Write the number 91.823 in fraction expanded form​

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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Answer:

When the graph of the linear relationship contains the origin, the relationship is proportional. A linear equation is an equation whose solutions are ordered pairs that form a line when graphed on a coordinate plane. A relationship may be linear but not proportional and the graph does not pass through the origin.

Step-by-step explanation:

The characteristics of a graph that represents a proportional relationship:

1. Straight Line

2. Passing Through the Origin

3. Constant Ratio

4. Linear Equation

A graph is proportional when it represents a proportional relationship between two variables.

In a proportional relationship, as one variable increases or decreases, the other variable changes in a consistent and predictable manner.

The key characteristics of a graph that represents a proportional relationship:

1. Straight Line: The graph of a proportional relationship is a straight line. This means that the points on the graph fall in a straight line, indicating a constant rate of change between the two variables.

2. Passing Through the Origin: In a proportional relationship, the graph passes through the origin (0, 0). This means that when both variables are zero, they are directly proportional to each other.

3. Constant Ratio: The ratio between the values of the two variables remains constant along the entire line. This ratio is often referred to as the "constant of proportionality."

4. Linear Equation: The equation of a graph representing a proportional relationship is in the form y = kx, where "k" is the constant of proportionality.

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Answer:

26/3 or 8 2/3

Step-by-step explanation:

= 13/5 x 10/3

= 13 x 10

  5  x  3

= 130/5

= 26/3

= 8 2/3

The kilometer-to-mile ratio is 0.621371 km/mile when represented as a unit ratio.

A unit ratio is a ratio that compares two quantities with the same unit of measure. In this case, we want to express the kilometer-to-mile ratio as a unit ratio.

We know that 4.82803 km is equivalent to 3 miles. To express this as a unit ratio, we need to compare the number of kilometers to the number of miles. We can do this by dividing both sides of the equation by the same value, such as by 3 or by 4.82803.

Let's divide both sides of the equation by 4.82803 km:

(4.82803 km) / (4.82803 km) = (3 miles) / (4.82803 km)

Simplifying this equation, we get:

1 = 0.621371 km/mile

Therefore, the kilometer-to-mile ratio expressed as a unit ratio is 0.621371 km/mile. This means that for every 1 kilometer, there are 0.621371 miles.

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Answer:

from the graph we can see that

for 2 gallones - it can travell 70 miles

4 gallones - 140 miles

we will take the first case

2 gallones - 70 miles

17 gallones - ? miles

cross multiply

\( \frac{17 \times 70}{2} \)

= 595 miles

Answer:

hi

Step-by-step explanation:

it is equal because 5/5 is 1

Answer:

(2+3)(2−3)(5+2)(5−2)=>(22−(3)2)(52−(22))=>(4−3)(25−2)=>(1)(23)=>23

Given:

There are given the formula:

Explanation:

According to the question:

We need to find the value of h.

So,

First, multiply by 2 on both sides of the equation.

Then,

Then,

Therefore, the value of h is:

Final answer:

Hence, the correct option is B.

Answer:

16x^3 + 8x^2 + 12x

Step-by-step explanation:

Given the product 4x(x^2+2x+3)

On Expanding

4x(x^2+2x+3)

= 4x(x^2)+4x(2x)+4x(3)

=  16x^3 + 8x^2 + 12x

Hence the Area of the model is 16x^3 + 8x^2 + 12x

The area model is as follows:

4x × (x²) = 4x³

4x × (2x) = 8x²

4x × (3) = 12x

The area model that will be use to multiply 4x(x² + 2x +3) is as follows:

4x × (x²) = 4x³

4x × (2x) = 8x²

4x × (3) = 12x

Therefore,

4x(x² + 2x +3)  = 4x³ + 8x² + 12x

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The resulting graph is a circle with center at (-3,-1) and radius 3.

The graph of the equation (x+3)²+(y+1)²=9

is a circle with center at (-3,-1) and radius 3. The equation of a circle with center (a,b) and radius r is given by the equation (x-a)² + (y-b)² = r². By comparing the given equation with the standard equation of a circle, we can easily see that the center of the circle is (-3,-1) and the radius is 3. To graph a circle, we need to first plot the center of the circle, which is (-3,-1) in this case. Next, we need to mark the radius of the circle, which is 3 units. We can do this by measuring 3 units from the center in any direction and marking the point. Since the radius of the circle is the same in all directions, we can repeat this process for other directions to get points on the circumference of the circle. We can use a compass to make this process easier. After plotting a sufficient number of points, we can draw a smooth curve passing through all the points to obtain the graph of the circle.

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The angle measure explained in the solution.

Given that, a || b, we need to find the missing angles,

∠1 = 42° [vertically opposite angles]

∠3 = 62° [vertically opposite angles]

∠2 = 180°-(∠1+62°) [angle in a straight line]

∠2 = 76°

∠4 = ∠2 [vertically opposite angle]

∠4 = 76°

∠4 = ∠9 = 76° [alternate angles]

∠9 = ∠12 = 76° [vertically opposite angle]

∠3 = ∠ 6 = 62° [alternate angles]

∠ 6 = ∠7 = 62° [vertically opposite angle]

∠3 + ∠5 = 180° [consecutive angles]

∠5 = 118°

∠5 = ∠8 = 118° [vertically opposite angle]

∠4 + ∠10 = 180° [consecutive angles]

∠10 = 104°

∠10 = ∠11 [vertically opposite angle]

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The statement that a clock that is set fifteen minutes fast is less precise than an identical clock that keeps correct time is false

When a time is set away from the correct time, the time on the clock would be incorrect.

However, this has nothing to do with the precision of the clock.

This is so because precision deals with closeness of the time measurement to the original time

Since the time is ten minutes fast, it would not be less precise

Hence, the statement is false

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Answer:

38.81 pounds

Step-by-step explanation:

Considering the definition of right rectangular prism and its volume,  the total weight of the contents is 38.81 pounds.

Right rectangular prism

A right rectangular prism (or cuboid) is a polyhedron whose surface is formed by two equal and parallel rectangles called bases and by four lateral faces that are also parallel rectangles and equal two to two.

Volume of right rectangular prism

To calculate the volume of the rectangular prism, it is necessary to find the product of its dimensions, or of the three edges that converge at a certain vertex.

That is, to calculate the volume of a rectangular prism, multiply its 3 dimensions: length×width×height.

Volume of the container

In this case, you know that:

the dimensions of the container built are 7.5 ft by 11.5 ft by 3 ft.

the container is entirely full and, on average, its contents weigh 0.15 pounds per cubic foot.

So, the volume of the container is calculated as:

7.5 ft× 11.5 ft× 3 ft= 258.75 ft³

Then, the total weight of the contents is calculated as:

258.75 ft³×  0.15 pounds per cubic foot= 38.8125 pounds≅ 38.81 pounds

Finally, the total weight of the contents is 38.81 pounds.

It should be noted that the letter welcoming the new student to class and explain how to complete a math problem with Order of Operations will be:

Hello John,

How are you doing? It's great to have you around.

I'm writing to inform you about the order to operations. It should be noted that in this case, it's important for you to open the paranthesis first.

Then you will divide the values, multiplication comes next before addition and finally subtraction.

You're sincerely,

Jude.

It should be noted that a letter is a form of communication between people.

In this case, the letter is welcoming the new student to class and explain how to complete a math problem with order of operations.

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The value of x in the similar triangle is 6 units.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Therefore, let's use the similarity ratio to find the value of x in the similar triangle as follows:

Hence,

5 / 40 = x / 48

48 × 5 = 40x

240 = 40x

divide both sides by 40

x = 240 / 40

x = 6

Therefore,

x = 6

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Answer:

The bonds yielded $798.40 more in profits than the stocks.

Step-by-step explanation:

egde

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:Yes, the point lies on the line.

Step-by-step explanation:

Given coordinate of the locus = (1,2)

 Equation of the line  2x+4y = 10

Unknown:

Does the given coordinate lie on the line?

Solution:

The equation given is that of a straight line. To solve this problem, we simply plug the coordinates of the point back into the equation and check if solves it.

  x  = 1 and y = 2;

  2x+4y = 10

So;

   2(1) + 4(2) gives 2 + 8 = 10

Yes, the point lies on the line.

The value of Sin(90) is equal to 1.

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Given here: Sin(90) and to find the value using the unit circle

Rotate ‘r’ anticlockwise to form a 90° angle with the positive x-axis.

The sin of 90 degrees equals the y-coordinate(1) of the point of intersection (0, 1) of unit circle and r.

The value of sin 90 degrees can be calculated by constructing an angle of 90° with the x-axis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of sin 90° is equal to the y-coordinate (1). ∴ sin 90° = 1.

Hence, Sin (90) is equal to 1.

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Answer: Do you wanna go out with me

Step-by-step explanation:

Answer:

conclude that there is no significant evidence to support the claim that difference exists between the mean number of miles run by the two groups.

Step-by-step explanation:

H0 : μ1 = μ2

H0 : μ1 ≠ μ2

The test statistic :

(x1 - x2) / √(s1²/n1) + (s2²/n2)

(49.5 - 48.5) / √(1.1²/38) + (2.6²/33)

1 / √0.2366905

Test statistic = 2.055

Using the Pvalue from Tstatistic calculator :

df = (smaller sample - 1) = 33 - 1 = 32

Pvalue from Test score calculator = 0.048

Pvalue > α ; Fail to reject the null ;

Hence, conclude that there is no significant evidence to support the claim that difference exists between the mean number of miles run by the two groups.

This might be the answer

The equation of the line is slope intercept form is y = 3x + 45.

What is a graph?

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, Danny is opening a savings account with an initial deposit of $45 and he saves $3 per day.

Let y be the total amount he saves and x is the no. of days.

As he starts with $45 deposit it'll be added as a constant.

∴ The equation of the required line is y = 3x + 45.

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Answer:

this is a ninth degree polynomial in m

Step-by-step explanation:

Inspect the polynomial for the highest power of the variable m.  It is m^9.  Thus, this is a ninth degree polynomial in m.

Answer:

45.24

Step-by-step explanation:

the formula for circumference is:

c=2πr

So,

45.24= 2π(7.2)

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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Answer:

y=-7-x

Step-by-step explanation:

-3y=21+3x     y=21/-3+3x/-3    y=-7-x

Hi there!

How are you?

Answer:

\(\boxed{y = - x - 7}\)

Step-by-step explanation:

⇒ First add 3x to both sides.

\(-3x - 3y + 3x = 21 + 3x\)

\(-3y = 3x + 21\)

⇒ Second divide both sides by -3.

\(\frac{-3y}{-3} = \frac{3x + 21}{-3}\)

\(y = - x - 7\)

Have good day/night!

A is either 45° or 135°.

To prove the given statement, let's assume that the points B and C lie on a coordinate plane, with the origin (0, 0) as the common vertex of the right angles at points B, C, and A. Let the coordinates of points B and C be (x₁, y₁) and (x₂, y₂) respectively.

Using the distance formula, we have:

AB² = x₁² + y₁²

AC² = x₂² + y₂²

According to the given equation, +b4+c4 = 20² (b²+c²), we can rewrite it as:

(x₁² + y₁²) + (x₂² + y₂²) = 20² [(x₁² + y₁²) + (x₂² + y₂²)]

Expanding and simplifying the equation, we get:

x₁² + y₁² + x₂² + y₂² = 20² (x₁² + y₁² + x₂² + y₂²)

This equation can be further simplified to:

(x₁² + y₁²) + (x₂² + y₂²) = (20² - 1) (x₁² + y₁² + x₂² + y₂²)

Since the left side represents the sum of the squares of the distances from the origin to points B and C, and the right side is a constant multiplied by the same sum, we can conclude that the points B and C must lie on a circle centered at the origin.

In a circle, the sum of angles subtended by two perpendicular chords at the center is either 180° or 360°. Since the given problem involves right angles, we consider the sum of angles to be 180°.

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