A food company sells its corn flakes in boxes of two different sizes: the regular box and the family value box. For the family value box, the length, width, and height of the box have all been increased by 20%.

Answer:

a) The maximum profit occurs at the vertex of the parabola, which has an x-value of -b/2a. In this case, the function is P(t) = -5t^2 + 70t + 600, so a = -5 and b = 70. Therefore, the vertex occurs at t = -b/2a = -70/(2*(-5)) = 7. The number 7 represents the number of years after 1990, so the company will reach its maximum profit in 1997.

b) To find the maximum profit, we need to evaluate the function at the x-value of the vertex. In this case, the vertex occurs at t = 7, so the maximum profit is P(7) = -5(7)^2 + 70(7) + 600 = $745,000.

c) To find the profit in 2002^2, we need to find the value of t that corresponds to the year 2002^2. 2002^2 = 4008004, which is 14 years after 1990. Therefore, we need to find P(14). P(t) = -5t^2 + 70t + 600, so P(14) = -5(14)^2 + 70(14) + 600 = $680.

As you can see below, both expressions result in the same value of 105. This demonstrates the application of the associative law in regrouping terms and maintaining the equivalence of the expression.

The associative law in mathematics states that the grouping of numbers in an addition or multiplication operation does not affect the result. In other words, you can regroup terms within parentheses without changing the value of the expression.

Using the associative law, we can regroup the terms in the expression s + (r + 75) by removing the parentheses and rearranging the terms:

s + (r + 75) = (s + r) + 75

The expression (s + r) + 75 is equivalent to s + (r + 75) because the addition operation is associative.

Let's take an example to illustrate this:

Suppose s = 10 and r = 20.

Using the original expression:

s + (r + 75) = 10 + (20 + 75) = 10 + 95 = 105

Using the expression with regrouped terms:

(s + r) + 75 = (10 + 20) + 75 = 30 + 75 = 105

As you can see, both expressions result in the same value of 105. This demonstrates the application of the associative law in regrouping terms and maintaining the equivalence of the expression.

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Answer:

Step-by-step explanation:

100(9801 - 8910)/8910 = 10%

Answer:

1244 DCD

Step-by-step explanation:

Step-by-step explanation:

4/11

please check the image above for confirmation

Answer:

.

Step-by-step explanation:

Express \(\sf0.\overline{36}\) in p/q form

\(\large\underline{\sf{Solution-}}\)

Given that:

\(\longmapsto\sf0.\overline{36}\)

Let this be equal to x.

So,

\(\longmapsto\sf x=0.\overline{36}- - - -(1)\)

Multiplying both side by 100,

\(\longmapsto\sf 100x=36.\overline{36}- - - -(2)\)

Subtracting (2) from (1),

\(\longmapsto\sf 100x-x=36.\overline{36}-0.\overline{36}\)

\(\longmapsto\sf 99x=36\)

So,

\(\longmapsto\sf x=\dfrac{36}{99}\)

Dividing by 9,

\(\sf\longmapsto x=\dfrac{4}{11}\)

Hence,

\(\sf\longmapsto\bf0.\overline{36}=\dfrac{4}{11}\)

Answer:

19

Step-by-step explanation:

The probability that a customer ordered a cold drink given that he or she ordered a large is 32%.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

P(Small | Cold) = n(Small and Cold)/n(Cold)

From the table:

P(Small | Cold) = 8/(8 + 12 + 5)

P(Small | Cold) = 0.32

or

P(Small | Cold) = 32%

Thus, the probability that a customer ordered a cold drink given that he or she ordered a large is 32%.

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Answer:

$74.49

(basically $74.50)

Step-by-step explanation:

hope that helps :))

Answer:

the Answer what have to be the fist bc c is the only on that is not with a ,g or b

Step-by-step explanation:

The last one.

........

Answer:

420 million

Step-by-step explanation:

There are up to 420 million numbers that were assinged.

The total weight of the liquid in the tank is approximately 12,628 pounds.

To calculate the weight of the liquid, we need to determine the volume of the hemisphere and then multiply it by the density of the liquid. The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius of the hemisphere.

In this case, the diameter of the tank is given as 24 feet, so the radius is half of that, which is 12 feet. Plugging this value into the formula, we get V = (2/3)π(12)³ ≈ 904.78 cubic feet.

Finally, we multiply the volume by the density of the liquid: 904.78 cubic feet * 92.5 pounds per cubic foot ≈ 12,628 pounds. Therefore, the total weight of the liquid in the tank is approximately 12,628 pounds.

In summary, to calculate the weight of the liquid in the tank, we first determine the volume of the hemisphere using the formula V = (2/3)πr³. Then, we multiply the volume by the density of the liquid.

By substituting the given diameter of 24 feet and using the appropriate conversions, we find that the total weight of the liquid is approximately 12,628 pounds.

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a. The functions domain expressed using interval notation is; ( -∞ , ∞ ).

b. The range of the function as required to be expressed using interval notation is; ( -∞ , 1 ).

c. The x-intercepts are at points; ( 0 , 0 ) and ( 4 , 0 ).

d. The y-intercepts is at the point; ( 0 , 0 ).

e. The missing values as required are; f (-2) = -3 and f (2) = 1.

As evident in the image attached to the task content; it follows that the graph is a quadratic graph which opens downward and has a vertex which is a maximum and hence;

It's domain is the set of all real numbers while its range is the set of all real numbers less than or equal to 1.

Also, the x- and y-intercepts represents the points at which the graph intersects the x- and y-axis respectively.

Finally; the missing points as required can be attributed to the value of the function at the instances; x = -2 and x = 2.

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Step-by-step explanation:

The expression you provided involves taking the square root of a negative number, which results in an imaginary number. In standard real number arithmetic, the square root of a negative number is undefined. However, in the realm of complex numbers, we can define a square root of negative numbers using the imaginary unit "i," where i is defined as the square root of -1.

Let's break down the expression step by step:

√(-25) / √9

The square root of -25 can be written as √(-1 * 25), which can further be simplified as √(-1) * √25.

√(-1) is equal to "i," and the square root of 25 is 5.

So, the expression becomes:

i * 5 / √9

The square root of 9 is 3.

Now, we can simplify further:

i * 5 / 3

Thus, the simplified expression is (5i) / 3, where "i" represents the imaginary unit.

Answer:

lien earned 29950, husband earned 28650

Step-by-step explanation:

you subtract 1300 from the total then divide by 2 and add the 1300 to liens half.

Answer:

1/4+1/3+1/8

=17/24

Step-by-step explanation:

1-17/24

=7/24

7/24×240

=70

The quadratic functions are: f(x) = 0.03x² for Design A and g(x) = 0.024x² for Design B.

A quadratic function is a type of polynomial function of the form f(x) = ax² + bx + c, where a, b, and c are constants and x is the variable. In a quadratic function, the highest power of the variable is 2.

The graph of a quadratic function is a parabola, which is a U-shaped curve that opens either upwards or downwards depending on the sign of the coefficient a. If a > 0, the parabola opens upwards, and if a < 0, the parabola opens downwards. The vertex of the parabola, which is the point where the curve changes direction, is given by the coordinates (-b/2a, f(-b/2a)).

Quadratic functions have a wide range of applications in various fields such as physics, engineering, economics, and finance. For example, they can be used to model the motion of projectiles, the trajectory of a rocket, the shape of a bridge arch, the optimization of business profits, and the behavior of financial markets.

Let's assume that each side of the cube has a length of x inches. Then, the surface area of the cube is 6x² square inches.

a. For Design A with a cost of $0.005 per square inch, the total cardboard cost can be calculated using the quadratic function:

f(x) = 0.005(6x²) = 0.03x²

b. For Design B with a cost of $0.004 per square inch, the total cardboard cost can be calculated using the quadratic function:

g(x) = 0.004(6x²) = 0.024x²

Therefore, the quadratic functions are:

f(x) = 0.03x² for Design A

g(x) = 0.024x² for Design B

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The complete question is:

Answer:

135 minutes

Step-by-step explanation:

Answer:

135 minutes

Step-by-step explanation:

1 hour= 60 minutes

2hours=60x2=120 minutes

120+15=135 minutes

plz mark me as brainliest.

Answer:

\(B(x_2,y_2)= (20,12)\)

Step-by-step explanation:

Given

\(A = (0,0)\)

\(Ratio; m : n = 1 : 3\)

\(Point\ at\ 1 : 3 = (5,3)\)

Required

Coordinates of B

This question will be answered using line ratio formula;

\((x,y) = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})\)

In this case:

\((x,y) = (5,3)\)

\((x_1,y_1) = (0,0)\)

\(m : n = 1 : 3\)

Solving for \((x_2,y_2)\)

\((x,y) = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})\) becomes

\((5,3) = (\frac{1 * x_2 + 3 * 0}{1 + 3},\frac{1 * y_2 + 3 * 0}{1 + 3})\)

\((5,3) = (\frac{x_2 + 0}{4},\frac{y_2 + 0}{4})\)

\((5,3) = (\frac{x_2}{4},\frac{y_2}{4})\)

Comparing the right hand side to the left;

\(\frac{x_2}{4} = 5\) -- (1)

\(\frac{y_2}{4} = 3\) -- (2)

Solving (1)

\(x_2 = 5 * 4\)

\(x_2 = 20\)

Solving (2)

\(y_2 = 3 * 4\)

\(y_2 = 12\)

Hence;

\(B(x_2,y_2)= (20,12)\)

Answer:

The answer is 6 seconds

Answer:

0 - 28

34 + (-62)

-7 x 4

28 - 56

The value of x that maximizes the area of the figure is 1.5 inches, and the maximum area is 3.375 square inches.

A rectangle is a two-dimensional form that has four full sides and four right angles. Because the opposing sides are parallel and congruent, it is a unique kind of parallelogram.

To find the maximum area of the figure, we need to determine the value of x that will maximize the area.

The area of the figure can be calculated as:

A = (1.5x)(x) + (1/2)(1.5x)(6-2x)

Simplifying the expression:

\(A = 1.5x^2 + 4.5x - 3x^2\)

\(A = -1.5x^2 + 4.5x\)

To find the value of x that maximizes the area, we need to take the derivative of A with respect to x and set it equal to zero:

dA/dx = -3x + 4.5 = 0

Solving for x:

3x = 4.5

x = 1.5 inches

Now that we know x=1.5 inches maximizes the area, we can substitute it back into the area equation to find the maximum area:

\(A = -1.5(1.5)^2 + 4.5(1.5)\)

A = 3.375 square inches

Therefore, the value of x that maximizes the area of the figure is 1.5 inches and the maximum area is 3.375 square inches.

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Answer:

I answered your duplicate question. Make sure to check out the answer, and I hope it helps!

The following prices fills the gas cost from top to bottom: Option D

0, $12.40, $24.79, $37.19, $49.58

The practical range of the function is 0 ≤ f(g) ≤ 49.58

Given data

The complete question is attached

f (g) = 2.479 g

f (0), f (5), f (10), f (15), f (20)

The cost of fill up gas, f(g) = 2.479g  

first

f ( 0 ) = $0

second

f ( 5 ) = 2.479 × 5 = $12.40

third

f ( 10 ) = 2.479 × 10 = $24.79

fourth

f ( 15 ) = 2.479 × 15 = $37.19

fifth

f ( 20 ) = 2.479 × 20 = $49.58

The practical range is found by getting an expression that encompass the values gotten. The expression for the range is given as:

0 ≤ f(g) ≤ 49.58

Option D is the correct answer

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Answer:

x2+y2−6y=0

Step-by-step explanation:

Answer:

\(\boxed {192 cm^{2}}\)

Step-by-step explanation:

Find the volume of separate cuboids :

Volume (top cuboid) :

⇒ V = 2 x 6 x (10 - 2)

⇒ V = 12 x 8

⇒ V = 96 cm²

Volume (lower cuboid) :

⇒ V = 8 x 6 x 2

⇒ V = 48 x 2

⇒ V = 96 cm²

Volume (prism) :

⇒ 96 + 96

⇒ 192 cm²

Answer:

Step-by-step explanation:

Solution:

We can simplify the ratio 305 : 60 by dividing both terms by the greatest common factor (GCF).

The GCF of 305 and 60 is 5.

Divide both terms by 5.

305 ÷ 5 = 61

60 ÷ 5 = 12

Therefore:

305 : 60 = 61 : 12

Answer:

what I found out is $402 but I might of Got it wrong lowkey XD

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

the equation of the line is y=18/5x-216/5 and then find the x intercept and that is 12

The x-intercept of the line is 1.

The line intersects the x-axis at the point (1, 0).

Here,

To find the x-intercept of a line, we need to identify the point at which the line intersects the x-axis.

At the x-intercept, the y-coordinate is always 0.

Let's use the given data to find the equation of the line first using two points (x, y):

Using (22, 36) and (27, 54):

Calculate the slope (m) of the line:

m = (change in y) / (change in x) = (54 - 36) / (27 - 22) = 18 / 5

Use the slope and one of the points to find the equation of the line

(y = mx + b).

Let's use (22, 36):

36 = (18/5) * 22 + b

36 = 39.6 + b

b = 36 - 39.6

b = -3.6

So, the equation of the line is y = (18/5)x - 3.6.

Now, to find the x-intercept (where y = 0), we can set y = 0 in the equation and solve for x:

0 = (18/5)x - 3.6

(18/5)x = 3.6

x = 3.6 * 5 / 18

x = 1

Therefore, the x-intercept of the line is 1.

The line intersects the x-axis at the point (1, 0).

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