a sign in an elevator says elevator can lift 450 kg. John has 10 boxes that weigh 13.75kg, and a number of additional boxes that weigh 15.5 kg each. If he puts 10 boxes in elevator, how many additional boxes can be lifted in the same load?

The expression can be rewritten by given term as;  3^15

We need to simplify the expression below:

(3^2 x 3^3)^3

Remember that we can add these exponents, so we get:

(9 x 9)^3 = 81^3

Then we can rewrite this as:

531441

Takin the product between the exponents we will get:

(3^5)^3

Thus, the solution is 3^15

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Answer:

15,240,960 numbers

Step-by-step explanation:

To solve this were going to use the principle of permutations. The formula for permutation is given as

P = n! / (n - r)!

Now, the question specifically stated that repeats aren't tolerated, thus for the needed number of serial numbers would be gotten by multiplying the permutation is 4 and 9, by that of the permutation of 4 and 10.

We then have something that is looking like this

Permutation of 4 and 9.

P = 9! / (9 - 4)!

P = 9! / 5!

P = 362,880 / 120

P = 3,024

Permutation of 4 and 10

P = 10! / (10 - 4)!

P = 10! / 6!

P = 3,628,800 / 720

P = 5,040

Multiplying both together would then fetch us our final answer

N = 5,040 * 3,024

N = 15,240,960

Answer:

B. 5/12

Explanation:

Total Letters mixed: {S, E, M, I, T, R, O, P, I, C, A, L} = 12 Letters

There are 5 vowels and they are: 'a', 'e', 'i', ' o', and 'u'

In here the vowels are: E, I, O, I, A = 5 vowels here

So,

probability: number of favourable outcomes/total number of outcomes

probability: 5/12

1) m∠1 = 62°, lines t and l intersect (given)

2) ∠1 and ∠4 are vertical angles (intersecting lines form vertical angles)

3) ∠1 and ∠4 are congruent (vertical angles are congruent)

4) m∠1 = m∠4 (congruent angles have equal measure)

5) 62° = m∠4 (substitution)

6) m∠4 = 62° (symmetric property of equality)

The distance between the points (2, 7/2) and (5/3, 1) is 2.52 units.

Distance between two points is the length of the line segment that connects the two given points. Distance between two points in coordinate geometry can be calculated by finding the length of the line segment joining the given coordinates.

The distance between two points using the given coordinates can be calculated by applying the distance formula. For any point given in the 2-D plane, we can apply the 2D distance formula or the Euclidean distance formula given as,

Let the coordinates of two points are (x₁,y₁) and (x₂,y₂), then

d = √[(x₂-x₁)²+(y₂-y₁)²]

Two points given in the question are (2, 7/2) and (5/3, 1), now putting them in above formula, we get

d = √[(5/3-2)²+(1-7/2)²]

d = √[(-1/3)²+(-5/2)²]

d = √[1/9+25/4]

d = √229/36

d = √6.36

d = 2.52

∴ The distance between the points (2, 7/2) and (5/3, 1) is 2.52 units.

Hence, 2.52 units is the required answer.

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Answer:

First choice.

Step-by-step explanation:

Th first  option.

(x + 1)^2 - 25

The minimum value is -25 because the minimum value of the squared term is 0.   A squared term cannot be negative,

The slope at the line would be the 360 point turn.

Answer:

The answer is (C) BFD

Step by step

We can see that angles DFE and AFB have a common vertex F but they do not have a common side, so the angles are not adjacent. The other options are also incorrect so the answer is C.

Brandon have a total of $32 originally

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

When he spends $24, he has 3/4 of the original amount left

Using the above as a guide, we have the following:

24 = Original * 3/4

Make "Original" the subject of the formula

So, we have the following representation

Original = 24/(3/4)

Evaluate the expression

Original = 32

Hence, the amount is $32

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Answer: The range is 101 degrees.

Using Pythagorean theorem, the length of the ladder is 10ft

In mathematical terms, if y and z are the lengths of the two shorter sides (also known as the legs) of a right triangle, and x is the length of the hypotenuse, the Pythagorean theorem can be expressed as:

x² = y² + z²

In the questions given, the only one we can use Pythagorean theorem to solve is the one with ladder since it's forms a right-angle triangle.

To calculate the length of the ladder, we can write the formula as;

x² = 8² + 6²

x² = 64 + 36

x² = 100

x = √100

x = 10

The length of the ladder is 10 feet

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Answer:

−4−(3)(0)−4−(3)(0)

=−8

Answer:

-2 and 1/3

Step-by-step explanation:

-4+-3+0+-4+-3+0 = -14

6 numbers

-14/6 = -2 1/3

The length of each side of the square is 16 cm, the perimeter is 64 cm, and the area is 256 cm^2.

Let's solve the problem step by step. We have a square ABCD, and we need to find the length of its sides when the diagonal is 16√2 cm long.

In a square, the diagonal forms a right triangle with the sides. The sides of a square are equal in length, so let's assume the length of one side of the square is 'x' cm.

Using the Pythagorean theorem, we can find the relationship between the side length and the diagonal:

x^2 + x^2 = (16√2)^2

2x^2 = 512

Dividing both sides by 2, we have:

x^2 = 256

Taking the square root of both sides:

x = √256

x = 16 cm

So, the length of each side of the square is 16 cm.

To find the perimeter of the square, we simply multiply the length of one side by 4 since all sides are equal:

Perimeter = 4 * 16 cm = 64 cm

To find the area of the square, we square the length of one side:

Area = (16 cm)^2 = 256 cm^2

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Note the complete question is:

Find the length of side of square ABCD when diagonal is 16√2 cm long. Also find the perimeter and area of the square?

Answer:

Refer to the step-by-step explanation.

Step-by-step explanation:

Come up with a monomial expression and solve it.

A monomial expression is an algebraic expression that consists of a single term. It is an expression that can contain variables, constants, and non-negative integer exponents, but there should be no addition or subtraction between different terms.

Here are a few examples of an monomial expression:

\(\hrulefill\)

Let's work with the monomial expression, 3x²y³z.

To solve this expression, I assume you would like to evaluate it for specific values of the variables x, y, and z. So let x=3, y=2, and z=1.

Plug these values into the expression:

3x²y³z

=> 3(3)²(2)³(1)

=> 3(9)(8)(1)

=> 27(8)(1)

=> 216(1)

=> 216

Thus, the expression is solved.

Answer:

165 square feet

Step-by-step explanation:

\((7 - ( - 4))(6 - ( - 9)) = 11 \times 15 = 165\)

It is shown below that the partition of G into left cosets of H is different from its partition into right cosets when n ≥ 3.

Let us first find the left cosets of H in G:

H = {1, s₀}

s₁H = {s₁, s₁s₀}

s₂H = {s₂, s₂s₀}

s₃H = {s₃, s₃s₀, s₂s₁, s₂s₁s₀}...

Now, find the right cosets of H in G:

H = {1, s₀}

Hs₁ = {s₁, s₀s₁}

Hs₂ = {s₂, s₀s₂}

Hs₃ = {s₃, s₀s₃, s₁s₂, s₀s₁s₂}...

Observe that the left cosets of H in G and the right cosets of H in G are not the same when n≥3. This is because s₁s₀ is not in H, but s₀s₁ is in H.

Therefore, the left coset s₁H is not the same as the right coset Hs₁. Similarly, s₂s₁s₀ is not in H, but s₀s₁s₂ is in H, so the left coset s₃H is not the same as the right coset Hs₃.

Thus, it is shown that the partition of G into left cosets of H is different from its partition into right cosets when n≥3.

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Work Shown:

A = old volume (large volume)

A = length*width*height = 7*9*7 = 441 cubic inches

B = new volume (smaller volume)

B = length*width*height = 8*5*5 = 200 cubic inches

C = change in volume = amount volume is reduced

C = A - B = 441-200 = 221 cubic inches

Answer:

24

Step-by-step explanation:

Remark

This can be done with a proportion which consists of 2 equal ratios. That's 4 parts total. If you know 3 of the parts, you can find the 4th.

Givens

Stars1  6

Moon1 4

Starts2 x

Moon2 16

Formula

stars1/moon1 = stars2/moon2

Solution

6/4 = x / 16         Multiply by 16

6 * 16/4 = x

Answer: 96/4 = 24

Answer:

The maximum distance between supports for the beam to support a weight of 1600 lb is also 4.5 feet.

Step-by-step explanation:

We are given that weight P is inversely proportional to the distance D between the supports of the beam, and for this certain type of wooden beam, we have:

P = 7200/D

To find the distance between supports needed to carry 1600 lb, we can substitute P = 1600 in the above equation and solve for D:

1600 = 7200/D

D = 7200/1600

D = 4.5 feet

So the distance between supports needed to carry 1600 lb is 4.5 feet.

To find the maximum distance between supports for the beam to support a weight of 1600 lb, we can use the same equation and solve for P = 1600:

1600 = 7200/D

D = 7200/1600

D = 4.5 feet

Therefore, the maximum distance between supports for the beam to support a weight of 1600 lb is also 4.5 feet.

Given statement solution is :- It  would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

To find the cost of installing tile in the dining room and carpet in the bedroom, we need to calculate the areas of both rooms first.

Given:

Every 2 centimeters on the floor plan represents 1 meter of the house.

Dining Room:

On the floor plan, the dining room is 8 cm by 10 cm.

Converting this to meters, the dimensions of the dining room are 8 cm / 2 = 4 meters by 10 cm / 2 = 5 meters.

The area of the dining room is 4 meters * 5 meters = 20 square meters.

Bedroom:

On the floor plan, the bedroom is 6 cm by 10 cm.

Converting this to meters, the dimensions of the bedroom are 6 cm / 2 = 3 meters by 10 cm / 2 = 5 meters.

The area of the bedroom is 3 meters * 5 meters = 15 square meters.

Now, let's calculate the costs.

Cost of Tile:

The cost of installing tile is $34 per square meter.

The area of the dining room is 20 square meters.

Therefore, the cost of installing tile in the dining room is 20 square meters * $34/square meter = $680.

Cost of Carpet:

The cost of installing carpet is $21 per square meter.

The area of the bedroom is 15 square meters.

Therefore, the cost of installing carpet in the bedroom is 15 square meters * $21/square meter = $315.

Therefore, it would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

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Carlos needs to earn at least 16 points on the final quiz to earn at least a 90% average.

We have,

Let's start by finding the total number of points that Carlos can earn in the class:

Total points

= 5 quizzes x 20 points per quiz

= 100 points

If Carlos needs an average of 90% or greater, that means he needs to earn at least 90 points out of 100.

Total points earned.

= 18 + 19 + 17 + 20

= 74 points

To find the minimum score Carlos needs on the final quiz, we can set up an inequality:

(74 + x) / 5 ≥ 0.9

where x is the score on the final quiz.

Simplifying this inequality.

74 + x ≥ 90

x ≥ 16

Therefore,

Carlos needs to earn at least 16 points on the final quiz to earn at least a 90% average.

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Answer:

C. $32.09, since it's not the fixed cost, it changes based on how much drinks are purchased.

Answer:

i can try :)

Step-by-step explanation:

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

First we will go find the angle measure of 3.

We already know that <1 & <2 are 55° & 60°.

Tip: The sum of all the angles in a triangle is 180°.

So now if we add those two angles we'd get 115°, then we could subtract it from 180 to get the measure of <3, which is 65°.

For <4 it should be easier if you know that line AB is parallel to line CD and then line AC is the transversal because it goes through both lines.

Tip: Alternate interiors are angles that are equal to each other.

Then when you know all this you can figure out that <2 and <4 are alternate interiors which makes them equal to each other. So if they said that <2 is 60° then it'll only make sense if <4 is also 60°.

Now for <5 we know that <3,<4, and <5 are all on a line so that makes the sum of those three angles 180°.

So we would do the sum of <3, <4, then x and all that is equal to 180°.

\(65+60+x=180\\125+x=180\\x=55\)

Great now we know <5 is 55°.

We will now move on to <6. It has the same relationship to <4 as <2 and <4. So if <4 is 60° that means <6 has to be 60°° as well.

Tip: The sum of these two angles (in this case are <5 and <6) are equal to t the outer angle (<7)

Now we have to figure out the measure of <7. First we have to notice that if we add <5 and <6 we will get <7. So 55 + 60 = 115 and that's it <7 is 115°.

Now the recap:

<3=65°

<4=60°

<5=55°

<6=60°

<7=115°

The amount of water left in the tub after 5 minutes is; 24 gallons

The given recursive formula is expressed as;

aₙ = aₙ ₋ ₁ - 12

We are told that a₀ represents the amount of water left, in gallons, in a bathtub n after the drain stopper was pulled.

Thus, when n = 1, we have;

a₁ = a₁ ₋ ₁ - 12

a₁ = a₀ - 12

a₁ = 84 - 12

a₁ = 72

Then;

a₂ = a₁ - 12

a₂ = 72 - 12

a₂ = 60

It will seem that it follows a sequence pattern of;

aₙ = 84 - 12n

Thus;

a₅ = 84 - 12(5)

a₅ = 24 gallons

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The Greatest Common Divisor (GCD) of 85 and 51 is 17.

The greatest common factor that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor is another name for it (HCF).

Explanation

Step 1: Divide 85 by 51. The quotient is 1 and the remainder is 34.

Step 2: Divide 51 by 34. The quotient is 1 and the remainder is 17.

Step 3: Divide 34 by 17. The quotient is 2 and the remainder is 0.

Step 4: Since the remainder is 0, the Greatest Common Divisor (GCD) of 85 and 51 is 17.

The GCD of 85 and 51 is 17.

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Answer:

15000 meters

Step-by-step explanation:

1 kilometer = 1000 meters

Therefore 15 Kilometer = 15 x 1000 = 15000

So Francis drove 15000 meters to get to the store and back.

Answer:

Step-by-step explanation:

If you add up all the male and female categories, the total is 400

the number of females between 22 and 39 is 51

P(22 - 39)  = 51 / 400

P(22 - 39) = 0.1275

I think the answer you want is 51/400

Answer:

$1107.55

Step-by-step explanation:

3,589.90 x .0590/12 = $17.653,589.90 + 17.65 =3,607.553,607.55 - 2,500 = $1,107.55