The Drury Lane Theater has 10 seats in the first row and 38 rows in all. Each successive row contains one additional seat. How many seats are in the theater?

The sum of the lengths of two legs of the 30°-60°-90° right triangle is 6.69 centimeters. Using the ratio of sides for the 30°-60°-90° triangle, the sum is calculated.

The ratio for the 30°-60°-90° triangle is 1:√3:2 or x:x√3:2x

where x corresponds to the length opposite the 30° angle and x√3 is opposite of the 60° angle and 2x is opposite to the 90° angle.

It is given that the triangle is a right triangle with angles 30°-60°-90°

For such a triangle, the ratio of side lengths is x: x[tex]\sqrt{3}[/tex]:2x

we have the length of the hypotenuse is [tex]2\sqrt{6}[/tex]

So, 2x = [tex]2\sqrt{6}[/tex]

⇒ x = [tex]\sqrt{6}[/tex]

So,

the other length of the other leg is x√3 = √6 × √3 = 3 √2

Then, the sum of these two legs = √6 + 3√2 = 6.69 centimeters.

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Answer:

c

Step-by-step explanation:

Starting price is $5.50. And for every mile it costs $1.50.

Using translation concepts, the graph of g(x) = -|x - 4| is shown at the end of the answer.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The graph of g(x) = -|x - 4| is the graph of f(x) = |x| with these following changes:

At the end of the answer, the graph shows functions f(x) in red and g(x) in blue.

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The distance from Jim's home to the gym is 12 km.

Speed is defined as the rate at which the position of object is changed.

Speed = Distance / Time

Here, there are two different speeds given for the same distance.

Average speed is the total distance travelled by the total time taken.

If distance is a constant,

Average speed = 2xy / (x + y), where x and y are two different speeds for the same distance.

Average speed = (2 × 15 × 10) / (15 + 10)

                          = 12 km/hr

So, Total distance travelled = Average speed × total time taken

                                              = 12 × 2

                                              = 24

Distance = 24 / 2 = 12

Hence, the distance from Jim's home to the gym is 12 km when average speed is taken.

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Answer:

Below in bold.

Step-by-step explanation:

Total number of marbles = 3+4+5 = 12

P(white, red) = 4/12 * 3/11

                      = 12/132

                      = 1/11,

P(blue, white, red)  = 5/12 * 4/11* 3/10

                                 = 60/1320

                                 = 6/132

                                 = 1/22.

Answer:

30

Step-by-step explanation:

18/60 =.3 x 100 = 30

The calculation of the dividends per share on each class of stock for each of the four years for Lightfoot Inc. are:

                                 1st Year       2nd Year       3rd Year      4th Year

Preferred stock          $0.19            $0.32            $0.99          $0.50

Common stock           $0                 $0                $0.79          $2.69

How is dividend per share calculated?

The dividend per share for each class of stock can be computed by dividing the total dividend distributed by the number of shares outstanding.

For cumulative preferred stock, the unpaid dividends in a year are carried forward for distribution when profits are made.  Note also that preferred stock dividends enjoy preferential payment before common stock dividends.

Cumulative preferred stock = 30,000 shares

Par value of preferred stock = $25

Dividend rate = 2%

The total value of preferred stock = $750,000 ($25 x 30,000)

Expected annual dividend for preferred stockholders = $15,000 ($750,000 x 2%)

Common stock = 38,000 shares

Par value of common stock = $75

The total value of ordinary stock = $2,850,000 ($75 x 38,000)

                                        1st Year       2nd Year       3rd Year      4th Year

Dividends distributed    $5,700           $9,600       $59,720       $117,220

Preferred stock             $5,700            $9,600      $29,700        $15,000

Preferred stock per share $0.19           $0.32        $0.99             $0.50 ($15,000/30,000)

Common stock                  $0                   $0         $30,020      $102,220

Common stock per share $0                  $0            $0.79           $2.69 ($102,220/38,000)

Thus, the dividends distribution of Lightfoot Inc. shows that the common stockholders started earning dividends after the second year.

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Calculate the dividends per share on each class of stock for each of the four years. Round all answers to two decimal places. If no dividends are paid in a given year, enter "O."

Total number of teams are 10

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation is one that includes a variable, such as x.

As given in the problem,

total number of students in class=30

now professor want to create study teams .

one team consist of 3 members,

lets suppose professor will form n teams

So,

3×n=30

solve this equation to get value of n

n=30÷3

n=10 teams

hence total number of teams are 10 .

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The profit Mrs karki made from the Sari she sold at RS 11300 was 28.25%

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

VAT = 13% = 0.13 * 8000 = 1040

Selling price - VAT = 11300 - 1040 = 10260

Profit = [(10260 - 8000)/8000] * 100% = 28.25%

The profit Mrs karki made from the Sari she sold at RS 11300 was 28.25%

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Considering the definition of an inequality, the maximum number of tickets that they can buy is 10.

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values ​​called unknowns, in addition to certain known data.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

In this case, you know that

So, they want to spend on the purchase of tickets for the merry-go-round a value less than or equal to $36 - $15= $21.

Being "x" the maximum number of tickets that they can buy, the inequality that expresses the previous relationship is

2x≤ 21

Solving:

x≤ 21÷2

x≤ 10.5

Then, the maximum number of tickets that they can buy is 10.

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Answer:

If f(-x) = f(x), f is even and is symmetric about y

If f(-x) = -f(x), f is odd and is symmetric about the origin

If [tex]f(-x)\neq f(x)[/tex] and [tex]f(-x)\neq -f(x)[/tex], f is neither even nor odd and does not have symmetry

Step-by-step explanation:

As we discussed in one of the previous questions, if f(-x) = f(x), we have an even function. One basic example of an even function is x^2 since (-x)^2 = x^2. On the other hand, if f(-x) = -f(x), we have an odd function. One common example is x^3 since (-x)^3 = -x^3. What we have not been over yet is the symmetry of the functions. In order to do this, let's examine x^2 and x^3. x^2, which is an even function, is symmetric to the y-axis. The graph is a parabola that looks exactly the same on the left and the right of the y-axis.

On the other hand, x^3, which is an odd function, is not symmetric to the y-axis. On the other hand, it is symmetric to the origin. You can imagine that if you flipped y = x^3 across the origin, you would end up getting a graph that looks exactly the same.

A function that is neither even nor odd, meaning [tex]f(-x)\neq f(x)[/tex] and [tex]f(-x)\neq -f(x)[/tex], one that is not odd or even, has no symmetry. It is not symmetric about the y-axis or the origin.

The other fraction is [tex]1\frac{1}{55}[/tex].

Provided that ,

One fraction = [tex]9\frac{3}{7}[/tex] = [tex]\frac{66}{7}[/tex]

The product of their fraction = [tex]9\frac{3}{5}[/tex] = [tex]\frac{48}{5}[/tex]

We have to find out the other fraction.

When one fraction and their product are given, the formula to find out another fraction = product / one fraction

So, the other fraction = [tex]\frac{48}{5}[/tex] / [tex]\frac{66}{7}[/tex]

= [tex]\frac{48}{5} * \frac{7}{66}[/tex]

= 336/330

= 56/55 [divided both the numerator & denominator by 6]

= [tex]1\frac{1}{55}[/tex]

Therefore it is concluded that the other fraction is [tex]1\frac{1}{55}[/tex] .

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The equations of the corresponding circles can be any equation only have to satisfy the  general equation for circle .

The question seems incomplete and complete question given in the image !!!!

A circle is the set of all points in a plane at a given distance (called the radius) from a given point (called the center.)

We know that the general equation for a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex]

where ( h, k ) is the center and r is the radius.

According to the question

The equation of circle given is [tex]x^2+y^2=1[/tex]

Center at origin

i.e

(h,k) = (0,0)

and radius = 1 unit

Now ,

By changing changing center (h,k) and radius of equation it will give following equations

h                      k                       r                            equation of circle

0                       1                       3                      [tex](x-0)^2+(y-0)^2=3^2[/tex]  

2                       2                       3                       [tex](x-2)^2+(y-2)^2=3^2[/tex]

1                        1                        1                     [tex](x-1)^2+(y-1)^2=1^2[/tex]  

-2                      -1                       2                      [tex](x+2)^2+(y+1)^2=2^2[/tex]

3                       2                       1                        [tex](x-3)^2+(y-2)^2=1^2[/tex]      

-5                      1                        3                       [tex](x+5)^2+(y-1)^2=3^2[/tex]

Hence, the equations of the corresponding circles can be any equation only have to satisfy the general equation for circle .

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Using the law of cosines, it is found that the distance across the lake is of 978.5 feet.

The law of cosines states that we can find the angle C of a triangle as follows:

[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]

in which:

In this problem, the parameters are:

a = 800, b = 900, C = 70º.

Hence the distance across the lake is c, found as follows:

[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]

c² = 800² + 900² - 2(800)(900)cos(70º)

c² = 957491

[tex]c = \sqrt{957491}[/tex]

c = 978.5.

The distance across the lake is of 978.5 feet.

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The graphed function, F(x), has a value greater than 0 over the intervals (-0.7, 0.76) and (0.76,  ∞) . F(x) > 0 over the intervals (-0.7, 0.76) and (0.76, ∞) is the correct statement [Fourth choice].

About a Graphed Function

The function graph of an object F stands for the set of all points in the plane that are (x, f(x)). The graph of f is also known as the graph of y = f. (x). The graph of an equation is thus a specific example of the graph of a function. A graphed function is a function that has been drawn out on a graph.

It is evident from the attached graph that the supplied function exceeds 0 for the following range:

-0.7 < F(x) < 0.76

And, 0.76 < F(x) < ∞

As a result, the intervals for which the given graphed function, F(x) is greater than 0 are as follows,

(-0.7, 0.76) and (0.76, ∞)

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Answer:

600ft

Step-by-step explanation:

The balloon falls 200 feet in one minute and we need the amount it fell in 3 minutes: 200feet*3minutes = 600 ft

See below for the solution to each question

Yes, the graph is a function.

This is because all x values have different y values

This is the set of input values of the graph.

From the graph, we have

x = 0 to x = 17

Hence, the domain is [0, 17]

This is the set of output values of the graph.

From the graph, we have

y = 0 to y = 10

Hence, the range is [0, 10]

This is the maximum point on the graph.

From the graph, we have

Maximum = (12, 10)

This is the minimum point on the graph.

From the graph, we have

Minimum = (0, 0)

These are the intervals where the y values increase as x increase.

From the graph, we have

Increasing intervals = (0, 5) ∪ (10, 12) ∪ (14, 15)

These are the intervals where the y values decrease as x increase.

From the graph, we have

Decreasing intervals = (7, 10) ∪ (12, 14) ∪ (15, 17)

These are the intervals where the y values remain unchanged as x changes.

From the graph, we have

Constant intervals = (5, 7)

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The probability that olga will select a red pair of socks and a red hairband is 14/47

Probability defines the likelihood of an event occurring. There are many situations in real life where we may need to predict the outcome of an event. We may or may not be certain of the outcome of the event. In such cases, we say that there is a probability that the event will or will not occur. Probability in general has great applications in games, in business for probabilistic predictions, and also probability has extensive applications in this new field of artificial intelligence.

The probability of an event can be calculated using the probability formula simply by dividing the number of favorable outcomes by the total number of possible outcomes. The value of the probability of an event occurring can lie between 0 and 1 because the number of favorable outcomes can never exceed the total number of outcomes. Also, a favorable number of results cannot be negative

For an experiment that has "n" number of outcomes, the number of favorable outcomes can be denoted by x. The formula for calculating the probability of an event is as follows.

Probability (event) = favorable outcomes/total outcomes = x/n

Olga has a drawer of socks with four red pears, two gray pears, and a black hairs. she also has a bag of hair bands with 10 red, six gray, and 24 black hair bands

Therefore total number of items are = 4 + 2 + 1 + 10 + 6 + 24 = 47

Probability that olga will select a red pair of socks and a red hairband is 4/47 + 10/47

= 14/47

Hence the probability that olga will select a red pair of socks and a red hairband is 14/47

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Answer:

y = 7.25 + 0.65x

Step-by-step explanation:

y = total cost

x = each mile

it starts at 7.25

any mile after that is an extra $0.65

y = 7.25 + 0.65x

Answer:

140g

Step-by-step explanation:

One pencil box has a mass of 140g, to find out the weight of 4 pencil boxes we multiply 140 by 4: 140*4 = 560g

Let the mass of the notebook be x: 560+x = 700

560+x = 700

x = 140g

The answer which are true about the two rectangular pyramids are;

It follows from the task content that the dimensions of the rectangular prisms are the same and are as given.

On this note, it follows that the volume of the composite figure is; 1.5(9)(5) + 1.5(9)(5) = 135units³.

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a) The length of p is 21.4 cm

b) The measure of angle P is 45.6°

From the question, we are to determine the length of p

From the Pythagorean theorem, we can write that

30² = 21² + p²

p² = 30² - 21²

p² = 900 - 441

p² = 459

p = √459

p = 21.4 cm

∴ The length of p is 21.4 cm

b)

Measure of angle P

Using SOH CAH TOA

[tex]cos P= \frac{21}{30}[/tex]

cos P = 0.7

P = cos⁻¹(0.7)

P = 45.6°

Hence, the measure of angle P is 45.6°

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Both ran equal and both covered equal distance.

As cruz ran 1 lap out of 4 to cover one mile.

and erica ran 3 lap out of 12 to cover one mile:

3/12 = 1/4

So Cruz = Erica = 1/4.

Hence Both ran equal.

Fraction:

Fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator.

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Answer:

a) 10√3 + 5√3 + 10√3 + 5√3 = 30√3 cm

b) (√10 + √2) + (√10 - √2) + (√10 + √2) + (√10 - √2)

= 4√10 cm

c) Simplifying √72: √36 x √2 = 6√2

   Simplifying √18: √9 x √2 = 3√2

   Finding the perimeter: 6√2 + 3√2 + 6√2 + 3√2 = 18√2 cm

Answer:

x = -5/2

Step-by-step explanation:

4x+2 = -8

We are solving for x

The first step in isolating x is to subtract 2 from each side

4x+2-2 = -8-2

4x = -10

Divide each side by 4

4x/4 = -10/4

x = -10/4

Simplify the fraction

x = -5/2

Answer:

Step-by-step explanation:

4x+2 = -8

4x = -10

4x/4 = -10/4

x = -5/2

The tree is 23.54 feet tall.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. It is not necessary for the angle to be in Euclidean space if it lies in the plane. Angles are referred to as dihedral angles if they are created by the intersection of two planes in a space other than Euclidean.

According to the question,

Height of tree= 22*tan [tex]47^{o}[/tex]

                       = 22* 1.07

                       = 23.54 ft.

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Answer:

It's attached you may see it!!

Answer:

see attachments

Step-by-step explanation:

Given equations:

[tex]\begin{cases}5x + 7y = 50\\7x + 5y = 46\end{cases}[/tex]

To plot the graphs of the given equations:

Equation 1

[tex]\implies 5x + 7y = 50[/tex]

[tex]\implies 7y = -5x + 50[/tex]

[tex]\implies y = -\dfrac{5}{7}x+\dfrac{50}{7}[/tex]

[tex]x=-4 \implies y = -\dfrac{5}{7}(-4)+\dfrac{50}{7}=10 \implies (-4,10)[/tex]

[tex]x=3 \implies y = -\dfrac{5}{7}(3)+\dfrac{50}{7}=5 \implies (3,5)[/tex]

Plot the points (-4, 10) and (3, 5) then draw a straight line through them (see attachment 1).

Equation 2

[tex]\implies 7x+5y=46[/tex]

[tex]\implies 5y=-7x+46[/tex]

[tex]\implies y=-\dfrac{7}{5}x+\dfrac{46}{5}[/tex]

[tex]x=3 \implies y=-\dfrac{7}{5}(3)+\dfrac{46}{5}=5 \implies (3,5)[/tex]

[tex]x=8 \implies y=-\dfrac{7}{5}(8)+\dfrac{46}{5}=-2 \implies (8,-2)[/tex]

Plot the points (3, 5) and (8, -2) then draw a straight line through them (see attachment 2).

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The statement indicates that the interval 12​%±5​% is likely to contain the true population percentage of people that prefer chocolate pie.

According to the statement

we have a given that the Among the 1000 respondents,

12​% chose chocolate​ pie, and the margin of error was given as

±5 percentage points.

and we have to explain the statement that the margin of error was given as ±5 percentage​ points.

We know that the interval is a set of real numbers that contains all real numbers lying between any two numbers of the set.

And this statements also indicates the interval between the like and unlike respondents of chocolate pie.

So, this statement indicates that the interval 12​%±5​% is likely to contain the true population percentage of people that prefer chocolate pie.

So, The statement indicates that the interval 12​%±5​% is likely to contain the true population percentage of people that prefer chocolate pie.

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Answer:

7 hot dogs

Step-by-step explanation:

Set up an equation:

2.5x + 1.25 = 21

2.5x = 19.75

x = 7.9

You cannot buy .9 of a hot dog, so the answer is 7