There 18 rows of seats in the auditorium there are 24 seats in each row how many seats are in the auditorium

Answer:

after the 30 years they would make 2325359.66 so 2025659 dollars and 66 cents.

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

a) To maximize its net savings, the company should use the new machine for 7 years.  b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar).  c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).

Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.

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To eliminate the roots in 1.1 and 1.2, we can use trigonometric substitution. In 1.1, we can substitute x = 4 sin(theta) to eliminate the root of 4. In 1.2, we can substitute z = 7 sin(theta) to eliminate the root of 7.

1.1. V64+2 + 1 We can substitute x = 4 sin(theta) to eliminate the root of 4. This gives us:

V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3 1.2. V4z2 – 49

We can substitute z = 7 sin(theta) to eliminate the root of 7. This gives us:

V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta) (2 – 1) = 7 sin(theta)

Here is a more detailed explanation of the substitution:

In 1.1, we know that the root of 4 is 2. We can substitute x = 4 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 2.

When we substitute x = 4 sin(theta), the expression becomes V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3

In 1.2, we know that the root of 7 is 7/4. We can substitute z = 7 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 7/4.

When we substitute z = 7 sin(theta), the expression becomes: V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta)

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Answer:

C

X=-16

Step-by-step explanation:

Debbie can buy a maximum of 4 t-shirts with the remaining $38 after purchasing the $22 jeans.

To determine the greatest number of t-shirts Debbie can buy, we need to find out how much money she will have left after purchasing the pair of jeans. Debbie has $60 to spend and the jeans cost $22. Therefore, she will have $60 - $22 = $38 left to spend on t-shirts.

Each t-shirt costs $8, so we divide the remaining amount by the cost per t-shirt: $38 / $8 = 4.75.

Since Debbie cannot buy a fraction of a t-shirt, we round down the decimal value to the nearest whole number. Therefore, Debbie can buy a maximum of 4 t-shirts with the remaining $38.

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Answer:

70

Step-by-step explanation:

The answer is 70 because complementary angles mean that two angles add up to 90. So if you do 90 - 20, you get 70.

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Thus, there is a 62.5% chance of getting at least one Canadian quarter when seven quarters are randomly picked from the bag.

To find the probability of getting at least one Canadian quarter when picking seven quarters from the bag, we can use complementary probability. This means we can find the probability of not getting any Canadian quarters and subtract it from 1.

The total number of quarters in the bag is 50.

The probability of getting at least one Canadian quarter out of seven quarters can be calculated as the complement of the probability of getting all U.S. quarters.

The probability of getting a U.S. quarter on the first draw is 46/50.

Since the coin is not replaced after each draw, the probability of getting a U.S. quarter on the second draw is 45/49, and so on.

Therefore, the probability of getting all U.S. quarters in seven draws can be calculated as follows:

= (46/50) x (45/49) x (44/48) x (43/47) x (42/46) x (41/45) x (40/44)

= 0.375

So, the probability of getting at least one Canadian quarter out of seven draws is:

1 - 0.375 = 0.625 or 62.5%

Therefore, there is a 62.5% chance of getting at least one Canadian quarter when seven quarters are randomly picked from the bag.

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Answer:

Ok, first of all, that's not an inequlity. An inequality includes < or >, and also ≤ or ≥. 7 is not an inequality, so perhaps you made a mistake typing the question?

Step-by-step explanation:

Answer:

its B :)

Step-by-step explanation:

I hope this helps ^^

Answer:

= 49

Step-by-step explanation:

\(\frac{-7^{7} }{-7^{5} }\)

= -7⁷⁻⁵

= -7²

= -7*-7

= 49

Answer:

The two possible solutions are x = 7, or x = -2

which agree with answer a) in the list of options

Step-by-step explanation:

Start by moving all terms to one side of the equal sign, and then factoring out the constant term:

\(x^2-5x-14=0\)

The constant term  "-14" has ossible factors: (-1), (1) (-2), (2), (-7), (7), (-14), (14) and we look for a pair whose combining results in "-5" (the coefficient of the middle term. We find (-7) and (2) the appropriate factors, so we use then to split the middle term and then factor by grouping:

\(x^2-5x-14=0\\x^2-7\,x+2\,x-14=0\\x(x-7)+2(x-7)=0\\(x-7)\,(x+2) = 0\)

Then if the product of these two binomial factors is zero, it means that the first binomial is zero, or the second one is zero. That is:

( x - 7 ) = 0  which means x = 7

or

( x + 2 ) = 0   which means  x = -2

So the two possible solutions are x = 7, or x = -2

Answer:

Step-by-step explanation:

\(x^2-5x=14\\\\x^2-5x-14=0\\\\x^2+2x-7x-14=0\\\\x(x+2)-7(x+2)=0\\\\(x+2)(x-7)=0\\\\x+2=0\quad\vee\quad x-7=0\\\\x=-2\quad\vee\quad x=7\)

The new coordinates of the image are

A' (1, -5)  

B' (5, -3)

C' (3, -1)

The coordinates of the preimage are

A (1, 3)

B (5, 1)

C (3, -1)

The absolute distance of the y coordinates to line y = -1 is obtained and added used to get the distance from -1 in any side of the reflection

Reflection over line y (x, y) → (x, -y) this considers only the y values

A (1, 3) from 3 to -1 is 4 units hence -1 - 4 = -5 = A' (1, -5)  

B (5, 1) from 1 to -1 is 2 units hence -1 - 2 = -3 = A' (5, -3)  

C (3, -1) from -1 to -1 is 0 units hence -1 - 0 = -1 = A' (3, -1)  

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Answer:

7/24

Step-by-step explanation:

The fraction was left

1-3/8=5/8

5/8-1/3=7/24

So your answer is 7/24

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Answer:

400 is the answer to the botom and a b c and d

Step-by-step explanation:

Answer:

2 \(\leq\) x < 7

Step-by-step explanation:

-9 \(\geq\) -3x - 3 > -24

Step 1: Add 3 to all sides; -6 \(\geq\) -3x > -21

Step 2: Divide all sides by -3 (when we divide an inequality, we flip the inequality signs); 2 \(\leq\) x < 7

Answer:

2,307,500 microliters

Step-by-step explanation:

There are 2,307,500 microliters

convert 7.5 mL to 7500 microliters

convert 2.3 L to 2,300,000 microliters

add 2,300,000 + 7500 =

2,307,500 microliters

The area of the triangle determined by the points P(1, 1, 1), Q(-4, -3, -6), and R(6, 10, -9) is approximately 51.61 square units.

To find the area of the triangle determined by the points P(1, 1, 1), Q(-4, -3, -6), and R(6, 10, -9), we can follow these steps:

1. Calculate the vectors PQ and PR by subtracting the coordinates of P from Q and R, respectively.

2. Find the cross product of PQ and PR.

3. Calculate the magnitude of the cross product.

4. Divide the magnitude by 2 to find the area of the triangle.

Step 1: Calculate PQ and PR

PQ = Q - P = (-4 - 1, -3 - 1, -6 - 1) = (-5, -4, -7)

PR = R - P = (6 - 1, 10 - 1, -9 - 1) = (5, 9, -10)

Step 2: Find the cross product of PQ and PR

PQ x PR = ( (-4 * -10) - (-7 * 9), (-7 * 5) - (-10 * -5), (-5 * 9) - (-4 * 5) ) = ( 36 + 63, 35 - 50, -45 + 20 ) = (99, -15, -25)

Step 3: Calculate the magnitude of the cross product

|PQ x PR| = √( (99)² + (-15)² + (-25)² ) = √( 9801 + 225 + 625 ) = √(10651)

Step 4: Divide the magnitude by 2 to find the area of the triangle

Area = 0.5 * |PQ x PR| = 0.5 * √(10651) ≈ 51.61

So, the area of the triangle determined by the points P(1, 1, 1), Q(-4, -3, -6), and R(6, 10, -9) is approximately 51.61 square units.

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Complete question is below

Find the area of the triangle determined by the points p(1, 1, 1), q(-4, -3, -6), and r(6, 10, -9)

Option A  is the correct answer because the ratio between the opposite side and the hypotenuse side is correct.

Triangle :

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle. Therefore, this triangle is also called the right triangle or 90-degree triangle. The right triangle plays an important role in trigonometry. Let us learn more about this triangle in this article.

A triangle with Side lengths a unit, b units, and c units.

"Opposite" is opposite to the angle θ

"Adjacent" is adjacent (next to) to the angle θ

"Hypotenuse" is the long one

A)

Sin 55 = a/c

Sin  θ = opposite / hypotenuse

Option A ) is correct  Sin 55 = a/c  

B)

Cos(55°)=c/b

Cos θ =  Adjacent / hypotenuse

Cos 55 = c/ b is not equal to the Adjacent / hypotenuse

Option B)  is not a correct answer because the ratio is between  Adjacent and Hypotenuse.  

C)

Cos(55°)=a/b

Cos θ =  Adjacent / hypotenuse

Cos 55 = a/ b is not equal to the Adjacent / hypotenuse

Option C)  is not a correct answer because the ratio is between Adjacent and Hypotenuse.  

D)

Tan(55°)=c/a

Tan θ  = Opposite / Adjacent

Tan 55 =  c/a is not equal to the  Opposite / Adjacent

Option D)  is not a correct answer because the ratio is between Opposite and Adjacent.  

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Answer:

I am thank you! HBU?

Step-by-step explanation:

The stream velocity has no influence on the amount of dissolved load it contains. The amount of dissolved material depends on erosion and deposition carried out in the watercourse. These are affected by factors such as the slope of the land, the resistance of the material to erosion, the size of the sediments transported, etc.

Stream velocity plays an important role in the transport of sediments and dissolved loads in a watercourse. It affects the erosion and deposition processes that occur in the watercourse, which in turn affect the amount of sediment and dissolved load that is carried by the stream. For example, faster stream velocities can cause more erosion of the stream bed, leading to more material being carried in the water.

Sediment is any particulate matter that is transported by a fluid, and it can come in many different forms. The three main types of sediment are:

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Answer:-15

Step-by-step explanation:

The angles of the triangles that measure 90° will be ABC and DEF.

The pairs of line segments that are formed by the triangle sides are line ED and AB.

It should be noted that parallel lines are the lines that maintains the same distance between them and never meet.

Also, the angle that has the same measurement as angle DEA will be BAC. This is based on alternate exterior angles.

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There are nC2 different votes possible, where n is the number of bands on the list and nC2 represents the number of ways to choose 2 bands out of n.

To calculate nC2, we can use the formula for combinations, which is given by n! / (2! * (n-2)!), where ! represents factorial.

Let's say there are m bands on the list. The number of ways to choose 2 bands out of m can be calculated as m! / (2! * (m-2)!). Simplifying this expression further, we get m * (m-1) / 2.

Therefore, the number of different votes possible is m * (m-1) / 2.

In the given scenario, we don't have the specific number of bands on the list, so we cannot provide an exact number of different votes. However, you can calculate it by substituting the appropriate value of m into the formula m * (m-1) / 2.

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The sum of given series is infinity ∑(n = 1) sin(nx)/(2n - 1).

What is sum of series?

A series' sum is the sum of the words or list of numbers that make up the series. If a series has a sum, it will be one integer (or fraction), such as 0, 1/2, or 99.

As given series is,

f(x) = sinx + sin(2x)/3 + sin(3x)/5+.....

The series function is trigonometric function such as sinx, sin(2x), sin(3x).

The nth term of series is sin(nx).

The coefficient of series is 1, 1/3, 1/5.

The coefficient of nth terms is 1/(2n - 1).

Sum of series is,

= infinity ∑(n = 1) sin(nx)/(2n - 1).

Hence, the sum of given series is infinity ∑(n = 1) sin(nx)/(2n - 1).

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Answer:

you would have 1,194.4

Step-by-step explanation:

i subtracted.

Correct option is C. Row 15 of pascal's triangle will be used.

Pascal's triangle:

                                              1                                            n = 0 , Row = 0

                                      1                 1                                  n = 1  , Row = 1

                             1               2                1                          n = 2 , Row = 2

                                               :

                                          .........

                                           .......

For n = 0, Row number 1

For n = 1,  Row number 2

For n = 2, Row number 3

We make pascal's triangle but sum of above two number, write below.

As we can see in pascal's triangle.

Exponent represent the number of row.

If binomial has exponent n then nth row of pascal's triangle use.

For

Here power is 15

So, we have to use 15 row of pascal's triangle.

Hence, Row 15 is correct

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