A middle school took all of its 6th grade students on a field trip to see a play. The
students filled 1491 seats, which was 71% of the total number of seats in the theater.
How many total seats were in the theater?

LINE 1 : 3x + 4y = 20

rearranging : 4y = -3x + 20

y= -3/4 + 5 (y =mx + b)

therefore, m1 (slope) = -3/4

slopes of perpendicular lines are negative reciprocals of each other

m1 = -1 / m2 and m2 = -1/ m1

slope of line 2 (m2) = -1 / m1 = -1 / (-3/4) = 4/3

LINE 2 :

POINT - SLOPE FORM : y- y1 = m2 (x-x1)

point (3, -2); x1 = 3 and y1 = -2

m2 = 4/3

substituting the values in the point-slope form

y-y1 = m2 (x-x1)

y-(-2) = (4/3) (x-3)

y+2 = 4/3 (x) - 4/3(3)

y+2 = 4/3 x - 4

y = 4/3 x -4 - 2

y= 4/3 x -6

multiplying both sides of the equation by 3

3y = 4x -18

transposing,

4x-3y-18 = 0

answer: 4x - 3y -18 = 0

A scientific observation must be reproducible (option a).

A scientific observation must be reproducible, meaning that the results can be consistently obtained by multiple researchers or through repeated experiments. Reproducibility is a fundamental principle of scientific research as it allows for independent verification and validation of observations.

It ensures that the observed phenomenon or data is not a chance occurrence or influenced by individual biases. By reproducing the observation, scientists can establish the reliability and robustness of the findings. The correct option is a.

To know more about reproducible:

https://brainly.com/question/27983325

#SPJ4

The trigonometric expression that has a value of three-fourths is; tan (x)

The basic trigonometric ratios are;

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

sec x = 1/cos x

csc x = 1/sin x

cot x = 1/tan x

Thus;

If csc x = 5/3, it means that;

sin x = 3/5

By trigonometric ratios, we know that;

cos x = 4/5 and tan x = 3/4

Read more about Trigonometric ratios at; https://brainly.com/question/13276558

#SPJ1

Answer:

(2a + 3b)² = 121

Step-by-step explanation:

given 4a² + 9b² = 25 and ab = 8

(2a + 3b)² ← expand using FOIL

= 4a² + 6ab + 6ab + 9b²

= 4a² + 9b² + 12ab ← substitute given values from above

= 25 + 12(8)

= 25 + 96

= 121

a) The time required to assemble the 8th unit is 0.876 hours.

b) The total time required to assemble the last 5 units is 1.752 hours

(a) the time required to assemble the 8th unit.

To solve this, we can first find the time required to assemble 7 units and then subtract it from the time required to assemble 8 units.

Time required to assemble the first unit = 3 hours

Given, the time required to assemble the 6th unit = 1 hour and 23 minutes = 1 + 23/60 hours = 1.383 hours

Average time required to assemble 1 unhours production= [(time required to assemble the first unit) + (time required to assemble the sixth unit)]/5= [(3) + (1.383)]/5= 0.876 hours

Time required to assemble 7 units= 7 × 0.876= 6.132 hours

Now, time required to assemble the 8th unit= Time required to assemble 8 units - Time required to assemble 7 units= 8 × 0.876 - 6.132= 7.008 - 6.132= 0.876 hours

(b) the total time required to assemble the last 5 units.

We have already calculated the time required to assemble the first 6 units.

Time required to assemble the first 6 units= 6 × 0.876= 5.256 hours

Now, the total time required to assemble the last 5 units= Time required to assemble 8 units - Time required to assemble the first 6 units= 8 × 0.876 - 5.256= 7.008 - 5.256= 1.752 hours

Learn more about time required at

https://brainly.com/question/4130932?

#SPJ11

Answer:

16

Step-by-step explanation:

(b/2)^2

(8/2)^2 = (4)^2 = 16

(x^2+8x+16) = -3+16

(x+4)^2 = 13

so on so forth, but basically you add 16 which completes the square

The value of the tangent TU for the circle with secant through U which intersect the circle at points V and W is equal to 12

Circle theorems are a set of rules that apply to circles and their constituent parts, such as chords, tangents, secants, and arcs. These rules describe the relationships between the different parts of a circle and can be used to solve problems involving circles.

For the tangent TU and the secant through U which intersect the circle at points V and W;

TU² = UV × VW {secant tangent segments}

(5x)² = 9 × 16

(5x)² = 144

5x = √144 {take square root of both sides}

5x = 12

x = 12/5

so;

TU = 5(12/5)

TU = 12

Therefore, the value of the tangent TU for the circle with secant through U which intersect the circle at points V and W is equal to 12

Read more about circle here:https://brainly.com/question/17023621

#SPJ1

Answer:

because there is always the part you had to start cutting

Step-by-step explanation:

The number of segments obtained during a partition exercise or problem is usually greater than the number of partitions by 1 because the first partition will always yield two segments.

The first partition obtained will yield two segments after which the subsequent partitions yields a value of 1.

Therefore, the increment by 1 in the number segments obtained is due to the two segments which the first partition yields.

Learn more : https://brainly.com/question/23575522

Answer:

8 1/3

Step-by-step explanation:

x+(x-1)+(x+2)=29

3x+1=29

3x=28

x=9 1/3

9 1/3-1= 8 1/3

A discrete-time linear time-invariant filter can be analyzed by drawing the block diagram. The following cases are possible with their corresponding block diagram implementation of the system:

i. Direct form II

The Direct Form II block diagram implementation of the system is as follows:

The input signal enters the diagram from the left side. It is then divided by R before being passed through the delay element. The output of this delay element is then multiplied by the poles before being summed. The output of the zero is then added to the sum and the result is multiplied by R before being passed as the output signal.

ii. Transposed Direct Form II

The Transposed Direct Form II block diagram implementation of the system is as follows:

The input signal enters the diagram from the left side. It is then passed through the zero before being summed. The sum is then passed through the poles before being delayed by a single sample. The delayed output is then multiplied by R before being added to the output of the zero. The result is multiplied by R before being passed as the output signal.

iii. Cascade Form

The Cascade Form block diagram implementation of the system is as follows:

The input signal enters the diagram from the left side. It is then passed through the first zero before being delayed by a single sample. The delayed output is then passed through the second zero before being delayed again. The output of the second delay element is then passed through the first pole before being delayed by a single sample. The delayed output is then passed through the second pole. The result is multiplied by R before being passed as the output signal.

To know more about discrete-time linear time-invariant filter, visit:

https://brainly.com/question/33184980

#SPJ11

The block diagram implementation of the system for the given LTI filter is presented in three forms: Direct Form II, Transposed Direct Form II, and Cascade Form.

The given discrete time LTI filter has the following data:

Poles are at 0.2R and 0.4R

Zeros are at -0.4 and Origin

Gain of filter is 5R

The block diagram implementation of the system in Direct Form II is given below:

Direct Form II

The block diagram implementation of the system in Transposed Direct Form II is given below: Transposed Direct Form II

The block diagram implementation of the system in Cascade Form is given below:

Cascade Form

Conclusion: The block diagram implementation of the system for the given LTI filter is presented in three forms: Direct Form II, Transposed Direct Form II, and Cascade Form.

To know more about Transposed visit

https://brainly.com/question/2263930

#SPJ11

442 is the answer thedjfbbxhcbdhx

Answer: 36 years

Step-by-step explanation:

You can use the Rule of 72 to calculate how long it might take the house to double in value.

The Rule of 72 works by dividing 72 by the interest rate as a whole number and the result will be a rough estimate of the time in years it will take for the investment to double in size:

= 72 / 2

= 36 years

Answer:

4

Step-by-step explanation:

A fundamental theorem of algebra,  the degree of a polynomial is the maximum number of roots the polynomial has.
The degree of the polynomial s 4 so it has 4 roots.

For the processor to be 95% certain that the sample mean does not deviate from the population mean by more than 0.2 pounds, they must sample around 24 boxes.

A confidence interval expresses the likelihood that a population parameter will fall between a range of values a predetermined percentage of the time.

Given the population's standard deviation σ is 0.5, the margin of error E is 0.2, and the confidence coefficient is 95% or 0.95.

Then, the formula to calculate the required sample size is calculated using the formula  \(n=\left(\frac{z\sigma}{E}\right)^2\).

For a confidence level of 95%, the z-score is 1.96 using the normal probability table. Then, z = 1.96. Substitute values of z, E, and σ to find the required sample size.

\(\begin{aligned}n&=\left(\frac{z\sigma}{E}\right)^2\\&=\left(\frac{1.96\times0.5}{0.2}\right)^2\\&=24.01\\&\approx 24\end{aligned}\)

The required answer is 24.

To know more about the margin of error:

https://brainly.com/question/17588303

#SPJ4

Answer:

2.333

or

7/3

Step-by-step explanation:

7(1/3)

7/1 x 1/3+

7/3

The graph of the new function compared to the first one will be shifted down.

Vertical translation describes the movement of a function graph upward or below. The function's form is preserved in this case. The graph moving or shifting along the y-axis is another name for it. Each point on the graph moves k units vertically during vertical translation, and the graph is said to have translated k units.

The two functions are

f(x) = x + 2

g(x) = x - 1

You can see that all you need to do to transform f into g is just take 3 off of it.

f(x) - 3 = (x+2) - 3

= x + 2 - 3

= x - 1

= g(x)

Every transformation, such as f(x) f(x) + k, now produces a vertical translation, which is translated upward if k > 0 and downward if k 0. The correct response is C since the function is translated three units down in our situation where k = -3.

To know more about vertical translation, visit:

https://brainly.com/question/17052587

#SPJ1

The complete question is:

"If y = x + 2 were changed to y = x - 1, how would the graph of the new function compare with the first one?

A. It would be shifted up.

B. It would be shifted left.

C. It would be shifted down.

D. It would be less steep."

If a room requires 25.4 square yards of carpeting,  the area of the floor is  228.6 ft².

The measurement that characterizes the size of a two-dimensional region, shape, or planar lamina in the plane is its area. The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

1 yard = 3 feet

Squaring on both side

1²yard² = 3² feet²

1yard ² = 9 feet²

so 25.4 yard² will be

25.4 x 9 = 228.6 ft²

Thus, the area of the floor is 228.6 square feet.

Learn more about areas, here:

brainly.com/question/1631786

#SPJ4

Answer:

A

Step-by-step explanation:

If the number of people in the theater must be under 240, then there must be less than 10 seats in each row on the floor to meet fire safety regulations.

if X=10 then, 15 times 10 plus 90 = 240.

Since the number of people must be under 240, there must be less than 10 seats in each row on the floor.

Answer: 15,473,000; 15,470,000; 15,000,000

Step-by-step explanation: none really:)

Answer:

1.6

Step-by-step explanation:

The stock turnover at retail is a measure of how many times a business sells its average inventory during a period of time. We can calculate the stock turnover by dividing the retail sales by the average inventory.

Stock turnover = Retail Sales / Average Inventory

Given the values :

Substituting these values

Stock turnover at retail = 196,450 / 123,456 = 1.6 (rounded to the nearest tenth)

On average, a person weighing 150 pounds can burn approximately 80 to 90 extra calories by slowly walking at a pace of 1.7 miles per hour for one hour instead of sitting.

The number of extra calories a person would burn by slowly walking instead of sitting for one hour depends on various factors, such as the person's weight, height, age, and gender. However, on average, a person weighing 150 pounds can burn approximately 80 to 90 calories by walking at a slow pace of 1.7 miles per hour for an hour.

This number may vary slightly based on individual differences and other factors, such as incline or terrain. Walking is a low-impact form of exercise that can help increase calorie burn and improve overall health, making it a great option for those looking to lead a more active lifestyle.

Learn more about calories here

brainly.com/question/28680077

#SPJ4

Can you explain the rest of the problem please?

The increase in the selling price is 1.818.

Test statistic:

A test statistic is a statistic used in statistical hypothesis testing. A hypothesis test is typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test.

The given values are:

a = 0.1

x = 94

μ = 90

The formula for test statistic will be:

t = ((x- μ) / (\(\frac{s}{vn}\))

Now put the values in the given equation we have:

t = (94-90) / (\(\frac{22}{10}\))

 = 4/2.2

  = 1.818

Therefore the increase in the selling price is 1.818.

To know more about the selling price refer to the link given below:

https://brainly.com/question/1153322

#SPJ4

Answer:

will remain the same

Step-by-step explanation:

Examples:

Your current exam mean is 97.2. If you receive a 99 on the next exam, this will have the effect of: increasing your mean

Your current exam mean is 93.2. If you receive a 87 on the next exam, this will have the effect of: decreasing your mean

Therefore, Your current exam mean is 95. If you receive a 95 on the next exam,this will have the effect of: Will remain the same

The expression for the statement is 20 - (6 + b).

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given statement is 20 decreased by the sum of 6 and b.

Sum means adding two or more numbers or expressions.

Sum of 6 and b means 6 + b.

Decreased means some number is subtracted.

The expression is 20 - (6 + b).

Hence the expression for the phrase is 20 - (6 + b).

Learn more about Expressions here :

https://brainly.com/question/14083225

#SPJ1

Your options for the question seems a little confusing. Probably the options for the question is given below :

Answer:

3/-4 i think

Step-by-step explanation:

one point is -2/1 and the other 2/-2

1 - -2=3

-2 -2=-4

Answer:

25 pieces

Step-by-step explanation:

let c = amt of candy

(c - 10 ) / 5 = 3

cross-multiply:

c-10 = 15

c = 25

Answer:

10

Step-by-step explanation:

2 x 5 = 10

The system of inequalities to represent the situation is 2x + 5y ≤ 77, x + y ≥ 19

You are in charge of getting food for the class from the corner store.  You can buy chips for $2 or a hoagie for $5.

There are 19 students in the class, so you need to buy at least 19 items, and you have $77 total.

Hence, the system of inequality to represent this situation is as follows:

let

x = number of chips

y = number of hoagies

Therefore, the inequalities is as follows:

2x + 5y ≤ 77

x + y ≥ 19

learn more on inequality here:https://brainly.com/question/2155328

#SPJ1

The properties of the graph are

The equation of the function is given as

f(x) = (x - 2)(x + 6)

The above equation is a quadratic function.

Next, we plot the equation on a graph (see attachment)

Set x = 0 to determine the y-intercept

y-intercept = (0 - 2)(x + 6)

y-intercept = -12

Expand the function to determine the symmetry axis

f(x) = x^2 - 2x + 6x - 12

Differentiate and set to 0

2x - 2 + 6 = 0

This gives

x = -2 --- axis of symmetry

Substitute x = -2 in the function to calculate the vertex/Min/Max

f(-2) = (-2 - 2)(-2 + 6)

f(-2) = -16

This means that

Direction = Up, Min = -16 and Vertex = (2, -16)

Set the function to 0 to determine the roots

(x - 2)(x + 6) = 0

Solve for x

x = 2 and x = -6

Read more about quadratic functions at

https://brainly.com/question/1214333

#SPJ1