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Considering the definition of area and volume, the hardwood floors​ will cost $1,125.

The area of ​​a two-dimensional figure describes the amount of surface that the figure covers, that is, it represents the region covered by the figure in space.

A cube is a regular figure made up of 6 equal squares. So the floor of the room will be a square, whose area is calculated from one of its sides. The area is calculated as the product of the base times the height of the square, and since both are equal, the area will be one side squared:

Area= side²

Volume is a measure of the space occupied by an object in three-dimensional space, that is, it corresponds to the space that the figure occupies.

The volume of a cube is equal to the measure of its side to the cube. That is to say:

Volume = side×side×side = side³

In this case, you know:

First, you need to find the area of ​​the floor, so you need to find the length of one side of the room. For that, you use the definition of volume:

3375 ft³ = side³

Solving:

∛3375 ft³= side

15 ft= side

The side length of the room is 15. Since all sides of the room are the same, this means that the area of the floor is:

Area of the floor= (15 ft)²

Solving:

Area of the floor= 225 ft²

The contractor charges ​$5 per square foot. Thus, the total cost will be:

Total cost= 225 ft²×​$5 per square foot

Total cost= $1,125

Finally, the hardwood floors​ will cost $1,125.

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Answer

Question 1

4 pants

11 shirts

Question 2

Shady has 30 video games.

Preston has 19 video games.

Question 3

1 muffin costs $1.5

1 quart of milk costs $3

Explanation

Question 1

Let the number of shirts be s

Let the number of pants be p

She bought a total of 15 shirts and shirts

s + p = 15

She bought 7 more shirts than pants.

s = 7 + p

So, we can solve the simultaneous equation.

s + p = 15

s = 7 + p

Substitute for s in equation 1

s + p = 15

7 + p + p = 15

7 + 2p = 15

2p = 15 - 7

2p = 8

Divide both sides by 2

(2p/2) = (8/2)

p = 4 pants

s = 7 + p = 7 + 4 = 11 shirts

Question 2

Let the number of games Shady has be s

Let the number of games Preston has be p

Together, they have a total of 49 video games

s + p = 49

Shady has 11 more games than Preston.

s = 11 + p

So, we can solve the simultaneous equation.

s + p = 49

s = 11 + p

Substitute for s in equation 1

s + p = 49

11 + p + p = 49

11 + 2p = 49

2p = 49 - 11

2p = 38

Divide both sides by 2

(2p/2) = (38/2)

p = 19 video games

s = 11 + p = 11 + 19 = 30 video games

Question 3

Let the cost of a muffin be m

Let the cost of a quart of milk be q

The cost of 8 muffins and 2 quarts of milk is $18.

8m + 2q = 18

The cost of 3 muffins and 1 quart of milk is $7.50

3m + q = 7.5

So, we can solve the simultaneous equation

8m + 2q = 18

3m + q = 7.5

Solving this,

m = 1.5 dollars

q = 3 dollars

Hope this Helps!!!

The new volume of the prism after applying a scale factor of 1.75 to the dimensions is 2520 cubic inches.

To find the new volume of the prism, we need to apply the scale factor to all three dimensions (length, width, and height) and then find the product of the new dimensions.

Let's say the original dimensions of the prism are:

Length = L inches

Width = W inches

Height = H inches

Then, the new dimensions after applying a scale factor of 1.75 will be:

New length = 1.75L inches

New width = 1.75W inches

New height = 1.75H inches

The new volume will be:

New volume = (1.75L) x (1.75W) x (1.75H) cubic inches

New volume = 4.578125LWH cubic inches

We don't know the exact values of L, W, and H, so we can't calculate the new volume in cubic inches. However, we can use the answer choices to see which one matches the calculated formula.

Let's substitute the answer choices for the new volume and see which one matches:

a. 7717.5 cubic in = 4.578125LWH

b. 2520 cubic in = 4.578125LWH

c. 4410 cubic in = 4.578125LWH

d. 2262.6 cubic in = 4.578125LWH

The only answer choice that matches the formula is (b) 2520 cubic inches.

Therefore, the new volume of the prism after applying a scale factor of 1.75 to the dimensions is 2520 cubic inches.

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Answer:

The lines mean "Absolute Value"

Step-by-step explanation:

"Absolute Value" is always positive. So the problem is actually, 2+3-24/3*2

Only the term "-2-3" is inside the lines so they are the only numbers that have to be or change to positive.

Answer:

-11

Step-by-step explanation:

Those lines are called Absolute Value which can be thought of the distance of the number away from zero.

| -2 - 3 | - 24/3 x 2

1) first we solve the absolute value.

| -5 | -24/3 x 2

2) then we know absolute value is the number from 0 so -5 would be +5 and we can remove the lines because we solved the absolute value.

5 -24/3 x 2

3) solve.

5 - 8 x 2

5 - 16

-11

Have a great day or night :)

The rectangular parking lot's area, which is 54.0 ft wide and 117 ft long, is 5718 square feet. The area of the parking lot is 531.7 square meters.

To convert square feet to square meters, you must first multiply by 0.3048. Because the area is in square feet, we must first calculate it and then convert it to square meters. Area of parking lot = length * breadth = 117 * 54 = 6318 square feet. Now we will convert the square feet to square meters by multiplying by 0.3048 as mentioned above.

Area of parking lot in square meters = 6318 * 0.3048² = 531.7 square meters. Therefore, the area of the rectangular parking lot is 531.7 square meters.

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The scenario which might be represented by the

expression below -100/4 is "Owing $100 on a credit card and making four equal payments totaling $25 each".

-100/4

= $-25

Hence, the expression is represented by the statement "Owing $100 on a credit card and making four equal payments totaling $25 each".

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The absolute maximum and absolute minimum values of f on the given interval f(t) = 2 cos (t) + sin (2t), [0, π/2] is 3√3/2 and 0 respectively.

Given :Y = 2cost + sin2t

differentiate wrt t

dy/dt = -2sint +2cos2t = 0

sint = cos2t = 1 - 2sin²t

2sin²t + sint -1 = 0

2sin²t + 2sint - sint - 1 = 0

2sint (sint +1 ) -(sint+1) = 0

sint = 1/2 and -1

but  t € [ 0, π/2 ] so, sint = 1/2 = sinπ/6

t = π/6

again, differentiate wrt t

d²y/dt² = -2cost -4sin2t

put t = π/6

d²y/dt² = -2× √3/2 - 4×√3/2 < 0

hence, d²y/dt² < 0

So, at t = π/6 function gain, Maxima

now,

f(0) = 2cos(0) +sin2(0) = 2

f(π/6) = 2cos(π/6) + sin2(π/6) = 3√3/2

f(π/2) = 2cos(0) + sin2(π/2) = 0

hence , absolute maximum = 3√3/2

and absolute minimum = 0

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Answer:

D: 20h + 45 = 165

Step-by-step explanation:

20 for EACH hour means that there's a variable (h) attached to 20 so it has to be 20h

Because of that, we can eliminate choices A and B.

Charges mean that it's ADDED to the price so it has to be 45 PLUS 20h

20h + 45 = 165

Answer:

Step-by-step explanation:

Answer:1 1/12

Step-by-step explanation: 3/4+1/3=13/12=1 1/12

The domain of the function f(x) is R and the range of the function f(x) is [3, ∞).

The given function is f: R → R, defined by f(x) = |x - 4| + 3. Now, we need to find the domain and range of the function f(x).

Let's consider the given function, f(x) = |x - 4| + 3.

We know that the domain of any function is the set of all real numbers for which the function is defined.

Hence, the domain of f(x) is R. Next, we need to find the range of the function. Range is the set of all possible values of the function.

To find the range of the function, we will first consider the possible values of |x - 4|, which is always positive or zero.

Now, the possible values of |x - 4| are:

|x - 4| = 0 when x = 4.

|x - 4| > 0 for all other values of x.

If we add a positive number to a positive number, the result will always be a positive number.

If we add a positive number to zero, the result will always be positive.

Thus, |x - 4| + 3 > 3 for all values of x.

Hence, the range of f(x) is [3, ∞).

Therefore, Domain = R and Range = [3, ∞).

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Solution

- The question asks us for which property is used in the following equation

- The question uses the Commutative Property of Multiplication.

- This property is stated below:

Final Answer

The answer is Commutative Property of Multiplication

The value of x is  46°

What is Transversal line?

A transversal is a line in geometry that connects two lines in the same plane at two different places. When determining whether two or more other lines in the Euclidean plane are parallel, transversals are important.

Given,

m || n

And there is a transversal line

Since, Sum of angle x and 134 is 180

and, The maximum angle on the straight line is 180

Therefore,

              x + 134° = 180°

              x = 180° - 134°

              x = 46°

Hence, The value of x is 46°

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The possible lengths for the widths of the machine parts is w = 3.63 inches and w = 3.55 inches

Given data ,

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Now , width of a machine part is designed to be 3.59 inches

And , manufacturing tolerance is within 0.04 inches

So , the possible widths of the machine be w

where w = 3.59 ± 0.04

On simplifying , we get

w = 3.63 inches and w = 3.55 inches

Hence , the percentage error is solved

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Answer:

There are 14 marbles in each red jar and 2 marbles in the blue jar

Step-by-step explanation:

There are two red jars of marbles and one blue jar of marbles.

Let the number of marbles in the red jar be x.

Let the number of marbles in the blue jar be y.

There are 30 marbles in total. This means that:

2x + y = 30 _____________ (1)

The difference between the number of marbles in a red jar and the number of marbles in a blue jar is 12. This means that:

x - y = 12 ______________(2)

We have a system of simultaneous equations:

2x + y = 30 _____________ (1)

x - y = 12 ______________(2)

Add them together:

3x = 42

=> x = 42/3= 14

Put the value of x in (2)

14 - y = 12

=> y = 14 - 12 = 2

Therefore, there are 14 marbles in each red jar and 2 marbles in the blue jar.

Answer:

using the formula

y= mx+ c

comparing these;

m= -5/8

when two lines are parallel they are always equal

so the slope of line k= -5/8

Step-by-step explanation:

PLS MARK BRAINLIEST

Answer:

- Life insurance: provides benefits to a policyholder's beneficiary (or beneficiaries) when the policyholder dies

- Health insurance: pays for medical treatment in the event of an illness

- Property and casualty insurance: covers damages to property

- Disability insurance: provides for the replacement of earned income lost because of a person's inability to work

The Matching of insurance is

1. Life insurance: provides benefits to a policyholder's beneficiary (or beneficiaries) when the policyholder dies

2. Health insurance: pays for medical treatment in the event of an illness

3. Property and casualty insurance: covers damages to property

4. Disability insurance: provides for the replacement of earned income lost because of a person's inability to work.

We know that,

Life insurance pays benefits to the beneficiary (or beneficiaries) of the policyholder in the event of the policyholder's demise.

and, Medical care is covered by health insurance in the event of illness.

and, Property and casualty insurance: protects against loss of or damage to property

and, Disability insurance replaces lost income from employment due to an individual's inability to do so.

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Using a unitary method, we have identified that the smaller pot has more water.

To compare the amount of water in the two pots, we need to find a common unit of measurement. In this case, both pots are measured in cups, so we can simply compare the number of cups in each pot. The chef filled the larger pot with 3.7 cups of water, and the smaller pot with 7.3 cups of water.

Now, we can use a unitary method to compare the two quantities. Let's assume that one cup is our unit of measurement. To find out how many cups of water are in the smaller pot, we can divide 7.3 by 1 cup. This gives us 7.3 cups of water. To find out how many cups of water are in the larger pot, we can divide 3.7 by 1 cup. This gives us 3.7 cups of water.

As we can see, the smaller pot has more water than the larger pot.

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Rounding to the nearest tenth: x = 7.6

What is an angle bisector?

An angle bisector is a line or segment that divides an angle into two congruent angles. It is called an angle bisector because it bisects, or cuts in half, the measure of the angle. An angle bisector can also divide the angle into two angles of different measures if the angle is not congruent.

In order to find x, we can use the Angle Bisector Theorem which states that the ratio of the length of the segment from the vertex of the angle bisector to the sides of the angle is equal to the ratio of the length of the other two segments formed by the angle bisector.

In this case, we know that QT is an angle bisector of angle X, so we can set up the following proportion:

(ST/x) = (TR/XT)

We are given that ST = 21, TR = 32 and XT = 18

Solving for x:

x = (21*18) / (32+18) = 378 / 50 = 7.56

Hence, Rounding to the nearest tenth: x = 7.6

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Answer:

x=2, y=6

Step-by-step explanation:

Ensure that the function is non-negative for all values of x and y. This is because a probability density function represents the probability of an event occurring, and probabilities cannot be negative.

Verify that the function integrates to 1 over the range of values for x and y. This means that the sum of probabilities of all possible outcomes must equal 1.

Check that the function is well-defined for all values of x and y. This means that the function should not have any singularities or discontinuities that would affect the calculation of probabilities.

Verify that the function satisfies the marginal probability density functions for x and y. This means that the probability density function for x and y, obtained by integrating the joint probability density function over the other variable, must satisfy the conditions for probability density functions.

Check that the function satisfies the independence property. This means that the joint probability density function must factorize into the product of the marginal probability density functions for x and y if the variables x and y are independent.

Finally, simulate the probability distribution using a computer program and compare the simulation results with the expected values from the probability density function.

By following these steps, you can verify that a probability density function f(x,y) is valid and can be used to calculate probabilities for events involving the variables x and y.

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AB and YX are corresponding sides, BC and XZ are corresponding sides, and AC and YZ are corresponding sides of given triangle.

What is triangle?

A triangle is a two-dimensional geometric shape that has three sides, three angles, and three vertices. It is one of the simplest polygonal shapes and is commonly studied in geometry.

Since we have:

∠A ≅ ∠Y

∠B ≅ ∠X

∠C ≅ ∠Z

We can conclude that the two triangles ABC and XYZ are similar by the Angle-Angle (AA) similarity theorem.

Therefore, the corresponding sides of the two triangles are proportional to each other. We can write this as:

AB : YX = BC : XZ = AC : YZ

where AB and YX are corresponding sides, BC and XZ are corresponding sides, and AC and YZ are corresponding sides.

In other words, the ratio of the length of each side in triangle ABC to the corresponding side in triangle XYZ is constant.

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Answer:

\(\sqrt{28} = 2\sqrt{7}\)

\(\sqrt {500} = 10 \sqrt {5\)

\(\sqrt {162} = 9 \sqrt {2\)

Step-by-step explanation:

Given (Correct Parameters)

\(\sqrt {28\)

\(\sqrt {500\)

\(\sqrt {162\)

Required

Express in simplified form

\(\sqrt {28\)

Express 28 as 4 * 7

\(\sqrt{28} = \sqrt{4} * \sqrt{7}\)

Take positive square root of 4

\(\sqrt{28} = 2 * \sqrt{7}\)

\(\sqrt{28} = 2\sqrt{7}\)

\(\sqrt {500\)

Express 500 as 100 * 5

\(\sqrt {500} = \sqrt {100} * \sqrt {5\)

Take positive square root of 100

\(\sqrt {500} = 10 * \sqrt {5\)

\(\sqrt {500} = 10 \sqrt {5\)

\(\sqrt {162\)

Express 162 as 81 *2

\(\sqrt {162} = \sqrt {81} * \sqrt {2\)

Take positive square root of 81

\(\sqrt {162} = 9 * \sqrt {2\)

\(\sqrt {162} = 9 \sqrt {2\)

Answer:

You have to apply Trigonometry Formula :

\( {sin}^{2} θ + {cos}^{2} θ = 1\)

\(1 + {tan}^{2} θ = {sec}^{2} θ\)

Next, you have to prove it :

\((1 + {tan}^{2} θ)(1 - {cos}^{2} θ) = {tan}^{2} θ\)

\(LHS = (1 + {tan}^{2} θ)(1 - {cos}^{2} θ)\)

\(LHS = ( {sec}^{2} θ)( {sin}^{2} θ)\)

\(LHS = ( \frac{1}{ {cos}^{2} θ} )( {sin}^{2} θ)\)

\(LHS = \frac{ {sin}^{2} θ}{ {cos}^{2} θ} \)

\(LHS = {tan}^{2} θ\)

\(∴LHS = RHS \: (proven)\)

Alex can make a total of 180 different sandwiches by choosing one kind of meat from 10 options and two kinds of cheese from 9 options.

To determine the number of different sandwiches Alex can make, we need to consider the combinations of meat and cheese. Since Alex can choose one kind of meat from 10 options, there are 10 choices for the meat component of the sandwich. For the cheese component, Alex can choose two kinds of cheese from 9 options.

To calculate the total number of combinations, we can use the formula for combinations without repetition. The formula is nCr = n! / (r!(n-r)!), where n is the total number of options and r is the number of choices. In this case, n is 9 (number of cheese options) and r is 2 (number of cheese choices). Thus, the number of combinations of two kinds of cheese is \(9C2\)= 9! / (2!(9-2)!) = 36.

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Answer:

I Deleted the Answer as i felt cheating was bad.

Note: If I am not mistaken, this is part of the Senior Challenge '22 Year 10 or below, which is part of the Mathematical Education Of Merseyside. This competition should be done during the February half term and seeing as I am also in high school and it is currently my February half term, I believe (although i may be very wrong) you are cheating. :)

It took him 2.6 hours to reach the top

Data;

Let us calculate the speed during uphill and downhill

Since the time it took them to descend is twice the time it took them to ascend,

\(x + 2x = 8 hours\\3x = 8\\x = \frac{8}{3} \\x = 2.6 hours\)

From the calculation above, it took him 2.6 hours to reach the top.

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