An auditorium has 40 seats in its first row. Each row after has 2 additional seats than the row before. Find the number of seats in the 75th row.

Answer: 156 degrees

Step-by-step explanation:

Answer:

\(\boxed {a_{24} = - 70}\)

Step-by-step explanation:

According to the following pattern sequence (\(-1, -4, -7, -10\) ), it is Arithmetic Sequence, because every negative number is subtracted by \(3\). So, to find the 24th term, you need to use the Arithmetic Sequence Formula and solve to find the 24th term:

\(a_{n} = a_{1} + (n - 1) d\)

\(a_{n}\): nth term in the sequence

\(a_{1}\): 1st term

\(n\): term position

\(d\): Common difference

-Apply to the formula:

\(a_{24} = -1 - 3 (24 - 1)\)

\(a_{n} = a_{24}\)

\(a_{1} = -1\)

\(n = 24\)

\(d = -3\)

-Solve:

\(a_{24} = -1 - 3 (24 - 1)\)

\(a_{24} = -1 - 3 (23)\)

\(a_{24} = -1 - 69\)

\(\boxed {a_{24} = - 70}\)

Therefore, the 24th term is \(-70\).

Answer:

3 two foot and 3 four foot

Step-by-step explanation:

In order to find how many of each he used, you have to find how much pipe in total with the options that were given you.

(3*2)+(3*4)=6+12=18 feet of pipe

The area and circumference of the given circle are 200.96 cm2 200.96 c m 2 and 50.24 cm 50.24 c m respectively.

Circumference of circle:

In geometry, a circumference is the circumference of a circle or an ellipse. That is, the circumference will be the length of the arc of the circle as if it were open and straight to the line segment. More generally, the perimeter is the length of the curve around any closed figure. The circumference can also designate the circle itself, the trajectory corresponding to the edge of a disk. The circumference of a sphere is the circumference or length of one of its great circles.

Area of circle:

The area of ​​a circle is the space the circle occupies in a two-dimensional plane. Alternatively, the space occupied inside the boundary/perimeter of a circle is called the area of ​​the circle. The formula for the area of ​​a circle is A = πr2, where r is the radius of the circle. Area unit is square unit, such as m2, cm2, in2, etc.

According to the Question:

The circumference C of a circle with radius r is given by

C = 2πr

where the units of C will be the same as the unit of R.

The problem tells us that the radius r = 8m.

And, we will say π = 3.14

So,

C = 2(3.14)(8) = 50.24m

The units are meters.

Now, the area A of a circle with radius r is given by

A = πr², where the units of A will be the units of r squared.

Again,

we know r = 8,π = 3.14, so

A= 3.14(8²)

8² = 8⋅8 = 64,

Thus,

A= 64(3.14) = 200.96m²

Learn more about Circumference:

https://brainly.com/question/28757341

#SPJ4

Answer:

3⅗

Step-by-step explanation:

5×3 =15

18 - 15 = 3

therefore

18÷5

is

3⅗

Convert in to mixed fractions 18 and 5

Multiply the newest quotient digit (3) by the divisor 5 . Subtract 15 from 18 . The result of division of 185 is 3 with a remainder of 3 .

Hopefully help:)

To apply the Economic Order Quantity (EOQ) model with service level, we need to calculate the EOQ and reorder point. Let's go step by step:

Calculate the EOQ (Economic Order Quantity):

EOQ formula: EOQ = sqrt((2 x Annual Demand x Ordering Cost) / Holding Cost per Unit)

Given:

Annual Demand (D) = 12,000 units

Ordering Cost (S) = $50

Holding Cost (H) = 22% of unit cost = 0.22 * $500 = $110

Using the formula:

EOQ = sqrt((2 x12,000 x $50) / $110) = sqrt(1,200,000 / $110) = sqrt(10,909.09) ≈ 104.47

Therefore, the EOQ for the kitchen-table at Smart Home is approximately 104 units.

Calculate the reorder point:

Reorder Point = (Demand per Day * Lead Time) + Safety Stock

Given:

Demand per Day = Daily Demand = 40 units

Lead Time = 3 days

Safety Stock = Z * Standard Deviation of Daily Demand

To calculate the safety stock, we need to determine the value of Z based on the desired service level. Let's assume a standard service level of 95%, which corresponds to a Z-value of 1.645 (for a normal distribution).

Safety Stock = 1.645 * Standard Deviation of Daily Demand

= 1.645 * 18

≈ 29.91

Reorder Point = (40 * 3) + 29.91

= 120 + 29.91

≈ 149.91

Therefore, the reorder point for the kitchen-table at Smart Home is approximately 150 units.

Please note that the calculations provided here assume that the demand and lead time are constant and that there are no stockouts or other factors affecting the inventory. In practice, these assumptions may not hold, and additional considerations may be required for accurate inventory management.

Learn more about: demand

brainly.com/question/30402955

#SPJ11

The values of E(X) = 3.25 and Var(X) ≈ 2.238 for the number of spades in a hand of 13 cards chosen at random from a 52-card deck.

To find E(X) and Var(X) for the number of spades in a hand of 13 cards chosen at random from a 52-card deck, we will use the concepts of probability and statistics.

E(X), or the expected value, is the average number of spades you would expect to get in a hand of 13 cards. To find E(X), we can use the formula:

E(X) = (Number of spades in the deck / Total number of cards in the deck) * Number of cards drawn

E(X) = (13 spades / 52 cards) * 13 cards drawn
E(X) = (1/4) * 13
E(X) = 3.25

So, the expected number of spades in a 13-card hand is 3.25.

Next, let's find Var(X), or the variance, which is a measure of how much the number of spades can vary from the expected value. We can use the formula for variance of a hypergeometric distribution:

Var(X) = (Number of cards drawn * Number of spades * Number of non-spades) / ((Total number of cards in the deck)^2 * (Total number of cards in the deck - 1))

Var(X) = (13 cards drawn * 13 spades * 39 non-spades) / ((52 cards)^2 * (52 cards - 1))
Var(X) = (13 * 13 * 39) / (52 * 52 * 51)
Var(X) ≈ 2.238

So, the variance for the number of spades in a 13-card hand is approximately 2.238.

In summary, E(X) = 3.25 and Var(X) ≈ 2.238 for the number of spades in a hand of 13 cards chosen at random from a 52-card deck.

To know more about "PROBABILITY" refer here:

https://brainly.com/question/30034780#

#SPJ11

It is not appropriate to compare two means at a time in the way described. This would inflate the overall Type I Error and is a 'Multiple Testing' problem. The one-way ANOVA controls for the Type I Error and should be used instead. Comparing multiple pairs of means using independent two-sample t-tests without adjusting for the multiple comparisons can lead to an increased probability of committing a Type I error.

When comparing three or more populations means within a set of quantitative data that is categorized according to one factor/treatment, it is appropriate to use a one-way ANOVA instead of multiple independent two-sample t-tests. The reason is that performing multiple t-tests increases the overall Type I error rate, which is the probability of falsely rejecting a true null hypothesis. This is known as the multiple testing problem, and it occurs when we conduct multiple hypothesis tests without controlling the overall error rate.

In contrast, the one-way ANOVA controls for the Type I error rate and tests the null hypothesis that all population means are equal. If the null hypothesis is rejected, then at least one population mean is significantly different from the others. We can then perform post-hoc tests, such as Tukey's HSD, to determine which population means are different.

To know more about ANOVA,

https://brainly.com/question/23638404

#SPJ11

Answer:

12 = 2 × 2 × 3

48 = 3 × 2 × 2 × 2 × 2

60 = 3 × 2 × 5 × 2

Thus HCF = 2 × 2× 3 = 12

Answer: the answer is 12 hope it helps

Step-by-step explanation:

Answer:

1) For \(x^2 + y^2 - 4x + 12y - 20 = 0\), the standard form is \((x-2)^2 + (y+6)^2 = 60\\\)

2) For \(x^2 + y^2 + 6x - 8y - 10 = 0\), the standard form is \((x + 3)^2 + (y - 4)^2 = 35\\\)

3) For \(3x^2 + 3y^2 + 12x + 18y - 15 = 0\),  the standard form is \((x + 2)^2 + (y+ 3)^2 = 18\\\)

4) For \(5x^2 + 5y^2 - 10x + 20y - 30 = 0\),  the standard form is \((x - 1)^2 + (y+ 2)^2 = 11\\\)

5) For \(2x^2 + 2y^2 - 24x - 16y - 8 = 0\),  the standard form is \((x - 6)^2 + (y+ 4)^2 = 56\\\)

6) For\(x^2 + y^2 + 2x - 12y - 9 = 0\), the standard form is \((x+1)^2 + (y-6)^2 = 46\\\\\)

Step-by-step explanation:

This can be done using the completing the square method.

The standard equation of a circle is given by \((x - a)^2 + (y-b)^2 = r^2\)

1) For \(x^2 + y^2 - 4x + 12y - 20 = 0\)

\(x^2 - 4x + y^2 + 12y = 20\\x^2 - 4x + 2^2 + y^2 + 12y + 6^2 = 20 + 4 + 36\\(x-2)^2 + (y+6)^2 = 60\\\)

Therefore, for \(x^2 + y^2 - 4x + 12y - 20 = 0\), the standard form is \((x-2)^2 + (y+6)^2 = 60\\\)

2) For \(x^2 + y^2 + 6x - 8y - 10 = 0\)

\(x^2 + 6x + y^2 - 8y = 10\\x^2 + 6x + 3^2 + y^2 - 8y + 4^2 = 10 + 9 + 16\\(x + 3)^2 + (y- 4)^2 = 35\\\)

Therefore, for \(x^2 + y^2 + 6x - 8y - 10 = 0\), the standard form is \((x + 3)^2 + (y - 4)^2 = 35\\\)

3)  For \(3x^2 + 3y^2 + 12x + 18y - 15 = 0\)

Divide through by 3

\(x^2 + y^2 + 4x + 6y = 5\)

\(x^2 + y^2 + 4x + 6y = 5\\x^2 + 4x + 2^2 + y^2 + 6y + 3^2 = 5 + 4 + 9\\(x + 2)^2 + (y+ 3)^2 = 18\\\)

Therefore, for \(3x^2 + 3y^2 + 12x + 18y - 15 = 0\),  the standard form is \((x + 2)^2 + (y+ 3)^2 = 18\\\)

4)  For \(5x^2 + 5y^2 - 10x + 20y - 30 = 0\)

Divide through by 5

\(x^2 + y^2 - 2x + 4y = 6\)

\(x^2 + y^2 -2x + 4y = 6\\x^2 - 2x + 1^2 + y^2 + 4y + 2^2 = 6 + 1 + 4\\(x - 1)^2 + (y+ 2)^2 = 11\\\)

Therefore, for \(5x^2 + 5y^2 - 10x + 20y - 30 = 0\),  the standard form is \((x - 1)^2 + (y+ 2)^2 = 11\\\)

5) For \(2x^2 + 2y^2 - 24x - 16y - 8 = 0\)

Divide through by 2

\(x^2 + y^2 - 12x - 8y = 4\)

\(x^2 + y^2 - 12x - 8y = 4\\x^2 - 12x + 6^2 + y^2 - 8y + 4^2 = 4 + 36 + 16\\(x - 6)^2 + (y+ 4)^2 = 56\\\)

Therefore, for \(2x^2 + 2y^2 - 24x - 16y - 8 = 0\),  the standard form is \((x - 6)^2 + (y+ 4)^2 = 56\\\)

6) For \(x^2 + y^2 + 2x - 12y - 9 = 0\)

\(x^2 + 2x + y^2 - 12y = 9\\x^2 + 2x + 1^2 + y^2 - 12y + 6^2 = 9 + 1 + 36\\(x+1)^2 + (y-6)^2 = 46\\\)

Therefore, for\(x^2 + y^2 + 2x - 12y - 9 = 0\), the standard form is \((x+1)^2 + (y-6)^2 = 46\\\\\)

For Plato / Edmentum

Just to the test and got it right ✅

The "St. Petersburg Workmen's Petition to the Tsar" was a document written in 1870 by a group of Russian workers, which expressed their grievances and called for greater rights and protections in the workplace.

While the text of the petition is too long to summarize in its entirety, the following points illustrate some of the connections that the authors draw between workers' rights and their quality of life:

- The petitioners argue that workers have the right to a fair wage that allows them to support themselves and their families, and that without this right, workers are forced to live in poverty and squalor.

- They also argue that workers have the right to safe and healthy working conditions, and that without this right, workers are subjected to disease and injury that can shorten their lives and reduce their quality of life.

- The petitioners further argue that workers have the right to organize and advocate for their own interests, that without this right, workers are powerless to negotiate with their employers and to protect themselves against exploitation.

- They also argue that workers have the right to education and self-improvement, and that without this right, workers are trapped in a cycle of ignorance and subservience that limits their potential and reduces their quality of life.

- Overall, the authors of the petition argue that workers' rights and their quality of life are inextricably linked, and that without the former, the latter is impossible to achieve.

To know more about Russian workers refer here

https://brainly.com/question/30391730#

#SPJ11

Answer:

Hi

Step-by-step explanation:

The answer is B and D.

Hope it's correct.

The square root function √x is defined for all non-negative real numbers, which means that the domain of the function f(x)= √=x is all non-negative real numbers.

However, when we take the square root of a negative number, we get a complex number which is not in the real domain. Therefore, the domain of the function is limited to non-negative real numbers. When the function is graphed, we can see that it starts at the origin and increases as x increases, with the curve becoming steeper and steeper. However, the curve will never reach the negative x-axis, since negative numbers are not part of the domain. It's important to note that the range of the function is also limited to non-negative real numbers, since the square root of a non-negative number is always non-negative. In summary, the statement that the domain of the graph of the function f(x)= √=x is all real numbers is not true. The domain is limited to non-negative real numbers.

Learn more about real numbers here :

https://brainly.com/question/31715634

#SPJ11

Answer:

18/x + 3

Step-by-step explanation:

This can be written algebraically as 18/x +3. This question is a little unclear, but I think it’s asking to write it as an equation

Answer:

7x + 13

Step-by-step explanation:

because the correct answer is 7x+13

On solving the problem, we get 90 inches as the width of a rectangle that has a length of 72.

The parallel sides of a rectangle are equal to one another, and each of its four vertices is 90 degrees, making it a type of quadrilateral. As a result, it is also referred to as an equiangular quadrilateral. The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.

As the proportion are same,

\(\frac{a}{b} = \frac{c}{d}\)

And here,

length of first rectangle, a

length of second rectangle, c

Width of first rectangle, b

Width of second rectangle, d

\(\frac{8}{10} = \frac{72}{\alpha }\)

\(\alpha = \frac{72 X 10}{8}\)

\(\alpha = 90 inches\)

Answer is 90 inches

To know more about rectangle visit:
https://brainly.com/question/15019502

#SPJ4

Answer:

Step-by-step explanation:

here hope it helps

The correct answer is there exists a value e ∈ (0, 3) such that f(e) = e.

To apply the Intermediate Value Theorem to the function g(x) = f(x) - x, we need to show that g(x) changes sign on the interval [0, 3]. Since f(x) is continuous on [0, 3], it is also continuous on the same interval.

First, let's consider the value of g(0):

g(0) = f(0) - 0

Since f(0) < -1, we have:

g(0) < -1 - 0

g(0) < -1

Next, let's consider the value of g(3):

g(3) = f(3) - 3

Since f(3) > 4, we have:

g(3) > 4 - 3

g(3) > 1

So, we have g(0) < -1 and g(3) > 1, which means g(x) changes sign on the interval [0, 3]. By the Intermediate Value Theorem, we can conclude that there exists e ∈ (0, 3) such that g(e) = 0.

Substituting g(x) = f(x) - x, we have:

f(e) - e = 0

f(e) = e

Therefore, there exists a value e ∈ (0, 3) such that f(e) = e.

Learn more about function here:

https://brainly.com/question/11624077

#SPJ11

At the 0.05 level of significance, there is evidence of a linear relationship between the number of cubic feet moved and labor hours.

The null hypothesis (H0) is that there is no linear relationship, meaning the slope of the regression line is zero (b1 = 0), while the alternative hypothesis (H1) is that there is a linear relationship (b1 ≠ 0).

To test this hypothesis, we can perform a t-test using the calculated b1 and its standard error (Sb1). The t statistic is computed as:

t = b1 / Sb1 = 0.0404 / 0.0034

=  11.88

The degrees of freedom for this t-test would be:

= n - 2

= 36 - 2

= 34

The critical t value for a two-sided test at the 0.05 level with 34 degrees of freedom (from t-distribution tables or using a statistical calculator) is approximately ±2.032.

Since our computed t value (11.88) is greater than the critical t value (2.032), we reject the null hypothesis.

Find out more on linear relationship evidence at https://brainly.com/question/31354900.

#SPJ4

Full question is:

The owner of a moving company wants to predict labor​ hours, based on the number of cubic feet moved. A total of 36 observations were made. An analysis of variance of these data showed that b1=0.0404 and Sb1=0.0034.

At the 0.05 level of​ significance, is there evidence of a linear relationship between the number of cubic feet moved and labor​ hours?

Answer:

The answer is of this question is 324.

We can use the integral test to determine the convergence of the series:

∫₂^∞ 1/(x^p ln(x)) dx

We integrate this using u-substitution with u = ln(x):

∫ln(2)^∞ 1/(u^p) du

This integral converges if and only if p > 1, so the given series converges if and only if p > 1.

Therefore, the series converges for all values of p > 1.

For more questions like convergence visit the link below:

https://brainly.com/question/31054770

#SPJ11

Answer:

$7969.24

Step-by-step explanation:

5000*1.06 to power of 8 = 7969.24037265

round to 2dp = $7969.24

Answer:

7400

Step-by-step explanation:

Answer:

B. It is isometric because all side lengths and angle measures remained the same

Step-by-step explanation:

Answer:

B) It is isometric because all side lengths and angle measures remained the same.

Step-by-step explanation:

Got it right on edge <3

In give word problem June 25, 1987 fell on Thursday.

What is word problem?

  Math word problems are math problems consisting of one or more sentences that require children to apply their math knowledge to "real world" scenarios. This means that in order to understand word problems, children must be familiar with the vocabulary associated with familiar mathematical symbols. Students must develop models.

One year = 365 days except for leap years = 366 days

52 weeks in a year 7 days per week = 364 days

1982 25th a Friday, if we move 365 days in the next year we end up on the 25th, but the weekday will be Saturday since we have moved 52 weeks + 1 day into the future.

Hence,

1982 25th Friday

1983 25th Saturday (+1 day)

1984 25th Monday (+1 day and +1 extra day for leap year)

1985 25th Tuesday (+1 day)

1986 25th Wednesday (+1 day)

1987 25th = Thursday

If the system had been 364 days per year, every year we would have end up on the same day every year.

Therefore June 25 , 1987 fell on Thursday.

To learn more about word problem refer the below link

https://brainly.com/question/21405634

#SPJ4

Answer: The unit value of a cubic centimeter (cm^3) is the same as the metric measurement of a milliliter (mL).

This is because 1 milliliter is equal to 1 cubic centimeter. In other words, if you have a cube that measures 1 centimeter on each side, its volume would be 1 cubic centimeter, which would also be equivalent to 1 milliliter of volume.

This relationship between cm^3 and mL is commonly used in scientific and medical measurements involving liquids and gases.

The unit value of a cubic centimeter (cc) is equivalent to one milliliter (mL) in the metric system. Both cubic centimeters and milliliters are used to measure volume, and their conversion is straightforward: 1 cc = 1 mL.

The metric system uses base units such as meters, liters, and grams, and applies prefixes like kilo-, centi-, and milli- to indicate larger or smaller units of measurement.
Cubic centimeters are often used to measure the volume of solid objects or the capacity of containers, while milliliters are more commonly used to measure the volume of liquids. However, both units represent the same volume and can be used interchangeably.
It is important to understand the difference between volume measurements and other metric measurements, such as length or mass. For instance, meters are used to measure length or distance, and grams are used to measure mass or weight. These units cannot be directly converted to cubic centimeters or milliliters, as they represent different physical properties.
In summary, a cubic centimeter (cc) is a unit of volume in the metric system that is equivalent to one milliliter (mL). Both units can be used to measure volume, and they have a simple conversion of 1 cc = 1 mL. Understanding the relationship between these units and other metric measurements is essential for accurately quantifying and comparing different physical properties.

To learn more about a cubic centimeter, refer:-

https://brainly.com/question/16670888

#SPJ11

Answer:

The domain of the function g(u) = √(1 + |u|) is all real numbers, or (-∞, +∞) in interval notation

Step-by-step explanation:

To find the domain of the function g(u) = √(1 + |u|), we need to consider the values of u for which the function is defined.

The square root function (√) is defined only for non-negative values. Additionally, the absolute value function (|u|) is always non-negative.

For the given function g(u) = √(1 + |u|), the expression inside the square root, 1 + |u|, must be non-negative for the function to be defined.

1 + |u| ≥ 0

To satisfy this inequality, we have two cases to consider:

Case 1: 1 + |u| > 0

In this case, the expression 1 + |u| is always greater than 0. Therefore, there are no restrictions on the domain, and the function is defined for all real numbers.

Case 2: 1 + |u| = 0

In this case, the expression 1 + |u| equals 0 when |u| = -1, which is not possible since the absolute value is always non-negative. Therefore, there are no values of u that make 1 + |u| equal to 0.

Combining both cases, we can conclude that the domain of the function g(u) = √(1 + |u|) is all real numbers, or (-∞, +∞) in interval notation.

Learn more about inequality:https://brainly.com/question/30238989

#SPJ11

Answer:

Step-by-step explanation:

\(3=\frac{a+r}{a-r} \\3a-3r=a+r\\3a-a=r+3r\\4r=2a\\r=\frac{1}{2} a\)