A hallway measuring 90 feet x 7 feet requires 1/2 a fluid ounce of cleaning solution per square foot. How much cleaning solution is required to clean the hallway

Answer: 0.65a = 39

Step-by-step explanation:

To calculate S(4), substitute the value of t with 4 into the function S(t), which results in S(4) = 9(4) - 4, giving the final answer of 32.

To find S(4), we need to substitute the value of t with 4 in the function S(t) = 9t - 4. This is a simple evaluation of a function for a given input.

Step-by-step calculation:

Therefore, S(4) is 32.

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Answer:

(a) 10π cm

(b) r = 5 cm

(c) h = √11 cm

Step-by-step explanation:

(a) The surface of the opening the cup is circular in shape and a sector is cut from circle is calculate by formula,

C = r × θ

here, r = 6 cm

and θ = [tex]\frac{5\pi}{3}[/tex]

⇒ [tex]C = 6 \times \frac{5\pi}{3} = 10\pi[/tex]

(b) For finding the radius of the cup,

As the circumference of the circle is 10π

and we know that area of cone is calculate by formula, 2πr

⇒ 2πr = 10π

⇒ r = 5 cm

(c) In cone we know slant height(l) = 6 cm

Radius = 5 cm

Thus, using Pythagoras theorem,

l² = h² + r²

⇒ h² = l² - r²

⇒ h² = 36 - 25

⇒ h = √11 cm

To find the height of the triangle with an area of 64 square kilometers and a base twice its height, we use the area formula: A = (1/2) × base × height, which leads us to determine that the height is 8 kilometers.

The question given involves finding the height of a triangle when the area is known and the relation between the base and height is given. Since the base is twice the height (b = 2h), and we know the formula for the area of a triangle is A = (1/2) × base × height, we can substitute the known area and the base-height relationship into this formula to solve for the height.

The area (A) is given as 64 square kilometers, which leads to the equation:

A = (1/2) × b × h = (1/2) × (2h) × h = h²,

Therefore, with A = 64 km², we obtain:

64 = h².

Taking the square root of both sides gives us the height (h):

h = √64 km = 8 km.

So the height of the triangle is 8 kilometers.

The width of the room is 7 meters and the length is 10.5 meters.

To find the dimensions of the rectangular room, let's assume the width of the room is x meters. According to the given information, the length of the room is 1.5 times the width, so the length would be 1.5x meters.

The perimeter of a rectangle is calculated by adding twice the length to twice the width. So, we have the equation:

2x + 2(1.5x) = 35

Simplifying the equation, we get:

2x + 3x = 35

Combining like terms, we have:

5x = 35

Dividing both sides of the equation by 5, we find that x = 7.

Therefore, the width of the room is 7 meters and the length is 1.5 times the width, which is 1.5 * 7 = 10.5 meters.

There are 23,490,600 committees that can be formed if each committee must have 3 Republicans and 2 Democrats

Used the concept of combination which states that,

A combination is a technique to determine the number of possible arrangements in a collection of items where the order of the selection does not matter.

Given that,

The Senate in a certain state is comprised of 51 Republicans, 48 Democrats, and 1 independent.

Since we have 51 Republicans,

So we can choose 3 Republicans out of 51 in [tex]^{51} C_3[/tex] ways.

Similarly, we have 48 Democrats, so we can choose 2 Democrats out of 48 in [tex]^{48} C_2[/tex] ways.

Hence, the number of committees:

[tex]^{51} C_3 \times ^{48} C_2[/tex]

Using the formula for combinations,

[tex]^{n} C_r = \dfrac{n!}{r! (n - r)!}[/tex]

[tex]= \dfrac{51!}{3!(51 - 3)!} \times \dfrac{48!}{2!(48 - 2)!}[/tex]

[tex]= \dfrac{51!}{3!(48)!} \times \dfrac{48!}{2!(46)!}[/tex]

[tex]= \dfrac{51 \times 50 \times 49 \times 48!}{3!(48)!} \times \dfrac{48\times 47 \times 46!}{2!(46)!}[/tex]

[tex]= \dfrac{51 \times 50 \times 49 }{3!} \times \dfrac{48\times 47 }{2!}[/tex]

[tex]= 20,825 \times 1,128[/tex]

So, the number of committees is,

[tex]= 23,490,600[/tex]

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The number is given by -3.

Equation is a mathematical relation between more than one variable, number or mathematical quantities involving mathematical operations using equal sign in between them.

Let the number be x

Five times the number is = 5x

6 more than the number is = x+6

Sum of five times a number and 6 more than the number is = 5x+(x+6) = 5x+x+6 = 6x+6

The difference between -18 and twice the number = -18-2x

According to condition,

6x+6 = -18-2x

6x+2x = -18-6

8x = -24

x = -24/8 = -3

Hence the number is -3.

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The time taken to assemble 125 amplifiers is required.

Time taken to assemble 125 amplifiers is 750 minutes or 12 hours and 30 minutes.

Time taken to assemble 5 amplifiers is 30 minutes

[tex]5\ \text{amplifiers}=30\ \text{minutes}[/tex]

So,

[tex]1\ \text{amplifier}=\dfrac{30}{5}=6\ \text{minutes}[/tex]

[tex]125\ \text{amplifiers}=125\times 6=750\ \text{minutes}=\dfrac{750}{60}=12.5\ \text{hours}[/tex]

So, time taken to assemble 125 amplifiers is 750 minutes or 12 hours and 30 minutes.

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To find the approximate number of red blood cells in a pint of blood, multiply 5 million by 473.We get approximately 2.365 billion red blood cells

To find the approximate number of red blood cells in a pint of blood, we can use the given information. One milliliter of blood contains approximately 5 million red blood cells. And one pint is about 473 milliliters. So, we can set up the equation:

Number of red blood cells in a pint = 5 million x 473

Using scientific notation for the first box of the equation:

Number of red blood cells in a pint = 5 x 106 x 473

Simplifying the equation, we get:

Number of red blood cells in a pint = 2.365 x 109 or approximately 2.365 billion red blood cells

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Answer: Hello mate!

this multiplication can be hard because of the numbers after the decimal point. You could use the next trick.

14.7*10 = 147 and 11.361*1000 = 11361

now you could do the multiplication without concerning about the decimals, and afther that divide it back by 10*1000.

and [tex]14.7*11.361 = \frac{147}{10}*\frac{11361}{1000} = \frac{147*11361}{10*1000}  = \frac{147*11361}{10000} = \frac{1670067}{10000}[/tex]

now you need to divide by 10000, that is equivalent to move the decimal point by 4 ) places to the left.

1670067/10000 = 167.0067

The problem is an optimization problem in mathematics where one must use algebra and calculus to maximize the area of a rectangular parking lot with a given amount of fencing along three sides. By setting up a function for the area in terms of width and differentiating, the maximum area can be found.

The problem presented involves finding the maximum area of a rectangular parking lot given a certain amount of fencing, when one side of the rectangle requires no fencing. This is a classic optimization problem in mathematics which involves the use of algebra and calculus. By setting up a function for the area of the rectangle in terms of one variable and differentiating to find the maximum value, we can determine the solution.

Lets assume that the length of the lot that is along the busy street doesn't require fencing, and let the width of the lot be w and the length be l. Since fencing is only required for three sides, and we have 2,200 feet of fencing, the perimeter equation is 2w + l = 2,200. Solving for l, we get l = 2,200 - 2w. The area A of the parking lot will be given by the equation A = w * l. Substituting the expression for l into the area equation, we get A = w(2,200 - 2w) or A = 2,200w - 2w^2. To find the maximum area, we take the derivative of A with respect to w, set it to zero, and solve for w. Once the width is found, we can find the length using the perimeter equation and thus calculate the maximum area of the lot.

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Jay's error was in the order of operations. The correct result is 17.

Jay's error lies in how he interpreted the expression. According to the order of operations (PEMDAS/BODMAS), multiplication and division should be performed before addition and subtraction.

So, the correct first step is to perform the division [tex]\( \frac{12}{3} = 4 \)[/tex]and then add 3 to the result, not add 3 and 12 together first.

The correct first step:

[tex]\[ 3 \times (3 + \frac{12}{3}) - 4 \][/tex]

[tex]\[ = 3 \times (3 + 4) - 4 \][/tex]

[tex]\[ = 3 \times 7 - 4 \][/tex]

= 21 - 4

= 17

Therefore, Jay's error was in the order of operations. The correct result is 17.

The crescent wrench is a type of lever, a simple machine that amplifies force to provide greater torque on fasteners with less input effort.

The crescent wrench is a type of simple machine, specifically it is a form of a lever. When you use a crescent wrench, you apply force to the handle, which then applies force to the object you are turning. The pivot point, or fulcrum, is the adjustable jaw which grips the nut or bolt. This allows the user to exert a greater torque on the fastener with less force than would be needed if just using one's hands.

Like other levers, the crescent wrench allows for a mechanical advantage, which is the ratio of output to input forces for any simple machine. By lengthening the handle of the wrench (the effort arm), we achieve a greater mechanical advantage, and thus, can apply more torque to the bolt or nut we are trying to turn.