There are 600 seats in the Marshall Middles School Auditorium. Students are sitting in 4/5 of the seats in the auditorium. Teachers are sitting in 55 of the seats. How many seats are not being used?

A. 60
B. 65
C. 70
D. 75​

The Vamers live on a corner lot. Often, children cut across their lot to save walking distance. the walking distance that is saved by cutting across their property instead of walking around the lot is 20 feet (to the nearest integer)

information given in the question

hypotenuse = 48 feet

opposite = x

adjacent = x + 6

The problem is solved using the Pythagoras theorem is applicable to right angle triangle.  the formula of the theorem is

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

48² = x² + (x+6)²

2304 = x² + x² + 12x + 36

equating to zero

0 = x² + x² + 12x + 36 - 2304

0 = 2x² + 12x - 2268

2x² + 12x - 2268 = 0

x = 30.808  OR   -36.808

taking the positive value, x = 30.808 feet

adjacent = x + 6 = 30.808 + 6 = 36.808

The total distance

= adjacent + opposite

= 20.808 + 36.808

= 67.616

walking distance saved

= total distance - hypotenuse

= 67.616 - 48

= 19.616

= 19.62 feet (to the nearest hundredth)

= 20 feet (to the nearest integer)

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michael is 4 times as old as brandon and is also 27 years older than brandon. then  the michael is 36 years old.

Let M represents the Michael and B represents the Brandon.

As per the given statement: Michael is 4 times as old as Brandon.

⇒  M= 4 B               .....[1]

Also, it is given that Michael is 27 years older than Brandon.

⇒ M= B+27               .....[2]

Substitute equation [1] into [2] we get;

4B= B + 27

Subtract B from both sides we get;

3B = 27

Divide both sides by 3 we get;

B = 9 years

M=36

Therefore, the michael is 36 years old.

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Recursive algorithm for minimum number of bills needed to make an amount, given n and k denominations:Calculate the minimum number of bills by considering each denomination and recursively reducing the remaining amount

Here's a description and analysis of a recursive algorithm that computes the minimum number of bills needed to make an amount n using a system of k denominations:

Algorithm: MinimumBills(n, denominations)

If n is zero, return 0 (no bills needed).

If n is negative, return infinity (impossible to make the amount).

If n is a value that has already been computed and stored, return the stored value.

Set minBills to infinity.

For each denomination d in the k denominations:

a. If n is greater than or equal to d, recursively call MinimumBills(n - d, denominations) and store the result in numBills.

b. If numBills is less than minBills, update minBills to numBills.

Store minBills for the value of n.

Return minBills.

Analysis:

The recursive algorithm computes the minimum number of bills needed to make the amount n using the given denominations. The algorithm explores all possible combinations of denominations to find the optimal solution.

Time Complexity: The time complexity of the algorithm depends on the values of n and k denominations. Since the algorithm explores all possible combinations, the worst-case time complexity is exponential, \(O(k^n)\).

However, if the denominations are limited and n is relatively small, the algorithm can run in polynomial time.

Space Complexity: The space complexity of the algorithm is determined by the recursion depth, which is equal to n. Therefore, the space complexity is \(O(n).\)

Note: To optimize the algorithm and avoid redundant calculations, you can use memoization by storing the results for previously computed values of n in a lookup table. This can significantly reduce the number of recursive calls and improve the overall performance.

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It is true that one method of conducting a survey involves selecting a sampling of a representative group of people. This is called survey sampling.

Survey sampling is defined as a statistical method that involves selecting and surveying individuals from a particular group of people. The population that is chosen to survey could be based on a range of attributes. The target audience could be a general group like the United States' population or a more specific group, like young adults, voters in California, or male pet owners from New England.

Survey sampling involves three steps, which are:

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Answer:

1) M(x) = 5 + 3x

2) Dependent variable; 3 dollar bills

Independent variable: chores

3) Range is continuous

Domain is discrete

4) Range: 0 ≤ x ≤ 10

Domain: 5 ≤ M ≤ 35

Step-by-step explanation:

We are told he started with 5 number of $1 dollar bills and that every Saturday, he earns 3 more $1 dollar bill.

Thus, total number of $1 bills earned after x number of Saturdays(weekly) is;

M(x) = 5 + 3x

After 10 weeks, total number is;

M(10) = 5 + 3(10)

M(10) = 35

The dependent variable is the 3 more dollar bills earned each Saturday because it depends on chores he completed. While the independent variable is the chores because it doesn't depend on anything.

After 10 weeks, the range and domain will be;

Range: 0 ≤ x ≤ 10

For the; Domain:

For x = 1, M(0) = 5 + 3(0) = 5

M(10) = 35

Thus;

Domain: 5 ≤ M ≤ 35

The range could be all numbers in the interval from 0 to 10. Thus, it is continuous.

Whereas, the domain doesn't contain all the numbers in the interval from 5 to 35. Thus it is Discrete.

Answer:

i am jisoo i am okey

Step-by-step explanation:

jinnie

The required slopes are:

(a) slope = 4

(b) slope = 6/7

(c) slope =  -3

(d) slope = 4

(e) slope = -5/2

We know that,

When a line passing through (x₁, y₁) and (x₂, y₂)

Then  the slope of the line be,

slope (m) = (y₂ - y₁) / (x₂ - x₁)

Using this formula, calculate the slope for each given points

a. (9, 10) and (7, 2)

⇒ slope (m) = (2 - 10) / (7 - 9)

                    = -8/-2 = 4

So, the slope is 4.

b. (-8, -11) and (-1, -5)

⇒ slope (m) = (-5 - (-11)) / (-1 - (-8))

                    = 6/7

So, the slope is 6/7.

c. (5, -6) and (2, 3)

⇒ slope (m) = (3 - (-6)) / (2 - 5)

                    = 9/-3

                    = -3

So, the slope is -3.

d. (6, 3) and (5, -1)

⇒ slope (m) = (-1 - 3) / (5 - 6)

                    = -4/-1

                    = 4

So, the slope is 4.

e. (4, 7) and (6, 2)

⇒ slope (m) = (2 - 7) / (6 - 4)

                    = -5/2

So, the slope is -5/2.

Therefore, the slope of the line that joins (-8, -11) and (-1, -5) is 6/7.

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The stationing of the end of the excavation is Station 2+080.

The volume of fill by end area method is 1440 cubic meters.

The volume of excavation by end area is 1080 cubic meters.

We have,

The stationing of the end of excavation can be determined by adding the given sections to the starting station.

Assuming the starting station is Station 2+020, the end of excavation would be at Station 2+080 (given as Station 2+020 + 60 meters).

To find the volume of fill by end area method, we need to calculate the area of the end section and multiply it by the distance between the start and end stations.

Given that the base for fill is 12 meters and the sideslope for fill is 2:1, the area of the end section can be calculated as follows:

Area of end section = (Base for fill) * (Sideslope for fill)

Area of end section = 12 * (2/1) = 24 square meters

Now, multiply the area of the end section by the distance between the start and end stations (60 meters) to find the volume of fill:

Volume of fill = Area of end section * Distance

Volume of fill = 24 * 60 = 1440 cubic meters

Therefore, the volume of fill by end area method is 1440 cubic meters.

Similarly, to compute the volume of excavation by end area, we calculate the area of the end section (base for cut * sideslope for cut) and multiply it by the distance between the start and end stations. Given that the base for cut is 12 meters and the sideslope for cut is 1.5:1, the area of the end section can be calculated as follows:

Area of end section = (Base for cut) * (Sideslope for cut)

Area of end section = 12 * (1.5/1) = 18 square meters

Multiply the area of the end section by the distance between the start and end stations (60 meters) to find the volume of excavation:

Volume of excavation = Area of end section * Distance

Volume of excavation = 18 * 60 = 1080 cubic meters

Therefore, the volume of excavation by end area is 1080 cubic meters.

Thus,

The stationing of the end of the excavation is Station 2+080.

The volume of fill by end area method is 1440 cubic meters.

The volume of excavation by end area is 1080 cubic meters.

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Answer:

5 blocks

Step-by-step explanation:

5 blocks for every barometer

Answer:

8

Step-by-step explanation:

If you plug in the answers it will give you 9x6= 54 which is wrong and 9x7=63 and 9x9=81 but 9x8=72.

Answer:

C   length = 8

Step-by-step explanation:

Area of Rectangle = lw

A = lw    Substitute l = (2x + 4) ; w = 9

72 = (2x + 4)9

72 = 18x + 36

36 =        -36

36 = 18x

36/18 = x

 2 = x

 Substitute into l = 2x + 4 ; l = 2(2) + 4; l = 4 + 4 ; l = 8

The probability that the temperature on a given day in February is 22º or lower is 0.16

The kind of distribution you'll choose as your foundation for your calculations will determine how to calculate probability with mean and deviation. We'll be working with scattered data in this case.

You can build models of your data using the usual distribution if you have data with a mean and standard deviation. By standardizing the normal distribution, we may determine the probability contained within this set of data based on its mean and standard deviation.

Given that: Average Temperature μ = 30.2°

Standard Deviation of Temperature σ = 8.5

Probability that the temperature is 22° or lower:

P[ X ≤ 22 ]

Let x be Temperature on a given day.

to calculate required probability.

Z = (x - μ)/σ

Z = (22-30.2)/8.5

Z = -0.965

First we convert X into Z using this relationship,

Now, Probability [ Z ≤ -0.965 ] = 0.16

The probability that temperature on a given day in February is 22º or lower is 0.16

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To find the sum of the first 26 terms of an arithmetic series, we need to use the formula for the sum of an arithmetic series.

The sum of an arithmetic series can be calculated using the formula:

Sn = (n/2)(a1 + an),

where Sn is the sum of the series, n is the number of terms, a1 is the first term, and an is the last term.

In this case, we have the first term a1 = 7 and the number of terms n = 26.

To find the last term, we can use the formula for the nth term of an arithmetic series:

an = a1 + (n-1)d,

where d is the common difference.

Since we are not given the common difference in the problem, we cannot determine the exact value of the last term an.

Therefore, without knowing the common difference, we cannot calculate the sum of the first 26 terms of the arithmetic series. None of the given answer choices (a, b, c, d) are valid in this case.

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Answer:

-4 is the answer

Step-by-step explanation:

Mark brainliest please if my answer is correct

The chemical formula for ammonium carbonate is (NH₄)₂CO₃. Therefore, option (C) is correct.

When heated, ammonium carbonate, also known as ()2, rapidly breaks down into ammonia and carbon dioxide. It functions as a smelling salt and a leavening agent. Ammonium carbonate, often known as baker's ammonia, was used before baking soda and baking powder as leaveners.

Sal volatile contains ammonium carbonate, and salt of hartshorn when baked emits a strong odour. At standard pressure and temperature, two processes lead to the gradual breakdown of ammonium carbonate. The pure ammonium carbonate sample will combine with different byproducts.

Upon spontaneous dissociation, ammonium carbonate can separate into ammonium bicarbonate and ammonia. which results in the addition of more ammonia, carbon dioxide, and water.

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Answer:

The formula for the ammonium ion: NH4+

The formula for the nitrate ion: NO3–  

A chromate ion consists of four oxygen atoms bonded to a chromium atom. It has two extra electrons. The formula of this ion: CrO42–

Heres all three. Hope i helped

Answer: 156!

Step-by-step explanation: i’m not going to lie, i guessed but, i ended up getting it right .

Answer:

5)23.80

Step-by-step explanation:

71.40/3=23.8

Have a nice Day , I would appreciate it if you could mark my answer brainliest

Answer:

Total earning in the summer = $1440

Step-by-step explanation:

Earning per hour for Samuel = $7.50

No. of hours worked in a day = 6

Earning for a day = Earning per hour for Samuel *No. of hours worked in a day

Earning for a day =  $7.50 *6 = $45

___________________________________________________

No of days worked in a week by Samuel = 4

Earning for week = Earning for a day *No of days worked in a week by Samuel

Earning for week =  $45*4 = $180

_____________________________________________________

No. of weeks worked in summer = 8

Total earning in the summer = Earning for week *No. of weeks worked in summer

Total earning in the summer =  $180*8 = $1440  (Answer)

On a circle with a radius of 4 and center at (0, 0), to find the x and y coordinates at an angle of 180 degrees (or π in radian measure), we can use the trigonometric functions.

At 180 degrees, the x-coordinate will be 0, as it lies on the y-axis. The y-coordinate can be found by using the sine function.  Using the equation y = r * sin(θ), where r is the radius and θ is the angle in radians, we can substitute the values. In this case, r is 4 and θ is π (since 180 degrees equals π radians).

Therefore, the x-coordinate is 0 and the y-coordinate is 4 * sin(π) = 0. So, the x-coordinate is 0 and the y-coordinate is also 0.
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The output value of f(1) in the function f(x) = 4 + 2x is 6.

A function is simply a relationship that maps one input to one output, that is, each x-value can only have one y-value.

Given the data in the question;

To determine the output value of f(1), replace all the occurrence of x with 1 in the function and simplify

f(x) = 4 + 2x

f(1) = 4 + 2(1)

Multiply 2 and 1

f(1) = 4 + 2

Add 4 and 2

f(1) = 6

The output value of f(1) in the function f(x) = 4 + 2x is 6.

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Answer:

A, B, D, E

Step-by-step explanation:

Given expression:

When multiplying decimals, multiply as if there are no decimal points:

\(\implies 6 \times 154 = 924\)

Count the number of digits after the decimal in each factor:

Therefore, there is a total of 5 digits.

Put the same number of total digits after the decimal point in the product:

\(\implies (0.06) \cdot (0.154)=0.00924\)

-----------------------------------------------------------------------------------------------

Answer option A

\(\boxed{6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}}\)

When dividing by multiples of 10 (e.g. 10, 100, 1000 etc.), move the decimal point to the left the same number of places as the number of zeros.

Therefore:

\(\implies 6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}=(0.06) \cdot (0.154)\)

Therefore, this is a valid answer option.

Answer option B

\(\boxed{6 \cdot 154 \cdot \dfrac{1}{100000}}\)

Multiply the numbers 6 and 154:

\(\implies 6 \times 154 = 924\)

Divide by 100,000 by moving the decimal point to the left 5 places (since 100,000 has 5 zeros).

\(\implies 6 \cdot 154 \cdot \dfrac{1}{100000}=0.00924\)

Therefore, this is a valid answer option.

Answer option C

\(\boxed{6 \cdot (0.1) \cdot 154 \cdot (0.01)}\)

Again, employ the technique of multiplying decimals by first multiplying the numbers 6 and 154:

\(\implies 6 \cdot 154 = 924\)

Count the number of digits after the decimal in each factor:

Therefore, there is a total of 3 digits.

Put the same number of digits after the decimal point in the product:

\(\implies 0.924\)

Therefore, as (0.06) · (0.154) = 0.00924, this answer option does not equal the given expression.

Answer option D

\(\boxed{6 \cdot 154 \cdot (0.00001)}\)

Again, employing the technique of multiplying decimals.

As there are a total of 5 digits after the decimals:

\(\implies 6 \cdot 154 \cdot (0.00001)=0.00924\)

Therefore, this is a valid answer option.

Answer option E

\(\boxed{0.00924}\)

As we have already calculated, (0.06) · (0.154) = 0.00924.

Therefore, this is a valid answer option.

the number of different possible teams that can be formed is equal to nCr, or n!/(r!(n-r)!).

Assuming that the state narcotics bureau has more than 5 agents from which to choose, the number of different possible teams that can be formed is equal to the number of combinations of 5 agents out of the total number of agents the bureau has. This can be calculated using the formula nCr (n choose r), where n is the total number of agents and r is the number of agents in each team, which in this case is 5.

Therefore, the number of different possible teams that can be formed is equal to nCr, or n!/(r!(n-r)!).

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Answer: Choice E

Explanation:

Alternate interior angles are ones that are inside the parallel lines (aka interior) and on alternating sides of the transversal cut. When we have parallel lines like this, alternate interior angles are congruent.

Answer:

6,336 inches, 0.1 mile, and 176 yards

Step-by-step explanation:

I just looked it up lol

Answer:

10 ml

Step-by-step explanation:

This is the volume for Zinc!

Answer:

Point A

Step-by-step explanation:

Point A is at ( -4, 4)

It was translated 3 units right, which means the x increased by 2.

So, the point is at (-2,4), and the answer is A.

The statement that proves that angle XWY is equal to angle ZYW is

A. If two parallels are cut by a transverse, then alternate interior angles are congruent

Alternate interior angles are a pair of angles that are formed on opposite sides of a transversal line when two parallel lines are intersected by the transversal.

When a transversal intersects two parallel lines, it creates eight angles. Among these angles, the alternate interior angles are located on the inside of the parallel lines and on opposite sides of the transversal.

In a parallelogram, the two opposite sides are parallel to each other hence the line crossing them will lead to formation of alternate interior angles

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Hi nice to meet u ! U seem like such a sweet cool person-----------------------------------------------------------i need friends too :)

Answer:

hi same im from the us and my fist language is Spanish also i hate math but like history and i like anime favorite anime is AOT favorite manga is berserk and favorite game to play is terraria

Step-by-step explanation:

Answer:14.13ft2

Step-by-step explanation: pi=3.14

3.14 x 4.5ft = 14.13ft2

Answer:

I beleive the answer is C

Step-by-step explanation:

Correct me if im wrong, but im pretty sure c is the most logical answer, next to D