Question 2/3 A swimming pool holds 18,000 gallons of water. A pool
company can drain the water in a pool at a rate of 60 gallons per minute. 300
gallons have already been drained. How long will it take to drain the remaining
water in the pool?

Answer:

38

Step-by-step explanation:

Notice that the first triangle is an isosceles triangle, meaning that the base angles are equivalent. Since one angle is 62, we know that the other is 62 as well, which makes 124. This means that angle 2 is 56 degrees. Since 2 and 3 are on the same 'line', they both add up to 180. If 2 is 56, then angle 3 is 124. So the three angles inside the triangle are 124, 18, and x. So, 124+18=142. 180-142= 38

Answer:

120 feet is the answer

Answer:

C. ME ZH

B. IG LM

F. TH= NM

Step-by-step explanation:

The correct congruence statements are A, B, and C such that ∠N = ∠I, GH = LM, and ∠M= ∠H are true for similar triangles.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

To determine which congruence statements are correct, we need to identify the corresponding sides and angles of the triangles.

The corresponding sides and angles are those that are in the same position in each triangle.

Using this information, we can check each statement:

A. ∠N = ∠I: This statement is true because ∠N and ∠I are corresponding angles in the congruent triangles.

B. GH = LM: This statement is true because GH and LM are corresponding sides in the congruent triangles.

C. ∠M= ∠H: This statement is true because ∠M and ∠H are corresponding angles in the congruent triangles.

D. IG = LM: This statement is false because IG and LM are not corresponding sides in the congruent triangles.

E. IH = NM: This statement is false because IH and NM are not corresponding sides in the congruent triangles.

F. ∠L = ∠I: This statement is false because ∠L and ∠I are not corresponding angles in the congruent triangles.

Therefore, the correct congruence statements are A, B, and C.

To learn more on similar triangles click:

https://brainly.com/question/25882965

#SPJ5

2^2(-9 + 4)

First step: solve the brackets.

2^2(-5)

Second step: solve the exponent.

4(-5)

Final step: multiply.

-20

PS: Could you please mark as brainliest? Thanks!

Answer:

-20

Step-by-step explanation:

Perenthasis: (-9 + 4)

-5

Exponent: 2^2

4

Multiplacation: -5 x 4

-20

Answer:

The statements are not provided, so let's do a complete description of f(x)

In the graph, we can see two asymptotes at x = 1.

This means that the denominator is equal to 0 when x = 1, then we can write:

f(x) = A/(x - 1)

Where we can start thinking that A is a constant.

Now we also can see that when x = 2, f(2) is equal to 1, or:

f(2) = 1.

Then:

f(2) = 1   = A/(2 - 1) = A/1

Then we have  A = 1.

Then our function is:

f(x) = 1/(x - 1)

Amplitude is the maximum displacement of a function on a graph.

Amplitude is the maximum displacement of a function on a graph. It refers to the maximum height or distance from the baseline of a wave or oscillation.

It is often used in physics and engineering to describe the strength or size of a signal, vibration, or wave. In simple terms, it can be thought of as the "peak-to-peak" distance of a waveform, or the height of the waveform above and below the baseline.

But the minimum displacement of a function on a graph would typically be referred to as the minimum value or the "valley" of the function.

Learn more about amplitude on:

https://brainly.com/question/25699025

#SPJ1

Answer:

a) Cost of a chicken shawarma wrap?

$10.99

b) Cost of one order of spiced potatoes?

$4.99

Step-by-step explanation:

Cost of a chicken sharwarma wrap = a

Cost of an order of spiced potatoes = b

Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95.

3a + 2b = $42.95 .............Equation 1

Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91.

5a + 4b = $74.91 ................Equation 2

So we have:

3a + 2b = $42.95 .............Equation 1

5a + 4b = $74.91 ................Equation 2

We use Elimination method to solve for this.

Multiply Equation 1 by coefficient of b in Equation 2

Equation 2 by coefficient of b in Equation 1

3a + 2b= $42.95 .............Equation 1 × 4

5a + 4b = $74.91 ................Equation 2 × 2

12a + 8b = 171.80..............Equation 3

10a + 8b = 149.82..............Equation 4

Subtract Equation 3 from Equation 4

2a = 21.98

a = 21.98/2

a = 10.99

Therefore, a = Cost of Chicken sharwarma wrap = $10.99

Subtitute 10.99 for 9in Equation 1

3a + 2b = $42.95 .............Equation 1

3(10.99) + 2b = 42.95

32.97 + 2b = 42.95

2b = 42.95 - 32.97

2b = 9.98

b = 9.98/2

b = 4.99

b = Cost of an order of spiced potatoes = $4.99

Hence,

The cost of a chicken sharwarma wrap = $10.99

The cost of an order of spiced potatoes = $4.99

Answer:

The answer is the "Null hypothesis and Alternative hypothesis".

Step-by-step explanation:

The null hypothesis is almost like a hypothesis test, which indicates the certain demographic characteristics which aren't varied.

The alternative presumption will be that the hypothesis besides making predictions is opposite to the void assumption. Its posts are generally taken as a result of a meaningful effect.

Difference:

The null hypothesis is indeed a gross generalization, which specifies there is no relation between different phenomenons under evaluation. There is no association between the two groups. An alternate solution hypothesis is a statement, that defines there is a relation between different chosen variables in this study.

Step-by-step explanation:

In a rectangle all four segments of the diagonals would be equal....they are not...so this is NOT a rectangle

The answers are k = 12√2 and \(\theta=\frac{\pi }{2}+2\pi n\)

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Given are questions related to trigonometric functions:

a) k cos² (π/6) - k sin² (π/6) = 6√2

Finding k,

k cos² (π/6) - k sin² (π/6) = 6√2

Taking k common,

k [cos² (π/6) - sin² (π/6)] = 6√2

Since, cos²x-sin²x = cos2x

Therefore,

k[cos2(π/6)] = 6√2

k[cos(π/3)] = 6√2

Since, cos(π/3) = cos 60° = 1/2

Therefore,

k[1/2] = 6√2

k = 6√2 × 2

k = 12√2

b) sinx / cscx+cotx

\(\frac{sinx}{cscx+cotx}= \frac{sinx}{\frac{1}{sinx}+\frac{cosx}{sinx}}= \frac{sinx}{\frac{1+cosx}{sinx}}= \frac{sin^2x}{1+cosx}= \frac{1-cos^2x}{1+cosx}= \frac{(1+cosx)(1-cosx)}{1+cosx}\\\\= 1-cosx\)

Hence, proved.

c) sinθ = 2cos²θ + 1

Solving for θ

\(\sin \left(\theta\right)-2\cos ^2\left(\theta\right)-1=0\)

\(-3+\sin \left(\theta\right)+2\sin ^2\left(\theta\right)=0\)

\(\sin \left(\theta\right)=1,\:\sin \left(\theta\right)=-\frac{3}{2}\)

\(\sin \left(\theta\right)=1 : \theta=\frac{\pi }{2}+2\pi n\\\sin \left(\theta\right) = -\frac{3}{2} : no solution\\\theta=\frac{\pi }{2}+2\pi n\)

Where n is any integer,

Hence, the answers are k = 12√2 and \(\theta=\frac{\pi }{2}+2\pi n\)

Learn more about trigonometric functions, click;

https://brainly.com/question/6904750

#SPJ1

Answer: Vertex: (0,0)

Point: (3, -3)

Step-by-step explanation:

Answer:

you just math you know pretty easy when you know what to do

Step-by-step explanation:

just practice

Answer:

  x ≈ 4.239

Step-by-step explanation:

A relative minimum is found at the bottom of any U-shape on the graph. If you expand the graph shown until it has a suitable scale, it can show you the relative minimum occurs at x ≈ 4.239.

__

Additional comment

The relative maximum occurs at the top of any ∩-shape. The graphing calculator can show you that occurs at x ≈ -1.573.

Answer:

Um... u have no picture so we can't answer.

Step-by-step explanation:

There is only 1 possible 11-card hand that can be formed from a 20-card deck.

To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.

The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.

The formula for combinations is:

nCk = n! / (k!(n-k)!)

Where "!" denotes the factorial of a number.

Substituting the values into the formula:

20C11 = 20! / (11!(20-11)!)

Simplifying further:

20C11 = 20! / (11! * 9!)

Now, let's calculate the factorial values:

20! = 20 * 19 * 18 * ... * 2 * 1

11! = 11 * 10 * 9 * ... * 2 * 1

9! = 9 * 8 * 7 * ... * 2 * 1

By canceling out common terms in the numerator and denominator, we get:

20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)

Performing the multiplication:

20C11 = 39,916,800 / 39,916,800

Finally, the result simplifies to:

20C11 = 1

Consequently, with a 20-card deck, there is only one potential 11-card hand.

for such more question on combinations

https://brainly.com/question/28065038

#SPJ8

Answer:

36 < (x - 2)² + (y + 3)² and 16 > (x - 4)² + y²

Step-by-step explanation:

This is because the shaded area is inside the first circle (centered at (4, 0) with a radius of 4) but outside the second circle (centered at (2, -3) with a radius of 6). The inequalities reflect these conditions by setting the inequality signs accordingly. The inequality with "<" for the first circle ensures that the shaded area is within the circle, and the inequality with ">" for the second circle ensures that the shaded area is outside the circle.

Aircraft A has 312 seats.

Let's assume that Aircraft B has x seats.

According to the given information, Aircraft A has 105 more seats than Aircraft B. So, the number of seats in Aircraft A can be expressed as x + 105.

The total number of seats in both aircraft is 519, which can be represented by the equation:

x + (x + 105) = 519

Simplifying this equation, we have:

2x + 105 = 519

Subtracting 105 from both sides, we get:

2x = 414

Dividing both sides by 2, we find:

x = 207

Therefore, Aircraft B has 207 seats.

To find the number of seats in Aircraft A, we substitute the value of x back into the expression x + 105:

Aircraft A = 207 + 105 = 312

Hence, Aircraft A has 312 seats.

for such more question on number of seats

https://brainly.com/question/859564

#SPJ8

Using the conversion of fraction to decimal, the list that shows these lengths in order greatest to least is:

\(\frac{\sqrt{3}}{11}, \frac{\pi}{24}, \frac{3}{25}, \frac{9}{100}\)

A fraction is converted to decimal dividing the numerator by the denominator.

Hence the numbers in this problem are given as follows:

Hence, considering the conversions to decimal above, the list that shows these lengths in order greatest to least is:

\(\frac{\sqrt{3}}{11}, \frac{\pi}{24}, \frac{3}{25}, \frac{9}{100}\)

More can be learned about the conversion of fraction to decimal at https://brainly.com/question/1306233

#SPJ1

Answer:

23 oz

Step-by-step explanation:

We must multiply 6 by 3 because the kitten gains 3 ounces every week for 6 weeks.

6x3=18

Now we add the amount the kitten already was from the beginning.

18+5=23

Answer:

23 ounces

Step-by-step explanation:

Equation: 5+ 3x=y

5+ 3(6)=y

5+ 18=y

23=y

Answer:

18 Bowls of Candy

Step-by-step explanation:

Camila has 6 bags of candy, and she can pour 1/3 of a bag into a bowl. To determine how many bowls of candy she can make in total, we need to divide the total amount of candy by the amount of candy per bowl.

Since Camila can pour 1/3 of a bag into a bowl, it means she can make 3 bowls of candy with a full bag.

Now, we can calculate the total number of bowls of candy:

Total bowls of candy = (Number of bags) x (Bowls per bag)

Total bowls of candy = 6 bags x 3 bowls per bag

Total bowls of candy = 18 bowls

Therefore, Camila can make a total of 18 bowls of candy with her 6 bags of candy.

The point slope equation and slope of some lines are given below

1) For y - 6 = 3(x - 5), slope = 3

2) For  y - 4 = -9(x + 8), slope = -9

3) y - 2 = 5x, slope = 5

4) Point slope equation of line whose slope = -10 and passing through   (1, 4)

   y - 4 = -10(x - 1)

5) Point slope equation of line whose slope = 2 and passing through    (5, -3)

      y  + 3 = 2(x - 5)

6) Point slope equation of line whose slope = \(\frac{1}{2}\) and passing through    (-7, -7)

   \(y +7 = \frac{1}{2}(x +7)\\\)

What is equation of line in point slope form?

The most general form of equation of line in point slope form is given by \(y - y_1 = m(x - x_1)\) , \((x_1, y_1)\) is a point on the line

Where m is the slope of the line

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If  \(\theta\) is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = \(tan\theta\)

1) y - 6 = 3(x - 5)

  y - 6 = 3x - 15

  y = 3x - 15 + 6

  y = 3x - 9

  Slope = 3

  If x = 0,

  \(y = 3 \times 0 -9\\y = -9\)

  (0, -9) is a point on the line

2) y - 4 = -9(x + 8)

   y - 4 = -9x - 72

   y = -9x - 72 + 4

   y = -9x - 68

   Slope  = -9

   If x = 0

   \(y = -9 \times 0 -68\\y = -68\)

   (0, -68) is a point on the line

3) y - 2 = 5x

   y = 5x + 2

  Slope = 5

    Putting x = 0

    \(y = 5 \times 0 + 2\\y = 2\)

    (0, 2) is a point on the line

4) Slope = - 10

    The line passes through (1, 4)

    Point slope equation

      y - 4 = -10(x - 1)

5) Slope = 2

    The line passes through (5, -3)

     Point slope equation

      y - (-3) = 2(x - 5)

      y + 3 = 2(x - 5)

6) Slope = \(\frac{1}{2}\)

      The line passes through (5, -3)

     Point slope equation

       \(y - (-7) = \frac{1}{2}(x - (-7))\\y +7 = \frac{1}{2}(x +7)\\\)

To learn more about  point slope equation and slope, refer to the link-

https://brainly.com/question/24907633

#SPJ9

Answer:

Add 438 + 2 + 60 + 300

440 + 360

Step-by-step explanation:

The last one does not add up to 800

Good luck <3

1 mg = 1/1,000,000 kg =10^-6 kg

multiply 7,000,000 by 1/1,000,000

7,000,000 x (1/1,000,000) = 7 kg

Answer:

2 2/11

Step-by-step explanation:

Answer:

the lines covering the -2 are the absolute value sign. the absolute value of a number is always positive. so positive of -2 is 2 and -1 times positive 2 is -2

its -2

Step-by-step explanation:

Answer:

+2

Step-by-step explanation:

two negatuves make a posotive so -(-2)

+ 2

6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

For more questions on prime number

https://brainly.com/question/145452

#SPJ8