How to find the volume of a hemispherical bowl depth h?

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Answer:

[tex]y=\frac{3}{2}x+10[/tex]

Step-by-step explanation:

Given equation of line : [tex]2x + 3y = -5[/tex]

Standard form of equation of line = [tex]y=mx+c[/tex]  ---A

Where m is the slope

Convert the given equation in standard form

[tex]2x + 3y = -5[/tex]

[tex] 3y = -5-2x[/tex]

[tex] y =\frac{-5}{3}-\frac{2}{3}x[/tex]

So, slope =[tex]m = -\frac{2}{3}[/tex]

If the two lines are perpendicular then the product of their slopes is -1

Let n be the slope of required equation of line

So, [tex]m \times n = -1[/tex]

[tex]-\frac{2}{3}\times n = -1[/tex]

[tex]n=\frac{3}{2}[/tex]

Substitute this value in A

[tex]y=\frac{3}{2}x+c[/tex]  --B

Now we are given that the required perpendicular line passes through the point (–6, 1)

So, substitute  (–6, 1)  in B

[tex]1=\frac{3}{2}(-6)+c[/tex]  

[tex]1-(\frac{3}{2}(-6))=c[/tex]  

[tex]10=c[/tex]  

Substitute the value of c in B

[tex]y=\frac{3}{2}x+10[/tex]

Hence the slope-intercept form of the equation of the line that passes through the point (–6, 1) and is perpendicular to the graph of 2x + 3y = –5? is  [tex]y=\frac{3}{2}x+10[/tex]

Answer:  The correct option is (B) [tex]\dfrac{9}{4}.[/tex]

Step-by-step explanation:  We are given to find the term that has to be added to [tex]x^2-3x[/tex] to be a perfect trinomial.

Let, c denote the term to be added.

Then,

[tex]x^2-3x+c\\\\=x^2-2\times x\times \dfrac{3}{2}+c\\\\\\=x^2-2\times x\times \dfrac{3}{2}+\dfrac{9}{4}+c-\dfrac{9}{4}\\\\\\=\left(x-\dfrac{3}{2}\right)+c-\dfrac{9}{4}.[/tex]

Therefore, the given expression will be a perfect trinomial if

[tex]c-\dfrac{9}{4}=0\\\\\\\Rightarrow c=\dfrac{9}{4}.[/tex]

Thus, the required term to be added is [tex]\dfrac{9}{4}.[/tex]

Option (B) is CORRECT,

Answer:

Third option 30° 28' 10"

Brainlist?

Step-by-step explanation:

m∠ROT, formed by adjacent angles m∠ROS (20° 15' 40") and m∠SOT (10° 12' 30"), measures 30° 28' 10" according to the Angle Addition Postulate.

Attached diagram.

To find the measure of angle ROT (m∠ROT), you can use the Angle Addition Postulate.

The Angle Addition Postulate states that the measure of an angle formed by two adjacent angles is equal to the sum of the measures of those two angles.

Here m∠ROS and m∠SOT as adjacent angles forming m∠ROT.

m∠ROS = 20 degrees 15 minutes 40 seconds

m∠SOT = 10 degrees 12 minutes 30 seconds

To find m∠ROT, add the measures of m∠ROS and m∠SOT:

m∠ROT = m∠ROS + m∠SOT

First, add the degrees, then the minutes, and finally the seconds separately:

Degrees: 20 degrees + 10 degrees = 30 degrees

Minutes: 15 minutes + 12 minutes = 27 minutes

Seconds: 40 seconds + 30 seconds = 70 seconds

Now, simplify the seconds by converting any excess seconds into minutes:

70 seconds = 1 minute and 10 seconds

Now, add the minutes to the total:

27 minutes + 1 minute = 28 minutes

So, m∠ROT is:

30 degrees 28 minutes 10 seconds

Therefore, the measure of the angle m∠ROT = 30 degrees 28 minutes 10 seconds.

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The above question is incomplete, the complete question is:

Use the following diagram to complete the required information. m∠ROS = 20 deg 15' 40", m∠SOT = 10 ° 12' 30"

m∠ROT =

30 ° 27' 10"

31 ° 28' 10"

30 ° 28' 10"

Attached diagram.

Answer: Option B

x = 10

Step-by-step explanation:

just did it on edge

if a spherical water tank holds 12,500 ft³of water then the diameter of the tank is 29 ft.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that the spherical water tank holds 12,500 ft³of water

We need to find the volume of the spherical water tank.

We know that volume of sphere=4/3πr³

Volume of sphere is 12,500  ft³

12500=4/3×3.14r³

12500=4.186r³

Divide both sides by 4.186

12500/4.186=r³

2986.144=r³

Take cube root on both sides

∛2986.144=r

14.40=r

We know diameter=2r

Diameter=2×14.4

=28.8=29

Hence, if a spherical water tank holds 12,500 ft³of water then the diameter of the tank is 29 ft.

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Final answer:

To calculate the number of employees at V&B Bank Company between the ages of 20 and 30 out of the total 13,220 employees, we multiply 13,220 by the ratio of 7/20, yielding 4,627 employees in that age range.

Explanation:

The question asks how many employees at V&B Bank Company are between the ages of 20 and 30, given that 7 out of every 20 employees are in that age bracket and that the total number of employees is 13,220.

First, find the fraction of employees that are between the ages of 20 and 30 by dividing 7 by 20.

Fraction of employees aged 20-30 = 7 / 20

Next, calculate the number of employees in that age bracket by multiplying the total number of employees (13,220) by the fraction calculated above.

Number of employees aged 20-30 = 13,220 * (7 / 20)

By performing that multiplication:

Number of employees aged 20-30 = 13,220 * 0.35

Number of employees aged 20-30 = 4,627

Therefore, there are 4,627 employees at V&B Bank Company who are between the ages of 20 and 30.

Here are the calculations to find the percentages:

1. [tex]15\text{m}$ is what percent of $60\text{m}?[/tex]

[tex]\frac{15\text{m}}{60\text{m}} \times 100\% = \frac{1}{4} \times 100\% = 25\%[/tex]

2. [tex]15\text{m}$ is what percent of $3\text{m}?[/tex]

[tex]\frac{15\text{m}}{3\text{m}} \times 100\% = 5 \times 100\% = 500\%[/tex]

3. [tex]15\text{m}$ is what percent of $30\text{m}?[/tex]

[tex]\frac{15\text{m}}{30\text{m}} \times 100\% = \frac{1}{2} \times 100\% = 50\%[/tex]

4. [tex]15\text{m}$ is what percent of $1.5\text{km}?[/tex]

[tex]1.5\text{km} = 1500\text{m}[/tex]

[tex]\frac{15\text{m}}{1500\text{m}} \times 100\% = \frac{1}{100} \times 100\% = 1\%[/tex]

Therefore, the percentages are:

1. [tex]15\text{m}$ is $25\%$ of $60\text{m}[/tex]

2.[tex]15\text{m}$ is $500\%$ of $3\text{m}[/tex]

3. [tex]15\text{m}$ is $50\%$ of $30\text{m}[/tex]

4. [tex]15\text{m}$ is $1\%$ of $1.5\text{km}[/tex]

yes,

a cuboid with dimensions 2, 4, 8 has volume = 64 unit^3

a cube with side 4 has volume = 64 unit^3

so, they have different shapes but same volume

The x-intercept is (-3,0) and the y-intercept is (0,-6/5).

The x-intercept is the point where the line crosses the x-axis. To find the x-intercept, we set y=0 and solve for x. In the equation 2x+5y=-6, we substitute 0 for y and solve for x:

2x + 5(0) = -6

2x = -6

x = -3

So, the x-intercept is the point (-3,0).

The y-intercept is the point where the line crosses the y-axis. To find the y-intercept, we set x=0 and solve for y. In the equation 2x+5y=-6, we substitute 0 for x and solve for y:

2(0) + 5y = -6

5y = -6

y = -6/5

So, the y-intercept is the point (0,-6/5).