what is the volume of a cereal box that is 2 inches thick, 12 inches high and 10 inches wide?

Answer:

4

Step-by-step explanation:

44 yeah yeah what about the other

Answer:

200 ÷ 5 = 40

Step-by-step explanation:

you round each number

197.6 becomes 200

5.48 becomes 5

The answer is:

32.4

Work/explanation:

These numbers need to be multiplied.

\(\sf{(540)(0.03)(2)}\)

\(\sf{16.2\times2}\)

\(\sf{32.4}\)

Hence, the product of these numbers is 32.4.

The students that are in the seventh grade is 60.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

Let the students that are in the seventh grade be x.

Since 12 students in the Environmental Club represent 20% of the students in the seventh grade. This will be:

20% × x = 12

0.2x = 12

Divide

x = 12 / 0.2

x = 60

Therefore, there are 60 students.

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A sequence of instructions that solves a problem is called an algorithm.

Answer: See image

Step-by-step explanation:

The bases are 5cm times 3cm, meaning that 2 parallel sides have to be 5cm by 3cm, 2 other parallel sides have to 2cm by 3cm, and the 2 other parallel sides have to be 5cm by 2cm.

Answer:

45

Step-by-step explanation:

Find prime factors

9 = 3 x 3

15 = 3 x 5

3 x 3 x 5 = 45

The dimensions of the rectangular garden which minimize the cost is equal to 9.6ft and 14.6ft respectively.

As given in the question,

Cost of brick wall is equal to $40/ft

Cost of metal fencing is equal to $20/ft

Let 'x' and 'y' are the dimensions of the rectangular garden

Area of the rectangular garden = 142 square feet

⇒ 142 = xy

⇒x = 142/y

Costing of four side fencing 'C' = 40x + 20x + 20y + 20y

⇒ C = 60x + 40y

⇒C = 60(142/y) + 40y

⇒C = 8520/y + 40y

Differentiate with respect to y

dC/dy = -8520/ y² + 40

Put dC/dy = 0

-8520/ y² + 40 = 0

⇒y² = 8520/40

⇒y = √213

⇒ y= 14.6 ft

⇒ x= 142/14.6

     = 9.7 ft

Therefore, the dimensions of the rectangular garden with the given area which minimize the cost is equal to 14.6ft and 9.7ft.

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The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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Answer:

Step-by-step explanation:

Combine like terms

\(6y + 3 + 3x^{2} - y^{2} - 5x + 2x^{2} + 3x + 2y\)

8y + 3 + 5\(x^{2}\) + 2x - \(y^{2}\)

The required simplified value of the given expression is given as 5x² - y² -2x + 8y + 3.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Given expression,
= 6y+3+ 3x² - y² – 5x + 2x² + 3x + 2y

Simplify, by adding alike terms,
= 5x² - y² -2x + 8y + 3

Thus, the required simplified value of the given expression is given as 5x² - y² -2x + 8y + 3.

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Answer:

\(perimeter = 2(length + breadth) \\ =2 (54 + 8) \\ = 124 \: cm\)

let assume the no. - x

x*94/5=42

x=42*5/94

x=21*5/47

x=105/47

Sorry if I’m wrong

Let the number should be multiplied be X

Given number = 9 4/5

⇛ (9×5+4)/5

⇛ (45+4)/5

⇛ 49/5

On multiplying 49/5 with X then the result

= (49/5)×X

= 49X/5

According to the given problem

The result = 42

⇛ 49X/5 = 42

⇛ 49X = 42×5

⇛ 49X = 210

⇛ X = 210/49

⇛ X = 30/7

⇛ X = 4 2/7

Answer↓

The required number is 30/7 or 4 2/7

Check↓

On multiplying 4 9/5 with 4 2/7

⇛ 4 9/5 × 4 2/7

⇛ (49/5)×(30/7)

⇛ (49×30)/(5×7)

⇛ 7×6

⇛ 42

Verified.

Answer:5

Step-by-step explanation:

Answer:

x = 16

Step-by-step explanation:

All angles in a triangle add up to 180°.

Step 1: Set up equation

9x - 8 + x + 10 + x + 2 = 180

Step 2: Solve for x

To achieve a comparable rate of return, Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly on his ordinary annuity.

To find the interest rate, compounded monthly, that Hank would need to earn on an ordinary annuity for a comparable rate of return, we can use the present value formula for an ordinary annuity.

First, let's calculate the present value of Hank's payments. He made payments of $219 per month for 30 years, so the total payments amount to $219 * 12 * 30 = $78840.

Now, we need to find the interest rate that would make this present value equal to the selling price of the property, which is $195,258.

Using the formula for the present value of an ordinary annuity, we have:

PV = P * (1 - (1+r)\(^{(-n)})\)/r,
where PV is the present value, P is the payment per period, r is the interest rate per period, and n is the number of periods.

Plugging in the values we have, we get:
$78840 = $219 * (1 - (1+r)\({(-360)}\))/r.

Solving this equation for r, we find that Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly, in order to have a comparable rate of return.

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Answer:

It will take 2.2 hours for the trains to meet.

Step-by-step explanation:

Given,

Distance between two trains = 396 miles

Speed of one train = 95 mph

Speed of other train = 85 mph

Combined speed of trains = 95+85 = 180 mph

Distance = Speed * Time

Time =

Time =

Time = 2.2 hours

It will take 2.2 hours for the trains to meet.

Keywords: speed, distance

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Step-by-step explanation:

The requried shading would occur above the solid line of the slope.

To graph the inequality 9x + 5y > 1, we first need to graph the equation 9x + 5y = 1, which is the equation of the line that separates the two regions determined by the inequality.

To graph this line, we can solve for y in terms of x:

9x + 5y = 1

y = (-9/5)x + 1/5

This is the equation of a line with slope -9/5 and y-intercept 1/5. We can plot this line on a coordinated plane. Since the slope of the line is negative, the shading should occur above the line, which means the correct answer is: The shading would occur above the solid line of the slope.

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An inequality that represents this word sentence is 1 + y ≤ -13.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Word:

One plus a number y is no more than −13.

No more than means it can be equal or less

So,

This can be written as,

1 + y ≤ -13

Thus,

1 + y ≤ -13

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Answer: the answer is 90

Step-by-step explanation:There is only one number between 61 and 107 that is a multiple of 3, 5 and 9. So that number will be  90.

it has the correct conditions and the correct formula for calculating the cost. \(C(x) = 3.25x + 5 if x > = 6\) Thus, option C is correct.

The correct function that models this scenario is:

\(C(x) = 3.75x if x < 6\)

\(C(x) = 3.25x + 5 if x > = 6\)

This is because for rentals less than 6 hours, the cost is simply $3.75 per hour, so the function is  \(C(x) = 3.75x\)  . For rentals of 6 hours or more, there is a discounted hourly rate of $\(3.25\) per hour, but there is also a $5 processing fee, so the function is \(C(x) = 3.25x + 5\)  .

Option (a) is incorrect because it does not include the $5 processing fee for rentals of 6 hours or more.

Option (b) is incorrect because it has the wrong conditions for the hourly rate discounts. It specifies that the discount starts at x = 6, but the correct condition is \(x > = 6.\)

Option (c) is correct, as it has the correct conditions and the correct formula for calculating the cost.

Option (d) is incorrect because it has the wrong condition for the hourly rate discounts (x < 5 instead of x < 6), and it does not include the $5 processing fee for rentals of 6 hours or more.

Therefore, it has the correct conditions and the correct formula for calculating the cost. \(C(x) = 3.25x + 5 if x > = 6\)

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Answer:

Mode: 2

Step-by-step explanation:

The number 2, is the most repeated number.

Answer:

2 is the mode.

Step-by-step explanation:

First you have to put the numbers in order, which you did. The number that shows up the most is the mode. In this case it's 2, since it shows up twice and all the other numbers only show up once.

Here's a tip to remember:

Mode sounds like most.

The most shown number is the mode.

The total centimeters that the plants grew in all was 200 centimeters or 2.00 centimeters when written as a decimal.

Centimetres (cm) is a unit of length in the metric system, equal to one-hundredth of a metre. It is commonly used in everyday life, for example when measuring the height of a person or the size of a room. Centimetres are also used in scientific and engineering measurements, such as the size of an object or the distance between two points. Centimetres are divided into millimetres, which are one-thousandth of a metre.

This can be written as a decimal as 2.00 centimeters.

To determine the total centimeters, we simply add the individual centimeter measurements of the two plants.

Daysha's plant grew 100 centimeters and India's plant grew 100 centimeters.

Therefore, the total centimeters that the plants grew in all was 200 centimeters, or 2.00 centimeters when written as a decimal.

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The area inside the polar curve R = 2cos(3θ) for three full rotations is 6π.

The polar curve R = 2cos(3θ) is symmetric about the x-axis, with three petals that extend from θ = 0 to θ = π/3, π to 4π/3, and 5π/3 to 2π. To find the area inside the curve, we need to integrate the expression for the area element in polar coordinates over the desired region:

dA = (1/2) \(R^{2}\) dθ

The limits of integration for θ are from α = -6π to β = 6π, since we want to find the total area inside the curve for three full rotations. Thus, the integral for the area is:

A = ∫(β=6π, α=-6π) (1/2) \(R^{2}\)dθ

= ∫(β=6π, α=-6π) (1/2) (2cos(3θ))^2 dθ

= 2∫(β=6π/3, α=-6π/3) cos^2(3θ) d(3θ) (using the identity cos^2(3θ) = (1 +    cos(6θ))/2)

= ∫(β=6π/3, α=-6π/3) (1/2 + (1/2)cos(6θ)) d(3θ)

= (1/2)θ + (1/12)sin(6θ) ∣(β=6π/3, α=-6π/3)

= (1/2)(6π - (-6π)) + (1/12)(sin(36π) - sin(-36π))

= 6π

Correct Question :

Find The Area Inside R=2cos(3θ) (Tip: Use Α=−6π And Β=6π )

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Answer:

That number is 230 × 1.08 = 248.4.

To find this number, we calculated 8% of 230, which is 18.4 , and then added it to 230, Hence The number that is 8% larger than 230 is 248.4.

To find a number that is 8% larger than 230, we can calculate the 8% increase of 230 and add it to the original number.

Step 1: Calculate the 8% increase of 230:

8% of 230 = (8/100) * 230 = 0.08 * 230 = 18.4

Step 2: Add the 8% increase to 230:

230 + 18.4 = 248.4

Therefore, a number that is 8% larger than 230 is 248.4.

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Question:

Consider the line which passes through the point P(-5, 1, 4), and which is parallel to the line x=1+7t,y=2+1t,z=3+7t. Find the point of intersection of this new line with each of the coordinate planes: xy-plane, xz-plane and yz-plane.

Answer:

The line intersects the xy plane at (-3, \(\frac{11}{7}\), 0)

The line intersects the xz plane at (-13, 0, -11)

The line intersects the yz plane at (0, \(\frac{13}{7}\), 2)

Step-by-step explanation:

Vector form of a line can be written as;

r(t) = r₀ + vt

Where;

r₀ = position vector of the point where the line passes through

v = direction or slope vector of the line.

From the question, we have a line passing through the point P(-5, 1, 4). This means that;

r₀ = (-5, 1, 4)

Also, the line is parallel to another line with parametric equations:

x=1+7t ------------------(i)

y=2+1t ----------------(ii)

z=3+7t ---------------(iii)

Since the first line is parallel to the second line, then their gradient or slope vector must be the same. This means that;

v = (7, 1, 7)           [which are the coefficients of t in the parametric equations]

Therefore, the first line can be written as;

r(t) = (-5, 1, 4) + (7, 1, 7)t

Now, to get the point of intersection of this line with each of the coordinates;

(i) The line will intersect the the xy plane when z = 0

Substitute z = 0 into equation (iii)

0 = 3 + 7t

t = \(\frac{-3}{7}\)

Now substitute t = \(\frac{-3}{7}\) into equation(i)

x = 1 + 7(\(\frac{-3}{7}\))

x = -3

Also, substitute t = \(\frac{-3}{7}\) into equation (ii)

y = 2 + 1(\(\frac{-3}{7}\))

y = \(\frac{11}{7}\)

Therefore, the line intersects the xy plane at (-3, \(\frac{11}{7}\), 0)

(ii) The line will intersect the xz plance when y = 0

Substitute y = 0 into equation (ii)

0 = 2 + 1t

t = -2

Now substitute t = -2 into equation(i)

x = 1 + 7(-2)

x = 1 - 14

x = -13

Also, substitute t = -2 into equation (iii)

z = 3 + 7(-2)

z = 3 - 14

z = -11

Therefore, the line intersects the xz plane at (-13, 0, -11)

(iii) The line will intersect the yz plane when x = 0

Substitute x = 0 into equation (i)

0 = 1 + 7t

t = \(\frac{-1}{7}\)

Now substitute t = \(\frac{-1}{7}\) into equation(ii)

y = 2 + 1(\(\frac{-1}{7}\))

y = \(\frac{13}{7}\)

Also, substitute t = \(\frac{-1}{7}\) into equation (iii)

z = 3 + 7(\(\frac{-1}{7}\))

z = 3 - 1

z = 2

Therefore, the line intersects the yz plane at (0, \(\frac{13}{7}\), 2)

Answer: x = 5

Step-by-step explanation:

3x + 6 = 21

3x = 21 - 6

3x = 15

x = 15/3

x = 5

Answer: X =5

Step-by-step explanation:  Subtract both sides by 6 to isolate 3x:

3x+6-6=21-6

3x=15

Divide both side by 3 to come up with x:

X=5.

A shortcut method but it does not follow the correct rules of math but if you're in a hurry it works:

3x+6=21

transfer +6 converting the sign to a -6

3x-=21-6

Subtract 3x=15

Divide by the number with x (3)

x=5

Since we need to choose 5 pencils from 12 colors, then we will use the combination

Where

n = 12

r = 5

Substitute n by 12 and 4 by 5 in the rule

We will simplify it

There are 792 sets of pencils