Simplify each expression.
10x³y²
5x³y
x = 0, y = 0

The rate of change of radius at radius 6cm is 0.79 cm/sec.

The rate of change of a function is simply the derivative of the function with respect to the changing parameter in the function i.e. variable in the function.

So for calculating the rate of change of radius, we calculate the rate of volume change as volume is the function of radius.

As we know volume of the cylinder is given by V=πr²h

where r is the radius and h is the height of the cyclinder.

Given that rate of change of volume = 563 cm/sec

⇒ dV/dt =563 cm/sec

⇒ d(πr²h)/dt =563

taking πh outside the derivative as π and h is constant term

⇒ πh dr²/dt =563

⇒ πh (dr²/dr)(dr/dt)= 563 (applying chain rule dy/dx = (dy/du)(du/dx))

⇒ πh(2r)(dr/dt) =563

⇒dr/dt= 563/(2πhr)

given height of the cylinder h= 19cm

rate of change of radius at radius r =6cm= dr/dt= 563/(2πhr)= 563/(2*π*19*6)= 0.79 cm/sec

Therefore rate of change of radius at radius 6cm is 0.79 cm/sec.

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Answer:

7s²7p⁴

Step-by-step explanation:

Livermorium is located in the seventh period and sixteenth column of the periodic table. The noble gas configuration for livermorium is [Rn]7s²5f¹⁴6d¹⁰7p⁴. The valence electrons are the ones in the orbitals with the highest quantum number (coefficient). Remember, there can be up to 8 valence electrons at one time. Therefore, the valence electron configuration is 7s²7p⁴.

Let's check

Electronic configuration

Valence electrons

The two types of transformations that can be used to transform f(x) to g(x).  g (x) = f(x) + 16 and g (x) = f(x + 8)

ABC has vertices at A (12, 8), B (4, 8)

f(x)= 0, -1 ,5,14

g(x)= -6, -1, -1, 14

g(x)=f(x)+k

-6= 0+k

k= -6

A) g (x) = f(x) + 16 and

g(x) = f(x + 8)

B) g(x)=f(x)+k

-1= -1+ k

k= -1+1=0

g(x)=f(x)+k

-1= 5+k

k= -1-5=-6

g(x)=f(x)+k

14= 14+k

k= 0

k= -6,0,-6,0

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Answer:

1)  x + 96 = 90°

2)  x + 89 = 80°

Step-by-step explanation:

Consecutive Interior Angles Theorem

When a transversal line intersects two parallel lines, it forms two pairs of consecutive angles on either side of the transversal line.  Each pair of consecutive interior angles are supplementary (sum to 180°).

To find the measure of the angle circled on the diagram, find the value of x by using the Consecutive Interior Angle Theorem:

⇒ (x + 96)° + (x + 96)° = 180°

⇒ x + 96 + x + 96 = 180

⇒ 2x + 192 = 180

⇒ 2x + 192 - 192 = 180 - 192

⇒ 2x = -12

⇒ 2x ÷ 2 = -12 ÷ 2

⇒ x = -6

Substitute the found value of x into the expression to find the measure of the angle circled on the diagram:

⇒ x + 96 = -6 + 96 = 90°

⇒ x + 96 = 90°

To find the measure of the angle circled on the diagram, find the value of x by using the Consecutive Interior Angle Theorem:

⇒ (x + 109)° + (x + 89)° = 180°

⇒ x + 109 + x + 89 = 180

⇒ 2x + 198 = 180

⇒ 2x + 198 - 198 = 180 - 198

⇒ 2x = -18

⇒ 2x ÷ 2 = -18 ÷ 2

⇒ x = -9

Substitute the found value of x into the expression to find the measure of the angle circled on the diagram:

⇒ x + 89 = -9 + 89

⇒ x + 89 = 80°

Answer:

[tex]\boxed {1) 90^{o}}\\\boxed {2) 80^{o}}[/tex]

Step-by-step explanation:

Part 1 :

Part 2 :

Answer:

-7

Step-by-step explanation:

you can use power rule of derivatives for that.

Answer:

m3+5

Step-by-step explanation:

m is miles

take the number of miles  multiply by3

take that answer add 5

The equation that represents the cab's total charge is  y = 3x + 5 , Option A is the correct answer.

A statement that relate two expressions with an equal sign is called an Equation.

It is given that

A cab company charges a $5 boarding

Charges for every mile is $3 per mile

Let x be the mile travelled

The cab's total charge is represented by y

then y = 3x + 5

Therefore the equation that represents the cab's total charge is  y = 3x + 5 , Option A is the correct answer.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: final \:\:value = -x + 6 \degree[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: (7x - 3x) - (5x - 6)[/tex]

[tex]\qquad \tt \rightarrow \: (4x) - 5x - ( - 6)[/tex]

[tex]\qquad \tt \rightarrow \: 4x - 5x + 6[/tex]

[tex]\qquad \tt \rightarrow \: - x + 6[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:6-x

Step-by-step explanation:

The solution is in the image

Answer:

[tex] \sqrt{10} [/tex]

Step-by-step explanation:

Rule: [tex] \sqrt{a} \times \sqrt{b} = \sqrt{ab} [/tex]

[tex] \sqrt{5} \times \sqrt{2} = \sqrt{5 \times 2} = \sqrt{10} [/tex]

The true statement regarding the intervals where the function is increasing and decreasing is option A: The function is increasing from (–∞, 0).

A function is defined as a relation between the set of inputs having exactly one output each.

On a coordinate plane, a parabola opens down with solid circles along the parabola at (-3, -5), (-2, 0), (-1, 3), (0, 4), (1, 3), (2, 0), (3, -5).

The domain is all real numbers.

The range is all real numbers.

If for an interval I, when x decreases meanwhile staying in interval I, the function's output increases (or can stay same), then we say that the function is increasing in the interval.

The true statement regarding the intervals where the function is increasing and decreasing is option A: The function is increasing from (–∞, 0).

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Answer:

A

Step-by-step explanation:

Answer:

x = 7

Step-by-step explanation:

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

3x - 12 - 5 = x - 3

2x = -3 + 12 + 5

2x = 14

x = 7

Answer:

- In 45 days = 4,5mm  ;    In 90 days = 9mm

Step-by-step explanation:

in 45 days = 0,1 * 45 = 4,5 mm  ; in 90 days = 0,1 * 90 = 9mm

Answer:

y = 5 and y = 1

Step-by-step explanation:

[tex]\textsc {Subtract 7 from each side :}[/tex]

⇒ (3y - 2)² + 7 - 7 = 43 - 7

⇒ (3y - 2)² = 36

[tex]\textsc {take the square root on each side :}[/tex]

⇒ √(3y - 9)² = √36

⇒ 3y - 9 = ±6

[tex]\textsc {When equal to +6, add 9 on each side :}[/tex]

⇒ 3y - 9 + 9 = 6 + 9

⇒ 3y = 15

[tex]\textsc {Divide by 3 on each side :}[/tex]

⇒ 3y/3 = 15/3

⇒ y = 5

[tex]\textsc {When equal to -6, add 9 on each side :}[/tex]

⇒ 3y - 9 + 9 = -6 + 9

⇒ 3y = 3

[tex]\textsc {Divide by 3 on each side :}[/tex]

⇒ 3y/3 = 3/3

⇒ y = 1

The correct statement compares the means of the data in the dot plots is option C; the mode is greater for Mrs. Ramos’s class.

Median represents the middle value of the given data when arranged in a particular order.

Mode is that number that appears most frequently in the given set of data.

Given;

The Number of pets in Mr. McIntyre’s class ;

0,0,0,0,0,1, 1, 1, 1, 1, 4, 4, 4, 4, 1,

Median = 1

Mode = 0 and 1

The Number of pets in Mrs. Ramos’s Class;

0, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 3, 3, 3

Median = 3

Mode = 4 and 5

Hence, C; The mode is greater for Mrs. Ramos’s class.

The remaining part of the question is

"Which statement correctly compares the measures of center of the data in the dot plots?

The median is greater for Mr. McIntyre’s class.

The median is the same for both classes.

The mode is greater for Mrs. Ramos’s class.

The mode is the same for both classes."

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Answer:

Step-by-step explanation:

The tax paid by the condominium owner  is $2,632.88.

Tax is a compulsory levy that is paid to the government. The type of tax that is paid by the condominium owner is known as property tax.

Tax paid = (78,584 / 100) x $3.49 x (1 - 0.04) = $2,632.88.

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1) The definitely true for the statement is b) P(-5) = 3.

2) The three roots are 5, 3 + 4i, and 3 - 4i. Option D is correct.

If there is a polynomial p(x), and a constant number 'a', then

[tex]\dfrac{p(x)}{(x-a)} = g(x) + p(a)[/tex]

where g(x) is a factor of p(x)

Given;

1) When the polynomial P(x) is divided by x+5, the remainder is 3.

If a polynomial P(x) is divided by (x-a), then the remainder is P(a).

If the polynomial P(x) is divided by (x+5), then the remainder will be P(-5).

So, P(-5) = 3

Therefore, the definitely true for the statement is b) P(-5) = 3.

2) P is a 3 degree polynomial with real coefficients and three zeros. Two of the zeros are 5 and 3+4i.

The complex roots always exist in conjugate pairs so,

3 + 4i and 3 - 4i

Thus, the three roots are 5, 3 + 4i, and 3 - 4i. Option D is correct.

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Answer:

Aprism =  483.246 yd2

Step-by-step explanation:

The surface area is the sum of the 2 circles areas and the rectangle area.

Ac1 = PI*r2

Ac1 = (3.14)*(11.4/2)2

Ac1 = 102.0186 yd2

Ac1 = Ac2 then

Ac2 = 102.0186 yd2

Now the perimeter of the circle is one the sides of the rectangle:

Pc = 2PI*r

Pc = 2*3.14*(11.4/2)

Pc = 35.796 yd

Now the area of the rectangle is:

Ar = 7.8yd*35.796yd

Ar = 279.2088 yd2

Then, the surface area of prism is:

Answer:

The height of the water increases 2 inches per minute.

Step-by-step explanation:

the slope is always the ratio of

y coordinate change / x coordinate change

in our case, x is the time (minutes), and y is the water height (inches).

we see, the longer the pool get filled, the higher the water gets. logical, right ?

by checking the data points we see :

with every 2 minutes passing the water height increases by 4 inches.

so, the slope is +4/+2 = 2/1 = 2

and that ratio tells us now the increase of the water height with every fraction or multiple of the measured 2-minute interval.

every 2 minutes 4 inches more.

so, e.g. every 3×2 = 6 minutes we get 3×4 = 12 inches more.

and - every 1/2 × 2 = 1 minute more we get 1/2 × 4 = 2 inches more.

Answer:

898

Step-by-step explanation:

898999

Step-by-step explanation:

x = total area of land

x - 1/6 × x - 5/9 × x = 48.5 | multiply both sides by 6

6x - x - 30/9 × x = 291

5x - 30/9 × x = 291 | multitude both sides by 9

45x - 30x = 2,619

15x = 2,619

x = 174.6 acres

pineapples were planted on 174.6 × 1/6 = 29.1 acres.

durians were planted on 174.6 × 5/9 = 97 acres.

Answer:

43

Step-by-step explanation:

31+12=43

Therefore adding 43 to -31 should give the answer 12.

Hii!

____________________________________________________________

Answer:

43

Step-by-step explanation:

We can find an answer to this question by setting up an equation.

-31+x=12

x is the unknown amount we should add to -31 to obtain 12.

Now, to solve it for the variable, x, we need to add 31 to both sides.

Upon doing this we obtain.

x=43

∴, 43 should be added to -31 to get 12

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Hope that this helped! Best wishes.

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The equation of the red graphed function is: g(x) = 1 - x².

Given the graph shown in the attachment below, the graphed function heads downwards, and the x - axis is intercepted at ( 1, 0 ) and (-1,0).

Thus, the x-intercepts, which is the zeros of the function, are: 1 and -1.

So, g(x) = (x + 1)(x -1)

Expand:

g(x) = 1 - x²

The equation of the red graph is: g(x) = 1 - x².

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Answer: 10

Step-by-step explanation: The diameter is twice the radius

The number of students is 33.2 million

Percent decrease refers to the percent change in the value when it is decreased over a period of time. Percentage decrease expresses the decrease in the given value with respect to its initial value in the form of a percentage.

Given:

In 2019= 16.6 million

% decrease = 5%

So,

% decrease= x - 16.6/ x

5% = x- 16.6/x

0.05= (x-16.6)/x

0.05x = x-16.6

-0.05 x = -16.6

x= 16.6/0.05

x= 16600000/0.05

x= 332,000,000

x= 33.2 million.

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Answer:

I think it's 80%

Step-by-step explanation:

Method 1: (40/50)*100 = 80%

Method 2: [tex]\frac{40*2}{50*2} = \frac{80}{100}[/tex] = 80%

Answer:

C

Step-by-step explanation:

y = 3x - 4

4y = 12x - 4

divide the bottom equation by 4

y = 3x - 4

y = 3x - 1

y = -3

3x - 1 = -3

3x = -2

x = -2/3

(-2/3, -3) is the answer. by this logic, there is a splution so can't be a, the answer is not (0, 4) so not b so it must be c

Answer:

the next number is 47+ 16 =63

A bag contains 3 blue, 7 green and 1 purple counter. One counter is picked at random, the probability of selecting a green or purple counter is 8/11.

Probability is a measure of the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur.

There are a total of 11 counters in the bag, 3 of which are blue, 7 are green, and 1 is purple.

The probability of selecting a green or purple counter is the sum of the probabilities of selecting a green counter and a purple counter, since the events are mutually exclusive (a counter cannot be both green and purple at the same time).

So the probability of selecting a green or purple counter is:

Probability = (Number of green counters + Number of purple counters) / Total number of counters

Probability = (7 + 1) / 11

Probability = 8/11

Therefore, the probability of selecting a green or purple counter is 8/11.

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