A trough is 12 ft long and its ends have the shape of isosceles triangles that are 5 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 13 ft3/min, how fast is the water level rising when the water is 8 inches deep?
I have been getting 13/30, but apparently, that is wrong?

V=.5 * h * l * b

Because of similar triangles:
b = 5h (b/h = 5/1)
l = 12

V = .5 * h * 5h * 12
V = 30h^2
(dV/dt) = 60 h (dh/dt)

dV/dt = 13
h = .5 (because this is in feet)

13 = 60*.5(dh/dt)
13/30 = dh/dt

The value of the 4 in the number 5,679.04 is 4,000.

The value of the 4 in the number 5,679.04 is 4,000. In the given number, 5,679.04, the digit 4 is in the thousands place, which means it represents 4,000.

Final answer:

The value of the 4 in the number 5,679.04 is in the thousandths place.

Explanation:

Place value is a fundamental concept in mathematics that assigns a numerical value to each digit in a number based on its position. The rightmost digit represents the units, the next digit to the left represents tens, and so on.

For example, in the number 60, the digit 6 is in the tens place, indicating 6 tens or 60. Understanding place value is crucial for performing arithmetic operations and comprehending numerical relationships.

Thus,

The value of the 4 in the number 5,679.04 is 4,000.

In the given number, 5,679.04, the digit 4 is in the thousands place, which means it represents 4,000.

Answer: Using the graph to find the solution of the given equation, the solutions are:

Option A.) -4 and 2

Solution:

The solutions in the graph are the values of "x" where the curves intercept. In this case the curves intercept at x=-4 and at x=2, then the solution of the equation are -4 and 2

The ages of  Edna, Ellie, and Elsa are 35, 36, 37 respectively.

For any integer say 'a', its consecutive integers will be → (a + 1), (a + 2), (a + 3), .... , (a + n).

Given is the sum of ages of Edna, Ellie, and Elsa is 108.

Assume that the age of Edna is x.

Then the ages of Ellie and Elsa will be (x + 1) and (x + 2) respectively.

From the question we can write -

x + (x + 1) + (x + 2) = 108

3x + 3 = 108

3x = 105

x = 35

So, we can write -

Age of Edna = 35

Age of Ellie = 36

Age of Elsa = 37

Therefore, the ages of  Edna, Ellie, and Elsa are 35, 36, 37 respectively.

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The y-intercept means that Karma was given $60 for her birthday. Therefore, option C is the correct answer.

The given equation that models the given situation is y=75x+60.

The y-intercept of a graph is the point where the graph intersects the y-axis.

We know that the x-coordinate of any point on the y-axis is 0. So the x-coordinate of a y-intercept is 0.

Now, Graph the line using the slope and y-intercept, or two points.

Slope: 75

y-intercept: (0, 60)

The coordinates to plot the graph is (0, 60) and (1, 135).

Here, in the graph, if we then look at the y-intercept we can see that the function crosses the y-axis at a value of 60.

Therefore we can safely say that the y-intercept means that Karma was given $60 for her birthday.

The y-intercept means that Karma was given $60 for her birthday.

Therefore, option C is the correct answer.

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The product of 7⋅(−4)⋅(−6) from the information illustrated is D. 168.

It should be noted that the product of a number simply means the multiplication of the numbers that are given.

This is quite a straightforward question. The product will be:

= 7⋅(−4)⋅(−6)

It should be noted that (-) × (-) = +

Therefore, 7⋅(−4)⋅(−6)

= 7 × 4 × 6

= 168

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Adding and subtracting decimals are easy to understand you are just adding a decimal point

For example, 2 plus 2 equals 4

2.0 plus 2.0 equals 4.0

Answer:

4, 12, 36, 108  is set of geometric sequence.

Step-by-step explanation:

Given  : geometric sequence.

To find : Which set of numbers is a geometric sequence.

Solution : We have given geometric sequence.

In a Geometric Sequence each term is found by multiplying the previous term by a constant.

Like : {a, ar, ar², ar³, ... }, where , a = first term , r = common ration .

We can see sequence 4, 12, 36, 108 in form of  4 , 4*3 , 4 (3)² , 4( 3)³.

Here, common ration is 3.

Therefore, 4, 12, 36, 108  is set of geometric sequence.

A vertical number line resembles a thermometer. It emphasizes that we count up in the number system.  Vertical number lines are just alternative way to look at the numbers.

This is commonly used in adding or subtracting

For example: 5 – 3

5 is the start, the sign determines whether you go down or go up, the minus sign denotes down then so the last number denotes how many steps you are going down where you land is the answer. The same goes with addition but instead of down, the plus sign denotes going up.

Answer:

The Standard form of number is,

⇒ 0.1588

We have to give that,

Scientific notation is,

⇒ 1.588 × 10⁻¹

Since Scientific notation is a way of writing very large or very small numbers.

For example; 230,000,000 can be written in scientific notation as

2.3 x 10⁸.

Hence, the Standard form of number is,

⇒ 1.588 × 10⁻¹

⇒ 1.588 / 10

⇒ 0.1588

Therefore, The solution is, 0.1588

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Answer:

The answer is option A : 4 gallons.

Step-by-step explanation:

A recipe for 10 servings of raspberry sorbet calls for 2 cups of water, 1/1.2 cups of granulated sugar, and 4 cups of frozen raspberries.

Now 10 servings need = 2 cups of water.

And 320 servings will need = [tex]\frac{2}{10}\times320= 64[/tex] cups of water.

Now, 1 cup = 0.0625 gallons

So, 64 cups are = [tex]0.0625\times64=4[/tex] gallons

Therefore, answer is option A : 4 gallons.