Challenge The Bells are adding a new room to their house. The room will be a cube with volume 4,096
ft³. They are going to put in hardwood floors, and the contractor charges $5 per square foot. How much
will the hardwood floors cost?
The hardwood floors will cost $

The rate in mm per hour at which the height of the water is changing when the height of the water is 2mm is 55.2

Given data,

A partially filled inverted cone contains water. The inverted cone has a 16 mm radius. The inverted cone is 18 mm in height. if the water's volume is growing at a pace of 548 cubic millimeters per hour.

The rate in mm per hour at which the height of the water is changing when the height of the water is 2 mm;

r/h = 16/18

    = 8/9

r = 8h/9

The volume of the cone is;

v = [tex]\frac{1}{3}\pi r^2h[/tex]

v = [tex]\frac{1}{3}\pi (8h/9)^2h[/tex]

v =  [tex]\frac{64}{243}\pi h^3[/tex]

Now, differentiating concerning x;

[tex]\frac{dv}{dt}[/tex]= [tex]\frac{d}{dt}[/tex]        [tex]\frac{64}{243}\pi h^3[/tex]

[tex]\frac{dv}{dt}[/tex]=  64π/243*[tex]\frac{d}{dt}[/tex] h³

[tex]\frac{dv}{dt}[/tex]= [tex]\frac{64}{81}\pi h^2\frac{dh}{dt}[/tex]

We have;

[tex]\frac{dv}{dt}[/tex]= 548 and h = 2mm

[tex]\frac{dh}{dt} = \frac{548*81}{256\pi }[/tex]

[tex]\frac{dh}{dt}[/tex] = 55.19

           [tex]\frac{dh}{dt}[/tex] = 55.2mm per hour.

Hence, the rate in mm per hour at which the height of the water is changing when the height of the water is 2mm is 55.2

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The distance between points (-1, 4) and (5, 4) is 6 units.

From the question, we are to determine the distance between two points.

The given points are (-1, 4) and (5, 4)

Using the formula for calculating the distance between two points

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

From the given information,

x₁ = -1

x₂ = 5

y₁ = 5

y₂ = 4

Put the parameters into the equation

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

d = √[(5 - (-1))² + (4 - 4)²]

d = √[(5 + 1)² + 0²]

d = √(6²)

d = 6 units

Hence, the distance is 6 units.

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Answer:

Step-by-step explanation: The distance between two points can be calculated using the formula:

d = √ ((x2 – x1)² + (y2 – y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

In this case, the two points are (-1, 4) and (5, 4). Therefore:

d = √ ((5 - (-1))² + (4 - 4)²)

d = √ (6² + 0²)

d = √36

d = 6

Therefore, the distance between (-1, 4) and (5, 4) is 6 units.

I hope that helps! Let me know if you have any other questions!

A vertical line passing through this point has the following equation is x=2 and A horizontal line passing through this point has the following equation is y=3.

Given that,

The point is (2,3).

We have to find the equation of the horizontal and vertical line that pass through point.

Take the point,

(2,3)

The value of x, in this example 2, will never change for a vertical line. This holds true regardless of y's value.

A vertical line passing through this point has the following equation:

x=2

The value of y, in this case 3, for a horizontal line will also never change. This holds true regardless of the value of x.

A horizontal line passing through this point has the following equation:

y=3.

Therefore, A vertical line passing through this point has the following equation is x=2 and A horizontal line passing through this point has the following equation is y=3.

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Answer:

3/5x 150

= 450/5

= 90

150+90

= 240 ans

Answer:

n + 2

Step-by-step explanation:

If n is the smallest of three consecutive integers, the largest in the sequence must be only two integers greater.

Answer:

1200

Step-by-step explanation:

1,500-300=1200

I hope this helps!

42x +55y =380

There is a 0.091125 probability that all three randomly chosen houses have dogs.

In light of this, imagine that a recent survey of American homes regarding pet ownership revealed that 45% of households with pets were dog-owning, 34% were cat-owning, and 10% were bird-owning households.

• Three families are chosen at random, replaced, and with mutually exclusive ownership.

The calculation of probability is as follows based on the facts above:

=0.43^3

= 0.091125

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The location of the points A and B on side PQ and PR, and the information that segment AB is parallel to QR indicates;

Part A: Triangle ΔPQR is similar to ΔPAB by AA similarity postulate

Part B: The line segment on triangle ΔPAB that corresponds to line segment QR is segment AB

Part C: The angle on triangle ΔPAB that corresponds to angle ∠Q is angle ∠A

Please find attached the drawing of triangles ΔPQR and ΔPAB created with MS Word

The in formation in the question are;

Line [tex]\overline{AB}{[/tex] is parallel to [tex]\overline{QR}[/tex], [tex]\left(\overline{AB} \parallel \overline{QR}\right)[/tex]

ΔPQR and ΔPAB overlap

Part A: Angle ∠PQR is congruent to angle ∠PAB (corresponding angles to parallel lines having a common transversal)

∠PRQ is congruent to ∠PBA (Corresponding angles formed by a common transversal to parallel lines)

ΔPQA is similar to ΔPAB (Angle-Angle, AA similarity postulate)

Part B: Corresponding sides of triangles are located on the same relative position within the triangle

Segment QR is the included segment to ∠PQR and ∠PRQ, which are each congruent to ∠PAB and ∠PBA, respectively in ΔPAB and segment AB is the included side to ∠PAB and ∠PBA, therefore, the line segment on triangle ΔPAB that corresponds to line segment QR is segment AB

Part C: Angle ∠Q on triangle ΔPQR is adjacent to segment QR on the right and angle ∠P on the left, while angle ∠A is adjacent segment AB on the right and ∠P on the right, segment AB in ΔPAB corresponds to segment QR on triangle ΔPQR, therefore, by the relative position of angle ∠A on triangle ΔPAB, it is the angle that corresponds to angle ∠Q

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The equation of the line that passes through the point (-8,-3) and has a slope of -3/4 is y = -3/4x - 9

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

Slope, m = -3/4

Points, (x₁, y₁) = (-8, -3)

A linear equation can be represented as

y = slope * x + y-intercept i.e. y = m(x - x₁) + y₁

Substitute the known values in the above equation

So, we have the following equation

y = -3/4(x + 8) - 3

Open the brackets

So, we have the following equation

y = -3/4x - 6 - 3

Evaluate the like terms in the above equation

So, we have the following representation

y = -3/4x - 9

The above equation cannot be further simplified

Hence. the linear equation is y = -3/4x - 9

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Answer:

3×10^7

Step-by-step explanation:

Write 30 000 000 in standard form.

=3×10,000,000

=3×10^7

Step-by-step explanation:

this is

3.0 × 10⁷

as 30 000 000 has 7 zeroes (7 sequential and continuously increasing powers of 10 starting with 10¹).

and the first non-zero digit is 3.

Answer: The answer is 8

Step-by-step explanation: 16 tablespoon is 1 cup now find half of 16. Half of 16 is 8. So 8 tablespoon should be equal 1/2 cup

Answer: 7/6

Step-by-step explanation:

Ok so first we must take these fractions and make them have a common denominator. The best way to do this is to take 2/3 and multiply the numerator and denominator by 8 giving us 16/24. Next take 4/8 and multiply the numerator and denominator by 3 giving us 12/24. Now we have both a common denominator. Now we add the numerators of both (16+12) to get 28/24 but now we have an improper fraction divide the numerator and denominator by 4 to get us 7/6.

Hope this Helps :)

Nadia was 1cm off the actual measurement of 5 cm. That is a percent error of 20%.

Sasha was 4 cm off the actual measurement of 100 cm. That’s a percent error of 4%.

From the information, the measurement was 4cm and the actual measurement was 5cm. Therefore, the difference will be:

= 5cm - 1cm

= 4cm

The percentage error will be:

= Difference in measurement / Actual measurement × 100

= 1/5 × 100

= 20%.

The percentage error for Sasha will be:

= 4/100 × 100

= 4%

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The expression equivalent to (-3.3x + (-3.2)) + (5.7x + (−1) is  -3.3x + 5.7x) + ((-3.2) + (-1))

The commutative property of addition states that any change in the order of the numbers being added does not affect the sum.

a + b = b + a

The given expression is  (-3.3x + (-3.2)) + (5.7x + (−1))

on simplifying we get, -3.3x - 3.2 + 5.7x - 1 = 2.4x - 4.2

Upon checking the options provided

-3.3x + (-3.2) + 5.7x + (-1)

= 2.4x - 4.2

(-3.3x (-1)) + ((-3.2)x - 5.7)

-9 - 6.7

-3.3x + (-3.2)) + (5.7x- (-1))

2.4x - 2.2

(-3.3x + 5.7x) + ((-3.2) + (-1))

2.4x - 4.2

Therefore, the expression equivalent to (-3.3x + (-3.2)) + (5.7x + (−1) is  -3.3x + 5.7x) + ((-3.2) + (-1))

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For emission of a surface, the average absorptivity of this surface at 1040 K is 0.899705900025.

Knowing that ε1 =0.15 and ε2 = 0.9, we first solve for the average emission, e, as follows:

ε = ε1 [tex]f_λ[/tex] [ λT]  +   ε2 [1- [tex]f_{λ}[/tex](λT)]

is also solved for reference in calculating fλ

(λ*T) = (5 μm)(1040 K)

       = 5200 μm K

[tex]f_{λ}[/tex]= 0.0003921333  when referencing this to a blackbody function.

Moving on, we solve for T1040 using the equation above:

ε = ε1 [tex]f_{λ}[/tex][λT] + ε2[1 -[tex]f_{λ}[/tex]( λT)]

  =0.9 + (0.15-0.9)0.0003921333  

  =0.899705900025

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The area of a bull's eye is equal to: B. 452.39 mm².

The area of a circle simply refers to the region enclosed or space occupied by a circle within its boundary, and in a two-dimensional plane.

Mathematically, the area of a bull's eye can be calculated by using this formula:

Area of bull's eye = πr²

Where:

r is the radius of a circle.

Note: The radius of the bull's eye is equal to 12 mm and π = 3.14159.

Substituting the given parameters into the formula, we have;

Area of bull's eye = π × (12)²

Area of bull's eye = 3.14159 × 144

Area of bull's eye = 452.39 mm².

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The value of y is 24 when x is 7.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

There are direct variations

y= 24 when x=2

We need to find value of y when x =7

This can be found by forming an equation.

Let the value of unknown y be a

2/24=7/a

Apply cross multiplication

2a=24(7)

2a=168

We need to divide by 2 on both sides

a=24

Hence the value of y is 24 when x is 7.

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A bit string of length 5 contains 2^5 = 32 potential values because each bit has two possible values.

The quantity of bits in a bit string determines its length. When the bit string is produced, this precise non-negative integer is fixed. The exact non-negative integers that are smaller than the bit string's length are the valid indexes. Bit strings can have zero bits or more. A series of bits is known as a bit string. Bit strings can be used to modify binary data or represent sets. In right to left order, a bit string's elements are numbered from zero to the number of bits in the string minus one.

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The linear equation that represent the amount vaccine that remain is g = 61 - 0.061n. The vaccine remains in the body 24 hours after it was administered 59.536 mg. There were only 5mg of the vaccine remaining in the body after 918.033 hours.

What is rate?

A rate is a unique ratio where the two words are expressed in several units.

Given that the amount of vaccine is 61 mg.

The vaccine leaves the body at a rate of 6.1% per hour.

After 1 hour the body will consume 6.1% = 6.1/100 = 0.061 mg.

After n hour the body will consume 6.1%× n =  0.061n mg.

The remaining amount of vaccine is (61 - 0.061n).

The required linear equation that represent the remaining amount of vaccine is g = 61 - 0.061n.

Putting n =24 in the equation:

g = 61 - 0.061×24

g = 59.536 mg

The vaccine remains in the body 24 hours after it was administered 59.536 mg.

The graph represents that there were only 5mg of the vaccine remaining in the body after 918.033 hours.

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Answer:

Step-by-step explanation:

We know that the area of a triangle is given by :-

Let b be the base (in feet)  of the triangle .

it is given that  , The school wants the height of the triangle to be 6 feet.

Then, the area of triangle will be :-

           (1)

The area of the logo must be at most (less than or equal to) 15 square feet.

i.e. Area ≤ 15 square feet         (2)

Now, Substitute the value of A from (1) into (2) , we get

Divide both sides by 3  , we get

Sam's average score based on the six quizzes is 78%.

The average is the mean, a central tendency value.

We compute the mean by summing the values of a data set and dividing by the number of items in the collection.

In this situation, the average of 5 quizzes multiplied by 5 gives the total score in the 5 quizzes, which resulted in the average score.

This total is added to the score in the sixth quiz to get the total score for the six examinations before dividing the sum by 6, giving the overall average.

The average score in 5 quizzes = 74%

Total score in the 5 quizzes = 370% (74 x 5)

The score on the sixth quiz = 99%

Total score in six quizzes = 469% (370 + 99)

The average score in the 6 quizzes = 78.167% (469/6)

= 78%

Thus, Sam scored an average of 78% on the six tests.

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42 is value of ∠JNM because ∠JNM & ∠KNL are vertically opposite angles.

What is vertically opposite angles?

∠JNM = ∠KNL

4x + 6 = 7x - 21

7x - 4x = 21 + 6

   3x = 27

   x = 27/3

   x = 9

∠JNM = 4 * 9 + 6 = 36 + 6

∠JNM =  42

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The number of months Ben can be a member of the fitness club is 7 months .

In the question ,

it is given that Ben wants to join a fitness club ,

initial membership fees for fitness club is = $49.50

monthly fees for fitness club = $17.50

let the number of months be [tex]=[/tex] x

the total fees that Ben paid = $172

So ,according to the question

the equation to represent the situation is  

49.50 + 17.50x = 172

17.50x = 172 - 49.50

17.50x = 122.5

x = 122.5/17.50

x = 7

Therefore , Ben can be a member of fitness club for 7 months .

The given question is incomplete , the complete question is

Ben wants to join a fitness club. The fitness club charges an initial membership fee of $49.50 and a monthly fee of $17.50 , Ben has $172 to spend on a membership at the fitness club . what is the number of months ben can be a member of the fitness club ?

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Answer:

The object has fallen [tex] \boxed{\sf 289} [/tex] feet from ts intial position.

Step-by-step Explanation:

Given:

Formula:

[tex] \rm v = \sqrt{2gh} [/tex]

Where,

v = velocity (in feet per second)

h = Height fallen (in feet)

g = acceleration due gravity (in feet per second squared) = approximately 32 ft/s²

To find:

How far an object has fallen if its velocity (v) is 136 ft/s

Solution:

By substituting the value of g & v in the formula we get:

[tex]\rm \implies 136 = \sqrt{2 \times 32 \times h} \\ \\ \rm \implies 136 = \sqrt{64h} \\ \\ \rm \implies 64h = {136}^{2} \\ \\ \rm \implies h = \dfrac{ {136}^{2} }{64} \\ \\ \rm \implies h = \dfrac{18496}{64} \\ \\ \rm \implies h = 289 \: ft[/tex]

Answer:6 is the correct answer

Step-by-step explanation:

Because 16 + 20 equals 36 and the sq root of 36 is 6. So you chose the correct answer.

Answer:

6

Step-by-step explanation:

[tex]\sqrt{16+20}[/tex]

[tex]\sqrt{36}[/tex]

6

Answer:

A. y = -4x

B. y = 20

Step-by-step explanation:

A. y = xk

Where k is constant

Substitute y for -8 and x for 2

-8 = 2k

Divide both sides by 2

-8/2 = 2k/2

-4 = k

k = -4

y = x(-4)

y = -4x

B. y when x = 5

y = 5(-4)

y = 20

Answer:

48cm = 480mm

Step-by-step explanation:

1cm = 10mm

48cm = 48 X 10 mm

48cm = 480mm

Answer:

480mm

When converting from cm to mm, multiply by 10.

48 x 10 = 480

The equation, y = 3x - 15, written in standard form is 3x - y = 15

From the question, we are to write the given equation is standard form.

The given equation is

y = 3x - 15

The standard form of a linear equation is

Ax + By = C

Where A, B, and C are constants

x and y are variables

Now, we will write the given equation is the standard form of a linear equation.

y = 3x - 15

Substract y from both sides

y - y = 3x - y - 15

0 = 3x - y - 15

That is,

3x - y - 15 = 0

Add 15 to both sides of the equation

3x - y -15 + 15 = 0 + 15

3x - y = 15

Hence, the standard form is 3x - y = 15

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