Simplify using PEMDAS and logic, 1 step at a time. (3+7) x(2 x 3) ​

The rate at which the volume of the cylinder is changing is 600 mm^3/min, and the rate at which the surface area is changing is 240π mm^2/min.

To find the rate at which the volume and surface area of the cylinder are changing, we can use the given formulas for volume and surface area and differentiate them with respect to time. Let's calculate the rates at the moment when the radius of the base is 10 mm.

Given:

Radius rate of change: dr/dt = 3 mm/min

Height: h = 20 mm

Radius: r = 10 mm

Volume of the cylinder (V) = \(r^2h\)

Differentiating with respect to time (t), we have:

dV/dt = 2rh(dr/dt) + \(r^2\)(dh/dt)

Since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dV/dt = 2(10)(20)(3) + (10^2)(0)

dV/dt = 600 + 0

dV/dt = 600 mm^3/min

Therefore, the rate at which the volume of the cylinder is changing at the given moment is 600 mm^3/min.

Surface area of the cylinder (SA) = 2πrh + 2π\(r^2\)

Differentiating with respect to time (t), we have:

dSA/dt = 2πr(dh/dt) + 2πh(dr/dt) + 4πr(dr/dt)

Again, since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dSA/dt = 2π(10)(0) + 2π(20)(3) + 4π(10)(3)

dSA/dt = 0 + 120π + 120π

dSA/dt = 240π mm^2/min

Therefore, the rate at which the surface area of the cylinder is changing at the given moment is 240π mm^2/min.

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Answer:

76

Step-by-step explanation:

450/100 = 4.5

342/4.5 = 76

The rate of decrease of the weather in degrees per hour is 2 degrees.

The time elapsed is from 5:00 PM to 9:00 PM, which is 4 hours.

The temperature dropped from 20 degrees to 12 degrees, which is a change of -8 degrees.

Therefore, the rate of decrease of the weather in degrees per hour is:

-8 degrees / 4 hours = -2 degrees per hour

A measurement of how quickly the temperature changes over time is the rate of change. Depending on the time frame being considered, it is typically represented in units of degrees per hour, degrees per minute, or degrees per second. Depending on whether the temperature is rising or falling, the rate of temperature change can be either positive or negative. The temperature rises when the rate of change is positive; it falls when the rate of change is negative.

Many variables, including the amount of sunlight, wind speed, humidity, and the time of day, have an impact on the pace of temperature change. Generally speaking, temperature varies more quickly during the day than it does at night, and it varies more quickly in places with less foliage and more exposed ground. Human activity, such as the emission of greenhouse gases into the atmosphere, which can eventually lead to an increase in global temperatures, can also have an impact on the pace of change of temperature.

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The smaller number is 6 .

The larger number is 22

Let's let x be the smaller number and y be the larger number.

From the problem, we know that one number is eight less than five times the other, so we can write:

y = 5x - 8

We also know that the sum of the two numbers is 28, so we can write:

x + y = 28

Now we have two equations in two variables. We can solve for one of the variables in terms of the other, and substitute that expression into the other equation to eliminate one variable.

Let's solve the first equation for x

x = (y + 8)/5

Now we can substitute this expression for x into the second equation:

(y + 8)/5 + y = 28

Multiplying both sides by 5 to eliminate the fraction, we get:

y + 8 + 5y = 140

Combining like terms, we get:

6y + 8 = 140

Subtracting 8 from both sides, we get:

6y = 132

Dividing both sides by 6, we get:

y = 22

Now we can use the equation y = 5x - 8 to solve for x:

22 = 5x - 8

Adding 8 to both sides, we get:

30 = 5x

Dividing both sides by 5, we get:

x = 6

Therefore, the smaller number is 6 and the larger number is 22.

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Answer:

that's 4,188.8 if it's gonna be a 10cm sphere

Answer:

1) 11^42. [. ( a^b)^c is a^bc]

2) 5^5. [a^b/a^c= a^(b-c)

3) 14^24

4) 3^10

The number of pounds of strawberries sold and the number of pounds of grapes sold is 32 and 20 respectively.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given that the selling price of strawberries each pound = $2.50,

The selling price of grapes each pound = $2

The total earning = $160

Let x is the no of a pound of strawberries and y is the no of a pound of grapes sold, then equation will be,

x = y + 12 and 2.50x + 2y= 160

Solve the equation by substitution method;

x = 32 and  y = 20

Therefore, the number of pounds of strawberries sold is 32

the number of pounds of grapes sold is 20.

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Answer:

Step-by-step explanation:

208

Answer:

It means that the both sides of the expression in the given equation must be/are congruent.

Hope this helps!

Answer:

I think the answer might be b.

Step-by-step explanation:

Answer:

Given the information in the question;

a) The parameter of interest is the population of artists who are left-handed and its is 10% = (10/1000 = 0.10

b) The Null hypothesis and alternative hypothesis are;

H₀ : p = 0.10

H₁ : p > 0.10

c) The sample proportion is calculated as:

p = number of left handed artist / sample size

p = 26 / 200

p = 0.13

d) To find the p-value, The researcher should calculate the probability that the sample proportion would be 0.13 or larger for a sample of size 200 if the population proportion is actually 0.10.

\(215.\)

Step-by-step explanation:

\(4 + 62 = 66.\)

\(66 + 9 = 75.\)

\(75 \times 3 =225.\)

\(225 - 10 = 215.\)

Answer:

A.) 32.5 Square Feet

Step-by-step explanation:

10ft + 6.5 = 16.5

16.5 + 13 = 19.5

19.5 + 13 = 32.5

10ft + 6.5 + 3 + 13 = 32.5

Answer: Te answer is A   32.5

Step-by-step explanation:

Answer:

bbbbbbbbbbbbbbbbbbbbbbbbb

Answer: No

To check if (-5,6) is a solution to the equation y=-7, we need to substitute -5 for x and 6 for y in the equation.

If the equation is true, then the ordered pair is a solution to the equation.

If we put (-5,6) into y=-7, we get 6=-7, which is not true.

So, (-5,6) is not a solution to the equation y=-7.

Answer:

the correct answer is 193

Step-by-step explanation:

25×1-0=25

25×2-1=49

49×2-1=97

97×2-1=193

Answer:

x=90°

Step-by-step explanation:

As in the angle, there is a box giving us info that x has to be 90°.

But to be sure that there is no mistake we have to do the following:

So we are looking at the surroundings of angle x (which is on a straight line) we see that it is a right angle and look at the angle on the same line is a right angle too.

The equation right angle=90° helps us see that because there are two right angles on a 180° line (90°+90°+180°).

Therefore the answer is:

x=90°

Answer:

4 and -5

Step-by-step explanation:

malfyrhxosddifufigif

Answer:

B) 5mm, 3mm, 7mm

Step-by-step explanation:

Triangles can only be formed when the sum of each two sides of the triangle is greater than the other side.

A.

\(6cm+9cm>2cm\)

\(9cm+2cm > 6cm\)

\(6cm+2cm < 9cm\) <-

Because \(6cm+2cm < 9cm\), ∴ Option A cannot form a triangle.

B.

\(5mm+3mm > 7mm\)

\(5mm + 7mm > 3mm\)

\(3mm+7mm > 5mm\)  

Because all combinations satisfy, ∴ Option B can form a triangle.

C.

\(4cm+8cm > 3cm\)

\(8cm+3cm > 4cm\)

\(4cm+3cm < 8cm\) <-

Because \(4cm+3cm < 8cm\), ∴ Option C cannot form a triangle.

D.

\(5mm + 2mm > 1mm\)

\(5mm+1mm>2mm\)

\(1mm+2mm<5mm\) <-

Because \(1mm+2mm<5mm\), ∴ Option D cannot form a triangle.

Hope this helps :)

Answer:

1. b, 20

Step-by-step explanation:

1. Irrational numbers between 4 and 5 are √17, √18,√19,√20,√21,√22,√23 ,√24.

Answer:

y = 3x - 6

Step-by-step explanation:

Slope-interecept form is a "fill-in-the-blank" formula for writing the equation of a line. It is in the form:

y = mx + b

You fill in the slope for m and fill in the y-intercept for b.

You could totally graph these points and see the slope and y-intercept. But here's how to find them on the table.

When x is 0, y is -6. The y-intercept is where x is 0. So here, the y-intercept is -6. That is b. Fill in -6 in place of b.

y = mx + -6

Next pick any two points. I'm using the last two (3,3) and (4,6). Subtract the y's. 6-3 is 3, put that on top of a fraction. Subtract the x's, 4-3 is 1. Put that on the bottom of a fraction. That is the slope, 3/1. That is the m. Fill it in.

y = 3/1 x + -6

Clean it up (simplify)

y = 3x - 6

Answer:

boom bam ba boom bam ba

Answer: -3/4

Step-by-step explanation:

The y value is decreasing by -0.75

-3.75 - 0.75 = -4.5

-4.5 - 0.75 = -5.25

-5.25 - 0.75 = -6

ect.

-0.75 in fraction form is -3/4

Answer:

Step-by-step explanation:

Slope of the line:

\(m = \frac{y-y1}{x-x1} \\\)

Given:

slope = -3/4

point (x1,y1) = (2, -1)

Substitute and solve

\(m = \frac{y-y1}{x-x1} \\-\frac{3}{4} = \frac{y-(-1))}{x-2} \\-3(x-2) = 4(y+1)\\-3x + 6 = 4y + 4 \\Transpose\\4y = -3x + 6 - 4\\4y = -3x + 2 \\y = -3/4x + 2/4\\y = -3/4x + 1/2\\OR\\4y +3x - 2 = 0\)

1/2 is the y-intercept

(0,1/2)

Since we have 2 points already, we can then graph the line.

(2, -1) and (0, 1/2)

Answer:

m = -1/3

Step-by-step explanation:

Find two points in order to calculate slope:

Slope (m) =

ΔY /ΔX= -1/ 3= -0.33333333333333

Slope intercept:

y = -0.33333333333333x + 2

Answer:

Slope = - 1/3

Step-by-step explanation:

Choose the point on the right and move upwards. How many times did you move upwards until you were at the same level as the point on the left? You moved once, which means your rise is 1.

Now from the point where you are at now, move right or left depending on where the point is. In this case, it's on the left which means our run will be negative. Now move left until you reach that point on the left. How many times did you move left? You moved three times, which means your run is 3.

Rise/Run = -1/3

Slope = Rise/Run

Slope: - 1/3

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Answer:

4/15

Step-by-step explanation:

2/5 drive

1/3 bus

and rest walk

fraction of those who walk is 1-(2/5+1/3)

2/5+1/3=(6+5)/15=11/15

15/15-11/15=4/15

John William is entitled to purchase 15,000 shares before the offering is made to the public.

a. To calculate the percentage of the total vote John William will control, we need to find the proportion of shares he owns out of the total shares represented at the meeting.

John William owns 6,000 shares out of the 20,000 shares offered so far. Therefore, the proportion of shares he owns is 6,000/20,000, which simplifies to 3/10 or 0.3.

To convert this proportion to a percentage, we multiply by 100:

Percentage of the total vote = 0.3 * 100 = 30%

Thus, John William will control 30% of the total vote at the.         shareholder meeting.    

b. Preemptive rights allow existing shareholders to purchase new shares before they are offered to the public. To determine the number of shares John William is entitled to purchase, we need to calculate the proportion of his current ownership.

John William owns 6,000 shares out of the total shares offered so far, which is 20,000. Therefore, his ownership proportion is 6,000/20,000, or 3/10.

If Peixotto Media plans to issue 50,000 new shares, John William's entitlement would be:

Entitlement = (3/10) * 50,000 = 15,000 shares.

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As per the given data, to enable the drain pipe to carry 60 liters per second, there needs to be a 66.67% increase in the diameter of the drain pipe.

We must comprehend the link between the carrying capacity and the area of the pipe's cross-section in order to calculate the percentage increase in the drain pipe's diameter required to make it capable of carrying 60 litres per second.

The cross-sectional area of the pipe directly relates to its carrying capacity. This implies that the carrying capacity will grow if the cross-section's area increases.

Q ∝ A

Q1/A1 = Q2/A2

A2 = (Q2/Q1) * A1

A2 = (60/36) * A1

A2 = (5/3) * A1

Percentage increase = (A2 - A1)/A1 * 100

Percentage increase = [(5/3) * A1 - A1]/A1 * 100

Percentage increase = (2/3) * 100

Percentage increase = 66.67%

Thus, the answer is 66.67%.

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