5. Convert 27 inches to yards by finding an
equivalent rate

The amount of cardboard needed to make a cuboid box of dimensions 8 inch, 3 inches and 3 inches is 114 sq. inches.

Let the three dimensions(height, length, width) be x, y,z units respectively.

The surface area of the cuboid is given by

\(S = 2(a\times b + b\times c + c\times a)\)

For this case, tissue box is almost cuboid shaped.

Also, its dimensions are given being 8 inches, 3 inches and 3 inches.

Suppose we measure the amount of cardboard needed in terms of area, then, the amount of cardboard needed to make that box(without any whole, full cuboid) is equal to the area of its surface(either outer or inner if we assume 0 inches thickness of cardboard),

Thus, we get:

Amount of cardboard needed = surface area of cuboid box with dimensions 8 by 3 by 3 (in inches)

= \(2(8 \times 3 + 3 \times 3 + 3 \times 8) = 114 \: \rm in^2\)

Thus, the amount of cardboard needed to make a cuboid box of dimensions 8 inch, 3 inches and 3 inches is 114 sq. inches.

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There are various classifications of angles, some of which include: Acute angles, Right angles, Obtuse angles, Straight angles, Reflex angles,  Complementary angles, Supplementary angles, Adjacent angles, Linear pair, Vertically opposite angles, Alternate interior angles, Alternate exterior angles, Corresponding angles, Conjugate angles, and Explementary angles.

It's important to note that this is not an exhaustive list and the classification may vary depending on the context.

Acute angles which measure less than 90 degrees, Right angles that measure exactly 90 degrees, Obtuse angles that measure more than 90 degrees but less than 180 degrees.

There is also Straight angles that measure exactly 180 degrees, Reflex angles that measure more than 180 degrees but less than 360 degrees, Complementary angles which add up to 90 degrees, Supplementary angles which add up to 180 degrees.

Then there is Adjacent angles that share a common vertex and a common side but no common interior points, Linear pair which add up to 180 degrees and share a common side, Vertically opposite angles that are formed by two intersecting lines and are opposite to each other, Alternate interior angles that are formed by two intersecting lines on opposite sides of a transversal and inside parallel lines, Alternate exterior angles that are formed by two intersecting lines on opposite sides of a transversal and outside parallel lines, Corresponding angles that are formed by two intersecting lines in the same relative position.

Conjugate angles are angles which are supplementary but non-adjacent, and Explementary angles are angles which add up to 90 degrees.

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Answer:

Step-by-step explanation:

To convert degrees to radians, we can use the following formula:

Then, for 35 degrees:

Answer:

-16x-28

Step-by-step explanation:

Break it into little pieces; start with distributing the -7:

-7(5+x)

-35-7x

Now add the rest of the problem: 7-35-7x-9x

Combine like terms: 7-35               7x-9x

7-35=-28             7x-9x=-16x

Rearrange so the coefficient and variable are upfront, giving you:

-16x-28

Answer: The equation for a straight line is a linear equation. Since linear usually stands for anything straight or in a line, thus the equation for lines in the XY plane is referred to be a linear equation. For example, 2x+3y = 5 is a linear equation in two variables.

Step-by-step explanation:

The scuba diver's rate is 24 feet per minute.

A rate of change is a rate that describes how one quantity changes in relation to another quantity.

Here, total distance covered underwater = 120 feet.

total time taken = 5 minutes.

Rate change = Distance covered / Time taken

                      = 120 / 5

                      = 24 ft per minute.

Thus, The scuba diver's rate is 24 feet per minute.

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the width of the river is approximately 62.9 meters.

We can start by drawing a diagram to visualize the problem:

    B              A               C

    |______________|______________|

                  x

Let's label the distance from point A to point B as x, and the distance from point A to point C as y (which is the width of the river we want to find). We know that the distance between posts B and C is 120m, so we have:

x + y + x = 120

2x + y = 120

We also know that the angle of sight between posts B and C is 37 degrees. Since point A is directly opposite point B, we can draw a line from point A to point B that is perpendicular to the river:

    B   *         A               C

    |__/*________|______________|

   x|  /37°      |  

    | /          |

    |/___________|

                  y

This forms a right triangle with angle of 37 degrees at point A. We can use the tangent function to find the value of x in terms of y:

tan(37) = x/y

x = y*tan(37)

Substituting this expression for x into the first equation we derived, we get:

2(y*tan(37)) + y = 120

Simplifying and solving for y, we get:

y = 120 / (2*tan(37) + 1)

Using a calculator, we can evaluate this expression to get:

y ≈ 62.9

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The three lengths 5, 7, and 10 do make a triangle

What is a triangle?

A triangle is a closed shape with three vertices, three sides, and three angles. △PQR is used to denote a triangle with the vertices P, Q, and R. Sandwiches and signboards in the shape of triangles are two of the triangles that are most frequently seen.

A triangle is a simple polygon with 3 sides and 3 interior angles. It is one of the basic shapes in geometry in which the 3 vertices are joined with each other

A triangle is formed by the three lengths, 5, 7, and 10. The length of the third side is greater than the sum of any two sides.

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Answer:

495 cm

Step-by-step explanation:

Remark

When you do the subtraction, whatever is left (the decimal part) is the length in cm when multiplied by 100.

Solution

Remaining rope = starting length - what was used.

Remaining rope = 6.15 - 1.2

Remaining rope = 4.95 meters

Answer

The remaining rope = 4.95 * 100 = 495 cm

Answer:

2 + 1 0 + 2 7

Step-by-step explanation:

We have to divide the shape into two

It will give us a Rectangle and a Trapezium

Answer:

$75.25

Step-by-step explanation:

Given data

Original price =$125

Discount =45%

Tax=5.2%

Let us find the discount

45/100*125

0.45*125

56.25

Let us find the tax

5.2/100*125

0.052*125

6.5

Hence the amount is

125-56.25+6.5

=$75.25

In order to calculate the diameter of the soap bubble, we need to use the Laplace equation and solve for the radius of the bubble.The diameter of the soap bubble is 8.04 x 10⁻⁴ mm.

We will then double the radius to get the diameter of the bubble.Here's the solution:

Given that:

Radius of the soap bubble =

r = 0.065 mm

= 6.5 x 10⁻⁵ m

Surface tension of soap in air =

σ = 0.019 N/m

Pressure outside the bubble =

P₂ = 75.0 kPa

= 75,000 Pa

Ambient temperature =

T = 300 K

Atmospheric pressure =

P₁ = 1 atm = 101,325 Pa

Laplace's equation states that the pressure inside the bubble is given by:

Pinside = Poutside + (2σ/r)

where σ is the surface tension and r is the radius of the bubble.

Rearranging the above equation to solve for the radius of the bubble:

2σ/r = Pinside - Poutside

r = 2σ/(Pinside - Poutside)

Substituting the given values into the above equation:

r = [2 x 0.019] / [Pinside - 101325]

After the soap bubble rises up, the pressure outside the bubble becomes 75 kPa.

Therefore:

Pinside - 101325 = 75000

Pinside = 176325 Pa

Substituting this value of Pinside into the above equation:

r = [2 x 0.019] / [176325 - 101325]

= 4.02 x 10⁻⁷ m

The diameter of the soap bubble is twice the radius:

D = 2r = 2 x 4.02 x 10⁻⁷ m

= 8.04 x 10⁻⁷ m

Converting the diameter to mm:

D = 8.04 x 10⁻⁷ m x 1000 mm/m

= 8.04 x 10⁻⁴ mm (answer)

Therefore, the diameter of the soap bubble is 8.04 x 10⁻⁴ mm.

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The unknown angle x in the triangle is 80 degrees

From the question, we have the following parameters that can be used in our computation:

The triangle

The unknown angle x is calculated using the sum of angles in a triangle theorem

So, we have

x + 60 + 40 = 180

Evaluate the like terms

x + 100 = 180

So, we have

x = 80

Hence, the unknown angle x is 80 degrees

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Answer:

Perimeter is 16x - 10

Step-by-step explanation:

\({ \sf{perimeter = 2(length + width)}} \\ p = 2 \{(5x - 7) + (3x + 2) \} \\ p = 2(8x - 5) \\ p = 16x - 10\)

The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

From the question, we have the following parameters that can be used in our computation:

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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Nine ears of sweetcorn will cost $2.25 at this store.

To determine the cost of nine ears of sweetcorn, given that four ears cost one dollar, you can follow these steps:

1. Determine the cost of one ear of sweetcorn: Since four ears cost one dollar, we can calculate the cost per ear by dividing the total cost by the number of ears: $1 / 4 ears = $0.25 per ear.

2. Calculate the cost of nine ears: Multiply the cost of one ear by the number of ears desired: $0.25 per ear × 9 ears = $2.25.

So, nine ears of sweetcorn will cost $2.25 at this store.

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In this case, the city planner is using a camera to record the number of cars passing through the intersection at different hours of the day and on different days of the week. This allows the planner to gather information on traffic patterns and congestion without directly influencing the traffic flow. The data collected will help the city planner identify trends and potential areas of improvement for traffic management and infrastructure planning.

The city planner is conducting a quantitative investigation using observational research methods. They are collecting numerical data through the use of a camera to record the number of cars that pass through the intersection at various times and days. This type of investigation involves the collection and analysis of data in a systematic and objective manner. The data collected will allow the city planner to identify patterns and trends in traffic congestion at the intersection, which can then be used to inform future decision-making and planning. Additionally, the use of observational research methods ensures that the data collected is reliable and unbiased, as it is based on direct observations of traffic flow rather than self-reported information from drivers or other subjective sources. Overall, the city planner's investigation is an important step in improving traffic flow and reducing congestion in the area.
The city planner's investigation can be best described as an observational study. In this type of investigation, the researcher collects data by observing and recording the occurrence of specific events or behaviors without interfering or manipulating the subjects or environment. In this case, the city planner is using a camera to record the number of cars passing through the intersection at different hours of the day and on different days of the week. This allows the planner to gather information on traffic patterns and congestion without directly influencing the traffic flow. The data collected will help the city planner identify trends and potential areas of improvement for traffic management and infrastructure planning.

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Answer:

A=12

Step-by-step explanation:

C=3

Answer:

Side a: 12

Side c: 4

Step-by-step explanation:

Answer:

5 6 + 4 2

Step-by-step explanation:

1 0 − 8 ( − 7 - 4 )

1 0 + 5 6 + 3 2

1 0 + 5 6 + 3 2

4 2 + 5 6

4 2 + 5 6

5 6 +42

The exponent of 3 in the simplified expression is -3.

The expression you've provided is \((3^{10)} / (3^5 * 3^8)\).

This can be simplified by using the properties of exponents, particularly the rule that says when you divide with the same base, you subtract the exponents.

Moreover, if you have a common base and want to multiply, you simply sum the corresponding exponents.

Thus, it is possible to alter your wording into the following form:

\(3^(10) / 3^{(5+8)\)

Then, this simplifies to:

\(3^{(10)} / 3^{(13)}\)

Now you subtract the exponents:

= \(3^{(10-13)\)

= \(3^{(-3)\)

So the exponent of 3 in the simplified expression is -3.

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\(the \: answer \: is \: \frac{1}{10} \)

\(\blue{———hope it helps———}\)

\(\large{ \pink{ \underline{ { \sf{Answer}}}}}\)

\(the \: answer \: is \: \frac{1}{10} \)

Answer:

\(y = 6x - 32\)

Step-by-step explanation:

\(y = 3(x - 6)2 + 4\)

\(y = 3 \times 2(x - 6) + 4\)

\(y = 6(x - 6) + 4\)

\(y = 6x - 36 + 4\)

\(y = 6x - 32\)

Answer:

y = 3x² – 36x + 112

Step-by-step explanation:

We can expand and simplify the quadratic equation y = 3(x – 6)² + 4 by multiplying out squared value in the parentheses.

y = 3(x – 6)² + 4

y = 3(x – 6)(x – 6) + 4

y = 3(x² – 6x – 6x + 36) + 4

y = 3(x² – 12x + 36) + 4

Note: We could have also used the formula: (x – a)² = x² – 2a + a²

Now, we can apply the distributive property: A(B + C) = AB + AC

y = 3(x² – 12x + 36) + 4

y = 3x² – 36x + 108 + 4

Finally, we can simplify by adding 108 and 4.

y = 3x² – 36x + 112

We cannot simplify the equation further because the expression on the right side: 3x² – 36x + 112, is not factorable.

According to the information, we can infer that the number of ounces of water, x, that Will could have put in each cup is 8 ounces.

Will initially had a cooler filled with 144 ounces of water. After using 16 ounces to fill his water bottle, there were 144 - 16 = 128 ounces of water remaining in the cooler.

Will then took out 16 plastic cups for his teammates. Since the same amount of water was put in each cup, the remaining amount of water, 128 ounces, needs to be divided equally among the cups.

Dividing 128 ounces by 16 cups gives us 8 ounces of water for each cup.

So, Will could have put 8 ounces of water in each cup.

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Answer:

C. (The purple/third table)

Step-by-step explanation:

x always multiplies by 2 to get y.

TIP: In a proportional relationship x always multiplies by the same number in every column.

Points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints.

True

Answer:

8 hours

Step-by-step explanation:

We know that since Lila earns $12/hr and works 6 hr/week, she earned 72 since 12 * 6 = 72.

We can let the amount Patrick earns each week represent 9h, where h is the amount of hours he works.

We can solve for h by setting Patrick's equation equal to 72, which is Lila's earnings:

\(9h=72\\h=8\\\\9(8)=72\\12(6)=72\)

The value of a is 20.

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.

Given that,

HL is perpendicular to HJ

m ∠2 = (a + 15)°

and

m ∠3 = (a + 35)°

If HL and HJ are perpendicular,

Then,

m ∠2 + m ∠3 = 90°

(a + 15)°  +  (a + 35)° = 90°

Now, solve for a

(a + 15)°  +  (a + 35)° = 90°

a + 15 + a + 35 = 90

a + a = 90 - 15 - 35

2a = 40

a = \(\frac{40}{2}\)

a = 20.

Hence, the value of a is 20

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Answer:

63 is 60% of 105.

Step-by-step explanation:

Divide 63 by 3 to get 21.  Now that you get 1/3 of that number, it would also mean that 21 is 20% of the full number.  Multiply 21 by 5 to get the full number which is 105.

Answer:

105

Step-by-step explanation:

63 = 60% x ?

60/100 x ? = 63

100/60 x 60/100 = 1 (you do this to cancel it out)

60/100 x 63 = 105