step explanation:

m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )

~~~~~

(3, 6)

(8, 4)

m = [tex]-\frac{2}{5}[/tex]

y - 6 = [tex]-\frac{2}{5}[/tex] ( x - 3 )

y = [tex]-\frac{2}{5}[/tex] x + [tex]\frac{36}{5}[/tex] in slope-intercept form

2x + 5y = 36 in standard form

Answer:

D.

Step-by-step explanation:

right on edge 2022

Answer:

8 $5 bills and 5 $1 bills

Step-by-step explanation:

5x8=40, which would be $40

1x5=5, which would be $5

$40+$5=$45

hope this helps! :)

Answer:

it's not possible. I've tried every way, r these the right amounts?

Answer:

64 cups

Step-by-step explanation:

Answer:

Easy lol mzvcn=48

Step-by-step explanation:

Answer:

A, 21

Step-by-step explanation:

84 divided by 3 =  28

28 per hour

3/4 of 28 is 21

The answer would be A. 21.

Answer:

0.76

Step-by-step explanation:

Hundredth is just the 2nd decimal point

Answer:

C and D

Step-by-step explanation:

Answer: The correct answer would be 164(c)

Step-by-step explanation:

You are Miguel Cervantes de Navas y Colon, captain in the Royal Spanish

Army in Sevilla in the year 1842. Outside your barracks window is a stack of

cannonballs, as shown in the illustration. On an idle afternoon you decide to

calculate the number of cannonballs in the stack. What is the number of

cannonballs?

650 is the number of cannonballs.  It typically fires a projectile propelled by an explosive chemical.

A cannon constitutes a large-caliber gun that belongs to the artillery category. It typically fires a projectile propelled by an explosive chemical. Prior to the development of smokeless powder in the late 19th century, gunpowder (sometimes known as "black powder") served as the main propellant.

Depending on their intended purpose on the battlefield, different types of gun combine and balance these characteristics to differing degrees. Cannons differ in gauge, effective range, mobility, rate of fire, angle of fire, and firepower. A large artillery weapon is a cannon.

By utilizing the formula of a square pyramid,

n(n+1)(2n+1)/6

12(12+1)(2(12)+1)/6

12(13)(25)/6

2*13*25

=650

Therefore, 650 is the number of cannonballs.

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Answer:

It’s 17.6

Step-by-step explanation:

Answer:

(2x-5)+(x+25)+x

4x+20

Step-by-step explanation:

Simplify the expression.