A conical tank has height 3 m and radius 2 m at the top. Water flows in at a rate of 0.7m^3/min. How fast is the water level rising when it is 0.8 m?

Final answer:

One strategy for converting a rate measured in one pair of units to a rate measured in a different pair of units is to use unit analysis. The conversion from ounces per cup to pounds per gallon is 1 lb / 2 gal.

Explanation:

One strategy for converting a rate measured in one pair of units to a rate measured in a different pair of units is to use unit analysis. This involves setting up conversion factors to cancel out the unwanted units. Here's an example:

Therefore, the conversion from ounces per cup to pounds per gallon is 1 lb / 2 gal.

To solve the equation 3(4d) – 14 = 15 – 5d – 4d, we need to simplify the equation and isolate d. The value of d is 29/21.

To find the value of d in equation 3(4d) – 14 = 15 – 5d – 4d, we need to simplify the equation and isolate d on one side of the equation. Let's start:

Therefore, the value of d in the equation is 29/21.

Jamie made $2375 of sales on one week and earns 20% of it as a commission.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Jamie is a salesperson in a shoe store and earns $95 per week, plus 20% of her weekly sales.

Jamie makes $475 in one week which is 20% of the total sale assuming he made $x worth of sales.

∴ (20/100)×x = 475.

0.2x = 475.

x = 475/0.2.

x = $2375

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The real number resulting from the expression x-y/xy is positive when x is negative and y is positive. This is determined by following the rules of signs in arithmetic where subtracting a positive number from a negative results in a negative and dividing a negative number by another negative results in a positive.

The given expression in question is x-y/xy. To understand the sign of the resulting real number we have to discern the signs of x, y and the result of subtraction, x-y.

As mentioned, x is less than 0 and hence negative and y is greater than 0, thus positive. So when you subtract a positive number y from the negative number x, the result will obviously be negative. This is due to the 'rules of signs' in arithmetic.

Then, for the division, when you divide this negative result by the multiplication of x (which is negative) and y (which is positive), the answer will be positive. This is again because of the 'rules of signs' for division - a negative number divided by a negative number yields a positive number.

So, the sign of the result of the real number expression x-y/xy is positive when x<0 and y>0.

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The answer is  

x ≥ 4

x + y ≤ 10

y ≥ 0

The linear equation to find the area of the carpet after applying Felix's $50 discount is 3.50 × A = 180, where A represents the area in square feet. After solving the equation, we find that the area is 51.43 square feet.

To find the area, A, of the carpet that Felix buys, we can set up a linear equation based on the total cost after the discount and the cost per square foot. The original price of the carpet is $230, but Felix has a coupon for a $50 discount, reducing the cost to $180. Since the cost per square foot of the carpet is $3.50, we can denote the area of the carpet as A, and set up the equation:

3.50 × A = 180

To solve for A, we divide both sides of the equation by 3.50:

A = 180 / 3.50

A = 51.43 square feet

Answer:

C) Step 3

Step-by-step explanation:

We are given that

[tex]4x+5< 6x+1[/tex]

We have to find the mistake made by Mia in her solution.

Step 1:[tex]4x+5<6x+1[/tex]

Reason: Given

Step 2: [tex]4x-6x+5<+1[/tex]

[tex]-2x+5<1[/tex]

Reason: Subtraction property of inequality

Step 3: [tex]-2x <1-5[/tex]

[tex]-2x<-4[/tex]

Reason: Using subtraction property of inequality

Step 4:[tex]-x<-2[/tex]

[tex]x>2[/tex]

Reason: Division property of inequality

Mia did mistake in step 3 .She using addition property instead of subtraction property.

Option C is true.

The moment of inertia of the thin rectangular sheet of metal about the specified axis is[tex]\( \frac{Ma^2}{4} + \frac{Mb^2}{12} \).[/tex]

To find the moment of inertia  I of the thin rectangular sheet of metal about an axis passing through its center and parallel to the side with length b, we can use the parallel axis theorem.

This theorem states that the moment of inertia about any axis parallel to the axis passing through the center of mass can be found by adding the moment of inertia about the center of mass and the product of the mass and the square of the perpendicular distance between the two axes.

The moment of inertia of a thin rectangular plate about its center and perpendicular to its plane is given by:

[tex]\[ I_c = \frac{M}{12}(a^2 + b^2) \][/tex]

where M is the mass of the plate, a and b are the lengths of the sides of the rectangle.

Now, let's denote d as the perpendicular distance between the axis passing through the center and the axis parallel to the side with length b. Since the axis is passing through the center of the rectangle, d is half the length of side a, so [tex]\( d = \frac{a}{2} \)[/tex].

Using the parallel axis theorem, the moment of inertia about the desired axis is:

[tex]\[ I = I_c + Md^2 \][/tex]

[tex]\[ I = \frac{M}{12}(a^2 + b^2) + M\left(\frac{a}{2}\right)^2 \][/tex]

[tex]\[ I = \frac{M}{12}(a^2 + b^2) + \frac{M}{4}a^2 \][/tex]

[tex]\[ I = \frac{Ma^2}{12} + \frac{Mb^2}{12} + \frac{3Ma^2}{12} \][/tex]

[tex]\[ I = \frac{Ma^2}{4} + \frac{Mb^2}{12} \][/tex]

Thus, the moment of inertia of the thin rectangular sheet of metal about the specified axis is[tex]\( \frac{Ma^2}{4} + \frac{Mb^2}{12} \).[/tex]

To simplify the expression (9x^8y^3)^1/2, distribute the 1/2 exponent to the numerical coefficient and to the variables, resulting in 3x^4y^(3/2).

To simplify the expression (9x^8y^3)^1/2, we will apply the rule that states when you have an exponent (in this case the 1/2, which denotes a square root) outside the parentheses, you distribute it to both the numerical coefficient and the variables inside the parentheses. Using this rule:

Thus, the simplified form of the expression will be 3x^4y^(3/2).

The expression (9x^8y^3)^(1/2) can be simplified as 3x^4y^(3/2).

To simplify the expression, we need to understand the properties of exponents. When we have a number or variable raised to a fractional exponent, it means taking the corresponding root of the number or variable.

In this case, we are taking the square root (1/2 exponent) of each term within the parentheses: 9, x^8, and y^3.

The square root of 9 is 3 because 3^2 = 9.

The square root of x^8 is x^(8/2) = x^4 because (x^4)^2 = x^8.

The square root of y^3 is y^(3/2) because (y^(3/2))^2 = y^3.

Combining these simplified terms, we get 3x^4y^(3/2).

Therefore, the expression (9x^8y^3)^(1/2) simplifies to 3x^4y^(3/2).

Answer:

Arc length XPY =28.26 m.

Step-by-step explanation:

Given : A circle with two arc XY and XPY and radius 6 m.

To find  : Arc length XPY.

Solution : We have given that arc XY and XPY .

Radius = 6 m.

Central angle formed by arc XPY = 360 - 90 = 270.

Arc length = 2 *pi* r ( [tex]\frac{central\ angle}{360}[/tex].

Plugging the values

Arc length = 2 *3.14 * 6 ( [tex]\frac{270}{360}[/tex].

Arc length =37.68 ( [tex]\frac{3}{4}[/tex].

Arc length =37.68 * 0.75

Arc length XPY =28.26 m.

Therefore, Arc length XPY =28.26 m.

Answer:

The length of arc XPY=28.26 m

Step-by-step explanation:

We are given that a circle in which

Radius=6 m

Central angle made by arc XPY=[tex]360-90=270^{\circ}[/tex]

We have to find the length of arc XPY.

We know that

Arc length formula:[tex]\frac{central\;angle}{360^{\circ}}\times 2\pi r[/tex]

Substitute the value in the formula then we get

Length of arc XPY=[tex]\frac{270}{360}\times 2\times 3.14 \times 6=28.26 m[/tex]    ([tex]\pi=3.14[/tex])

Hence, the length of arc XPY=28.26 m

First, rearrange the equation so that only zero will be on the right side:

x^2 + 14x +24 = 0

Let the coefficients be:

a = 1

b = 14

c = 24

To complete the square, add (b/2)^2 to both sides of the equation:

(b/2)^2 = 49

x^2 + 14x + 49 + 24 = 49

x^2 + 14x + 49 = 25

(x+7)^2 = 25

Therefore, the solution set of the equation is {-12, -2}

The solution set of the quadratic equation x² + 14x = −24 is [-12, -2] option (a) is correct.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

We have a quadratic equation:

x² + 14x = −24

It is required to solve the equation by completing the square.

First, arrange the quadratic equation

x² + 14x + 24 = 0

x² + 14x + 7² - 7² + 24 = 0

(x + 7)² -25 = 0

(x + 7)²  = 25

x + 7 = ±5

Taking positive sign:

x + 7 = 5

x = -2

Taking negative sign:

x + 7 = -5

x = -12

The solution set is [-12, -2]

Thus, the solution set of the quadratic equation x² + 14x = −24 is [-12, -2] option (a) is correct.

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The answer is $62.59

The correct answer is:

Row 15.

Explanation:

Each row of Pascal's triangle corresponds with the exponent of a binomial. The first row is a binomial to the first power; the second row, to the second power; the third row, to the third power; etc.

For the 15th power, we would want the 15th row of the triangle.

Answer:

option c

Step-by-step explanation:

because i said soooo

Answer

Find out the what is the minimum simple interest rate Maggie needs to reach her goal .

To proof

Formula

[tex]Simple\ interest = \frac{principle\times rate\times time}{100}[/tex]

As given

Maggie has $14,100 to invest, and wishes to gain $4,000 in interest over the next eight years.

put all the values in the formula

[tex]4000 = \frac{14100\times rate\times 8}{100}[/tex]

Solving

[tex]rate = \frac{4000\times 100}{14100\times8}[/tex]

solving the above

[tex]rate = \frac{400000}{112800}[/tex]

rate =3.55% (approx)

the minimum simple interest rate Maggie needs to reach her goal is 3.55% .

Option (b) is correct .

Hence proved

To compare 77% and 3/5, we convert them to the same format. 77% is equivalent to 77/100 and 3/5 is equivalent to 60/100, or 60%. Therefore, 77% is greater than 3/5.

In order to compare 77% and 3/5, you should convert them both to the same format. Percentages are a way of expressing a number as a fraction of 100. Hence, 77% can be written as 77/100.

Similarly, the fraction 3/5 remains as is, which is equivalent to 60/100, or 60% when converted into a percentage.

Comparing these values, it is clear that 77% is greater than 3/5, or 60%.

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Final answer:

After converting 3/5 to a percent (60%), we can see that 77% is greater than 60%, making 77% the greater value.

Explanation:

To determine which is greater, 77% or 3/5, we need to compare them either as percentages or as decimals. First, let's convert 3/5 to a percent. To do this, we divide the numerator by the denominator to get the decimal: 3 ÷ 5 = 0.6. Then, we convert the decimal to a percent by multiplying by 100: 0.6 × 100 = 60%.

Now that we have both numbers as percentages, we can easily compare them: 77% is greater than 60%. Therefore, 77% is greater than 3/5.