a pool can hold up to 850 gallons. It now has 598 gallons of water and is being filled at the rate shown. How many more minutes, m, can water continue to flow into the pool before it overflows? write and solve an inequality.

Answer:

The figure obtained is a cylinder

The exact surface area is 1440π.

Step-by-step explanation:

* Lets study the rotation of a rectangle around one of its sides

- If the dimensions of the rectangle are length (L) and width (W)

- If we rotate the rectangle around its length (L), we will construct

 a cylinder with radius = W and height = L

- If we rotate the rectangle around its width (w), we will construct

 a cylinder with radius = L and height = W

∵ The surface area of any cylinder =

   perimeter of base × height + 2 base area

∵ The base is a circle

∴ perimeter base = 2πr and base area = πr²

∴ The surface area = 2πrh + 2πr²

* In first case:

- Surface area = 2π(W)L + 2π(w)² = 2πWL + 2πW²

* In second case:

- Surface area = 2π(L)W + 2π(L)² = 2πLW + 2πL²

* Now lats check our question:

∵ L = 22 and W = 18

- It will rotate around the largest side

∴ It will rotate around L

∴ The figure obtained is a cylinder

* From the explanation above this is the first case

∵ L = 22 and W = 18

∵ The surface area = 2πWL + 2πW²

∴ The surface area = 2 × 18 × 22 × π + 2 × (18)² × π

                                = 792π + 648π = 1440π

* The exact surface area is 1440π.

Answer:

The 16 term will be 28,697,814

Step-by-step explanation:

The pattern here is that Each number is being Multiplied by 3

Example= (2x3=6)  (6x3=18)  (18x3=54) (54x3=162) keep doing that until you get the  16th term.

Took me a while....

Hopes this helps you!

To help u out

Change equation to 145-40=

Subtract.

Replace c with 105 so; 40+105=145

Answer:

F

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

Simplify the following:

43 + 2 (3 - 2)

3 - 2 = 1:

43 + 2×1

2×1 = 2:

43 + 2

43 + 2 = 45:

Answer:  45

Answer:

STOP SAYING ITS 45 BECAUSE ITS NOT THE 43 IS SUPPOSED TO BE 4 TO THE POWER OF 3

Step-by-step explanation:

okay?

Answer:

rational

Step-by-step explanation:

any number that can be written as a fraction is rational, it is also a termintating decimal.

Answer:   rational

Step-by-step explanation:

[tex]\dfrac{1}{4}=0.25\\\\\text{Since the decimal terminates (ends), it is a rational number.}[/tex]

n can be whatever number u want it to be or whatever number given because it is a variable

Answer:

30 Mintues to get there + 30 Mintues early = 1 hour

2:00 PM - 1 hour = 1 PM

Step-by-step explanation:

B is the answer hope this helps!

B) is the answer, my reasoning is that A) is 2n - 15 and four tenths which is the wrong way around , C) is just nonsense and D) is n multiplied by 15 and four tenths take away 2 which is also wrong , as that would be n x 13 and four tenths , hope this helps :)

Answer:

false

Step-by-step explanation:

because it doesn’t have the three complete angles

Answer:

False

Step-by-step explanation:

Answer:

[tex]\large\boxed{V=\dfrac{256\sqrt3}{3}\ cm^3}[/tex]

Step-by-step explanation:

The formula of a volume of a square pyramid:

[tex]V=\dfrac{1}{3}(b^2)(H)[/tex]

b - edge of a base

H - height

We have b = 8cm and the triangle 90 - 60 - 30. The sides of that triangle are in ptoportion 1 : √3 : 2 (look at the picture).

From the picture we have

[tex]a=\dfrac{b}{2}\to a=\dfrac{8}{2}\ cm=4\ cm[/tex]

Therefore

[tex]H=a\sqrt3\to H=4\sqrt3\ cm[/tex]

Substitute:

[tex]V=\dfrac{1}{3}(8^2)(4\sqrt3)=\dfrac{1}{3}(64)(4\sqrt3)=\dfrac{256\sqrt3}{3}\ cm^3[/tex]

To find the volume of any cube you need to know the length, width and height. The formula to find the volume multiplies the length by the width by the height. The good news for a cube is that the measure of each of these dimensions is exactly the same. Therefore, you can multiply the length of any side three times.

Answer:

#6.  36    #30. 24

Step-by-step explanation:

6. You add 7+29=36 so 36 is the missing number

Answer:

The value of x is [tex]58\°[/tex]

Step-by-step explanation:

we know that

The measurement of the external angle is the semi-difference of the arcs which comprises

so

In this problem

[tex]51\°=\frac{1}{2}(160\°-x\°)[/tex]

solve for x

[tex]102\°=(160\°-x\°)[/tex]

[tex]x=160\°-102\°=58\°[/tex]

This is very spread out just to show properly but you could get it smaller haha

In this algebra problem, we created two equations from the problem and solved them simultaneously, finding that Darlene burns 15 calories per minute jogging and 10 calories per minute cycling.

This question is about working out two equations using two variables, a classic application in

algebra

. Let's call the calories burned per minute jogging as

J

, and the calories burned per minute cycling as

C

. From the information given in the question, we know that:

These equations can be solved simultaneously. To make things easier, let's multiply the second equation by 2, which gives us:

By subtracting equation 1 from this, we get:

30C = 300

, simplifying this, we find that

C = 10 calories per minute for cycling

. Substitute C=10 into the first equation, we get:

20J + 100 = 400

, which simplifies to

J = 15 calories per minute for jogging

. Thus, Darlene burns 15 calories for each minute of jogging and 10 calories for each minute of cycling.

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Answer:

428,820,000 pounds

Step-by-step explanation:

The amount of garbage is number of person times the amount produced by each person. Thus, we have:

Amount of Garbage (in pounds) = 2.61 × 10^5 * 1.643 × 10^3

Note: We multiply 2.61 and 1.643, which is 4.28823 & multiplying 10^5 and 10^3 is 10^(5+3) = 10^8

Thus, we have 4.28823 * 10^8 = 428,823,000 pounds

This is approximately 428,820,000 pounds, last answer choice.

Answer:

Other answer is correct, confirmed on E2020

Step-by-step explanation:

Answer:

(C)$62.00

Step-by-step explanation:

$200 x .31 = $62.00

the answer is C it is $62.00

I also need help with this too so I'm just here to wait and see the answer

The speed is the distance covered by an object at a particular time. The speed at which the fisherman travels in still water is 11 mph.

The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.

[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]

Let the speed of the boat be represented by x mph.

A fisherman travels 8 miles downstream with the current at the same time that he travels 3 miles upstream against the current. Also, the speed of the current was 5 mph. Therefore,

8 miles/ (x + 5)mph = 3 miles/(x - 5) mph

8x - 40 = 3x + 15

5x = 55

x = 11 mph

Learn more about Speed:

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The solution to the given inequality is [tex]b\leq 1.7[/tex]

From the question, we to determine the solution to the inequality.

To determine the solution of the inequality, we will determine the value of the variable. The variable in the given question is b.

The inequality can be solved as shown below.

[tex]\frac{7}{2} \geq b + \frac{9}{5}[/tex]

Multiply through by 10

That is,

[tex]10 \times \frac{7}{2} \geq 10\times b + 10\times \frac{9}{5}[/tex]

This becomes

[tex]5 \times 7 \geq 10b + 2 \times 9[/tex]

[tex]35 \geq 10b + 18[/tex]

Now, subtract 18 from both sides

[tex]35 - 18\geq 10b + 18-18[/tex]

[tex]17 \geq 10b[/tex]

This becomes,

[tex]10b \leq 17[/tex]

Divide both sides by 10

[tex]\frac{10b}{10} \leq \frac{17}{10}[/tex]

[tex]b\leq 1\frac{7}{10}[/tex]

OR

[tex]b\leq 1.7[/tex]

Hence, the solution to the given inequality is [tex]b\leq 1.7[/tex]

Learn more on Inequalities here: https://brainly.com/question/24372553

60 people claimed they they got at least eight hours of sleep.

Answer:

Step-by-step explanation:

We know that 30 people claimed that they get an average of seven hours of sleep. Using the circular diagram, we find that these 30 people represent 25% of the total number of people.

According to the graph, people that get at least eight hours of sleep each night represent 65%, that is, 50% of the people sleep eight hours and 15% sleep nine or more.

Then, we use the rule of three, if 30 people represent 25% of the total, how many people would represents 65%?

[tex]x=65\%\frac{30 \ people}{25 \%} = 78 \ people[/tex]

Therefore, 78 people claimed that they get at least eight hours of sleep each night.

Answer:

-4j-4k-4g

Step-by-step explanation:

Answer:

Hello there! How are you doing? I am doing fine! I'll answer the question now.

So basically, your hunger would be satisfied with the 2 slices of 8 inches, because although one slice of 8 inches is two inches less than the 10 inch slice. But then you could add another 8 inch slice and it would make it greater and bigger than the one 10 inch slice itself. So in conclusion, the 2, 8 inch slices would be better than the 1, 10 inch slice because 16 inches is greater than 10 inches.

Hope this helped! Your welcome! I can help with other history stuff too! And byee! :)

Step-by-step explanation:

Two slices from an 8-inch pizza provide more pizza than one slice from a 10-inch pizza based on the calculation of the areas of the pizza slices. Therefore, your hunger would be better satisfied with the two pieces from the 8-inch pizza.

The subject here is a mathematical comparison of the area of different pizza sizes and the number of slices eaten. The location of a pizza can be calculated using the formula for the circle size, which is πr², where r is the radius of the pizza.

In the case of a 10-inch pizza, the radius is 5 inches (half of the diameter). So the area is π(5)² = 78.5 square inches. One slice of this pizza would be 1/8th of the total area, approximately 9.81 square inches.

For an 8-inch pizza, the radius is 4 inches. So the area is π(4)² = 50.24 square inches. Two slices of this pizza would amount to 1/4th of the total area, approximately 12.56 square inches.

So, when it comes to fulfilling your hunger at lunch, two slices of an 8-inch pizza would be more satisfying as it offers more pizza than one slice of a 10-inch pizza.

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all real numbers such that y is less than or equal to 4

ANSWER

all real numbers less than or equal to 4.

EXPLANATION

The given function is

[tex]f(x) = - (x + 5)(x + 1)[/tex]

Expand

[tex]f(x) = - ( {x}^{2} + x + 5x + 5)[/tex]

[tex]f(x) = - ( {x}^{2} + 6x + 5)[/tex]

[tex]f(x) = - {x}^{2} - 6x - 5[/tex]

a=-1,b=-6,c=-5

The x-value of the vertex is given by

a=-1,b=-6,c=-5

[tex]x = \frac{ - b}{2a} [/tex]

[tex]x = - \frac{ - 6}{2( - 1)} = - 3[/tex]

The y-value of the vertex is

[tex]f( - 3) = - ( - 3 + 5)( - 3 + 1)[/tex]

[tex]f( - 3) = - ( 2)( - 2) = 4[/tex]

Since a=-1, the function opens downwards.

The highest value is the y-value of the vertex which is 4.

Therefore the range is all real numbers less than or equal to 4.

The correct choice is A.

Answer:

|-----|-----|-----|-----0-----|-----|     |------|------|------|------|------0------|-----|

0  1/6 2/6 3/6 4/6 5/6  1     0    1/7   2/7  3/7  4/7  5/7  6/7   1

Step-by-step explanation:

since 4/6 means the fourth one of the 6 spots, we can just make a number line that is split into 6 parts and find the fourth line. we do the same thing with seven to get the answers above

Final answer:

To show 4/6 and 5/7 on a number line, mark 42 equal sections between 0 and 1, and place 4/6 at the 28th mark and 5/7 at the 30th mark, as they equate to 28/42 and 30/42 respectively.

Explanation:

To show 4/6 and 5/7 on a number line, you would follow these steps:

Both 4/6 and 5/7 will be placed between 0 and 1 on the number line, with 4/6 slightly to the left of 5/7.

Answer:

2/5

Step-by-step explanation:

it is 2/5

Probability = 12/25 or 48%.

To find the probability that a number chosen at random from the positive, even integers from 2 to 50 is divisible by 3 or 8, we need to count the number of even integers within this range that are divisible by 3 or 8, and then divide this count by the total number of even integers in the range.

First, let's find how many even integers between 2 and 50 are divisible by 3.

The even integers divisible by 3 in this range are: 6, 12, 18, 24, 30, 36, 42, 48.

Count: 8

Now, let's find how many even integers between 2 and 50 are divisible by 8.

The even integers divisible by 8 in this range are: 8, 16, 24, 32, 40, 48.

Count: 6

Notice that 24 and 48 are counted twice because they are divisible by both 3 and 8. We only want to count them once.

So, the total count of even integers between 2 and 50 that are divisible by 3 or 8 is 8 (from being divisible by 3) + 6 (from being divisible by 8) - 2 (counting 24 and 48 once) = 12.

Now, we calculate the total number of even integers between 2 and 50:

Total even integers between 2 and 50 = (50 - 2) / 2 + 1 = 25

Now, we can calculate the probability:

Probability = (Number of favorable outcomes) / (Total number of outcomes)

            = 12 / 25

            = 0.48

So, the probability that a number chosen at random from the positive, even integers from 2 to 50 is divisible by 3 or 8 is 0.48.

Answer:

(x - 7)² + (y - 2)² = 130

Step-by-step explanation:

The first step is finding the length of the radius.

r² = (2 - -5)² + (7 - -2)²

    = 7² + 9²

    = 49 + 81

   = 130

The general equation of a circle is:

(x - a)² + (y - b)² = r²

Where (a, b) is the coordinate of the center and r is the radius.

∴ The equation of the required circle is;

 (x - 7)² + (y - 2)² = 130

Answer:

The correct answer option is [tex]r^2-6rsin(\theta)=8[/tex].

Step-by-step explanation:

We are given the following equation and we are to rewrite it in polar form:

[tex]x^2 + y^2 - 6y - 8 = 0[/tex]

[tex]\left \{ {{x^2+y^2=r^2} \atop {y=rsin \theta}} \right.[/tex]

Here, we need to make a perfect square trinomial:

[tex][r^2-6rsin(\theta)+[/tex] ___[tex]^2]=8[/tex]

[tex]6rsin(\theta)[/tex] ---> [tex]2 .r.3.sin \theta[/tex]

Completing the square to get:

[tex]r^2-6rsin(\theta)+[3sin(\theta)]^2-[3sin(\theta)]^2=8[/tex]

[tex][r-3sin(\theta)]^2=8+[3sin(\theta)]^2[/tex] --> [tex][r-3sin(\theta)]^2=8+9sin^2(\theta)[/tex]

[tex]r-3sin(\theta)=\sqrt{8+9sin^2(\theta)}[/tex] --> [tex]r=\sqrt{8+9sin^2(\theta)} +3sin(\theta)[/tex]

the correct answer is B. r^2=6r sin 0+8

Answer:

see explanation

Step-by-step explanation:

Given f(x) = - 20x² + 23x - 6

To find the zeros set f(x) = 0, that is

- 20x² + 23x - 6 = 0 ( multiply through by - 1 )

20x² - 23x + 6 = 0

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 20 × 6 = 120 and sum = - 23

The factors are - 15 and - 8

Use these factors to split the x- term

20x² - 15x - 8x + 6 = 0 ( factor the first/second and third/fourth terms )

5x(4x - 3) - 2(4x - 3) = 0 ← factor out (4x - 3)

(4x - 3)(5x - 2) = 0

Equate each factor to zero and solve for x

4x - 3 = 0 ⇒ 4x = 3 ⇒ x = [tex]\frac{3}{4}[/tex]

5x - 2 = 0 ⇒ 5x = 2 ⇒ x = [tex]\frac{2}{5}[/tex]

Answer:

-(4x - 3)(5x - 2) = 0

Step-by-step explanation: