A 40-liter fish tank is being filled with a faucet at a constant rate of 2 liters per minute. Before the faucet is turned on, the fish tank has a volume of 3 liters. The volume of water V in the fish tank is a function of time t. Time is measured in minutes and volume of water is measured in liters. Use the equation to complete the function table.
​

Answer:

-3/2

Step-by-step explanation:

slope= rise/run = -60/40 = -6/4 = -3/2

Check the picture below.

a) The average rate of change of a function over an interval is the change in the function's output (f(b) - f(a)) divided by the change in the function's input (b - a). So, to find the average rate of change of f over the interval -4 <= x <= 3, we can use the formula:

(f(3) - f(-4)) / (3 - (-4)) = (sqrt(25 - 9) - sqrt(25 - 16)) / (3 - (-4)) = (-2sqrt(7) + 4sqrt(3)) / 7

b) To find the derivative of f(x), we need to use the power rule and the chain rule. The power rule states that the derivative of x^n is nx^(n-1), and the chain rule states that the derivative of f(g(x)) is f'(g(x)) * g'(x).

So, the derivative of f(x) = sqrt 25 - x^2 is:

-2x

c) To find the equation of the line tangent to the graph of f at x = -3, we need to use the point-slope form of a line, which is:

y - y1 = m(x - x1)

where m is the slope of the line (which is f'(-3) = -6), (x1, y1) is the point on the graph where the line touches (which is (-3, f(-3)) = (-3, sqrt(25 - 9) = 2sqrt(7))

so we have: y - 2sqrt(7) = -6(x + 3)

d) To check if g(x) is continuous at x = -3, we need to check if the limit of g(x) as x approaches -3 exists and is equal to g(-3).

Since g(x) = f(x) for -5 <= x <= -3 and g(x) = x + 7 for -3 <= x <= 5, we have:

g(-3) = f(-3) = sqrt(25 - 9) = 2sqrt(7)

and the limit of g(x) as x approaches -3 is:

lim x->-3 g(x) = lim x->-3 (x + 7) = -3 + 7 = 4

Since g(-3) = 2sqrt(7) and lim x->-3 g(x) = 4, g(x) is not continuous at x = -3.

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Answer:

Step-by-step explanation:

no

Answer:

22:18

Step-by-step explanation:

In this case, firstly you have to add 11 and 9 together, which makes 20.

Then, 40 ( number of sweets ), divided by 20 gives us 2.

This means that every piece, or block, of our ratio will be 2.

Therefore, the last step is multiplying 11x2 and 9x2.

So, Andy has 22 sweets an Trevor has 18.

Answer:

a = 3

Step-by-step explanation:

The point (- 5, 7a ) satisfies the equation

Substitute the coordinate points into the equation and solve for a

7a = 7(- 5) + 56 = - 35 + 56 = 21 ( divide both sides by 7 )

a = 3

Answer: The explicit formula for this sequence is given by the expression a_n = 3^n, where n is the position in the sequence (starting from n=1 for the first term).

The recursive formula for this sequence is given by the expression a_n = 3a_(n-1), where n is the position in the sequence (starting from n=1 for the first term) and a_(n-1) is the previous term in the sequence.

Here's how you can use the recursive formula to find the terms of the sequence:

a_1 = 2

a_2 = 3a_1 = 3 * 2 = 6

a_3 = 3a_2 = 3 * 6 = 18

a_4 = 3a_3 = 3 * 18 = 54

a_5 = 3a_4 = 3 * 54 = 162

and so on.

To find the explicit formula, you can try to find a pattern in the terms of the sequence. For example, you might notice that each term is simply the previous term multiplied by 3. This pattern can be expressed using the recursive formula a_n = 3a_(n-1). To find the explicit formula, you can then solve for a_n in terms of n:

a_n = 3a_(n-1)

a_n / 3 = a_(n-1)

a_n / 3 = (3a_(n-2)) / 3

a_n / 3 = 3^(n-2)

a_n = 3^n

Therefore, the explicit formula for this sequence is a_n = 3^n.

Step-by-step explanation:

Answer:22 days

Step-by-step explanation: since 6days are each given 5ml spoons of medicine three times a day,

Therefore consumption of each day is 90 ml and we have 2000 ml(2litre=2000 ml)

so, 2000/90 = we will get number of days

therefore 22.22 days

Which emplies 22 days.

The expression is 8n – 3; The 100th term is 797

The nth term of an arithmetic sequence is given by:

an=a1+(100-1)d          ....[1]

where

a1  is the first term

d is the common difference of two consecutive terms.

n is the number of terms.

Given the sequence:

5, 13, 21, 29, 37, 45, …

This is an arithmetic sequence with first term  = 5 and common difference(d) = 8

Since;

13-5 = 8,

21-13 = 8,

29-21 = 8  and so on....

We have to find the 100th term in the sequence

Substitute in [1] we have;

an=a1+(100-1)d

an=5+(n-1)8=5+8n-8 = 8n-3

Substitute the given values and n=100 we have;

a100= 800 - 3 = 797

Therefore, the 100th term in the sequence is, 797 and an expression to describe a rule for the sequence is, 8n – 3;

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Answer:

Hello! answer: x = 3

each rectangle = 48 Hope that helps!

Answer:

Average rate of change

=

26.5

Explanation:

Use the slope formula to find average rate of change:

m

=

y

2

−

y

1

x

2

−

x

1

To use the slope formula, you need 2 points on the curve - we only have to x values, so we need to find f(8) and f(10).

f

(

8

)

=

92

f

(

10

)

=

145

These means are points are

(

x

1

,

y

1

)

=

(

8

,

92

)

and

(

x

2

,

y

2

)

=

(

10

,

145

)

.

m

=

145

−

92

10

−

8

m

=

53

2

m

=

26.5

Step-by-step explanation:

The average rate of change on the interval from 0 to 10 is 30

The function is given as:

f(x)=3x^2-8

The interval is given as:

0 to 10

Calculate f(0) and f(10)

f(0)=3 *(0)^2 -8

f(0) = -8

f(10)=3 *(10)^2 -8

f(10) = 292

The average rate of change is then calculated as:

Rate = (f(10) - f(0))/(10 - 0)

This gives

Rate = (292 +8 )/(10 - 0)

Evaluate

Rate = 30

Hence, the average rate of change on the interval from 0 to 10 is 30

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a) The given relation is function.

b) The function is, $x = 18.5 y

c) The value of (f+ g)(9) is 5.

d) The he original amount of her loan is 6000.

A function with one or two variables and no exponents is referred to as a linear function. It is a function with a straight line as its graph.

Given:

a) The given relation is function because is input have have output, no two outputs have same input.

b) After 8 hours, a person earned $148 in wages.

So, the unit rate change = 148/ 8

                                        = 18.5

So, if y represents the number of hour and $x the wages, then the function is $x = 18.5 y.

c)  Let f(x)=x and g(x)=x-13

(f+ g)(9)

= (x+  x-13) (9)

= 2x -13

= 2(9)- 13

= 5

d) The modeled function. P(m) = 6000 - 300m.

so, the original amount of her loan is 6000.

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1. You have $25 to spend on snacks for movie night with 4 of your friends. If individual boxes of raisins are $1.50, find the amount of money that remains per person for popcorn and a drink.

To find the amount of money that remains per person after buying raisins, we first need to find the total cost of the raisins. If 4 boxes of raisins cost $1.50 each, then 4*1.50 = $6 is spent on raisins.

To find the amount of money that remains for popcorn and drinks, we subtract the cost of the raisins from the total amount of money: 25-6 = $19.

Since there are 5 people in total (you and 4 friends), we divide the remaining money by 5 to find the amount per person: 19/5 = $3.80 per person.

2. The cost for a town’s soccer league banquet is $960. There are 60 players in the soccer league. Determine the cost per player for the town if each player pays $5 to attend the banquet.

To find the cost per player, we divide the total cost of the banquet by the number of players: 960/60 = $16 per player

3. To solve the equation 2/3(x−4)=−10, Izzy wants to multiply both sides of the equation by the reciprocal of the fraction. Name the reciprocal.

The reciprocal of the fraction 2/3 is 3/2

4. There are 2 types of tickets to attend an awards dinner—silver and gold. The gold tickets are $8 more than the silver. If Patrick bought 10 tickets at each level and spent a total of $140, find the price of each ticket.

Let's call the cost of a silver ticket x.

The cost of a gold ticket is x + 8.

We know that Patrick spent 10x + 10(x+8) = $140

We can simplify that: 10x + 10x + 80 = 140

Then we have 20x + 80 = 140

Then we have 20x = 60

And x = 3

Then the price of a silver ticket is $3 and the price of a gold ticket is $3+8 = $11

5. Kendra is making bread, but the recipe she’s using makes 4 loaves. She only wants to make one loaf. The changed recipe calls for 2 1/2 cups of flour and sugar combined. If the original recipe calls for 2 cups of sugar, find the amount of flour (in cups) in the original recipe.

If the original recipe calls for 2 cups of sugar and the changed recipe calls for 2 1/2 cups of flour and sugar combined, then the original recipe calls for 2 1/2 - 2 = 1/2 cup of flour.

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Answer:

key note is that when the angles are added it equals 180 degrees

Answer: A

Step-by-step explanation: A shows a turkey sandwich with all the types of bread and a ham sandwich with all the types of bread.

Answer:

24(w+2)

Step-by-step explanation:

You must look for a common denominator between the two parts of the expression. In this case, 48 is divisible by 24. 48/24 = 2. So you can now move the common denominator out to the front. Then use this common denominator and divide each term by it. 24w/24 = w and 48/24 = 2. Therefore, your expression factored is 24 (w+2)

Answer:

3

Prime factorization:

2^2 × 3 × 5 = 60

Answer: c 1/6

Step-by-step explanation

Becouse it has six numbers so that means that 1 is a factor so taking in every other number the answer should be 1/6

Answer:

[tex]108\pi[/tex] or approx. [tex]339.3 m^{2}[/tex]

Step-by-step explanation:

The question asks us to find the total surface area of the given hemisphere. The question gave us the formula for total surface area of a sphere, [tex]SA_{tot} =4\pi r^2[/tex]. But we need it for a hemisphere, so multiply the equation by [tex]\frac{1}{2}[/tex].

[tex]SA} = (\frac{1}{2}) 4\pi r^2[/tex] => [tex]SA} =2\pi r^{2}[/tex]

We also need the area of the base, which is circle. [tex]A_{circle}=\pi r^{2}[/tex].

Now add these equations together to get our equation.

[tex]SA_{tot} =2\pi r^2 +\pi r^{2}[/tex] => [tex]SA_{tot} =3\pi r^2[/tex]

Now we have the proper equation for total surface area of a hemisphere, [tex]SA_{tot} =3\pi r^{2}[/tex]. Plug in the value of [tex]r[/tex] which is given in the problem, [tex]r=6m[/tex].

=> [tex]SA_{tot} =3\pi (6)^{2}[/tex] => [tex]SA_{tot} =3\pi (36)[/tex] => [tex]SA_{tot} =108\pi m^{2}[/tex] or approx. [tex]339.3 m^{2}[/tex]

Answer:

z ∗ = 2.326

Step-by-step explanation:

The percent of broken bulb will be 5%.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

He takes a random sample of 500 bulbs.

He finds that 25 bulbs arrived broken.

The percentage of broken bulb will be,

= (25/500) * 100

= 0.05 * 100

= 5%

Thus, 5 percent of bulb are broken.

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Answer:

You are absolutely correct!

Step-by-step explanation:

An inscribed angle in a circle has half the measure of the corresponding arc.

Answer:

[tex]2x+3 \geq 35[/tex]

x is meetings

Step-by-step explanation:

5

9x⁵=5

5y³=3

so 5>3=5

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Find the percent decrease from 133 to 120. Round your answer to the nearest tenth

1. Subtract  

133-120= 13

2. Find

13/133 x 100

1300/133

= 9.77443609

3. Round

9.77 rounded is 9.8

Answer: 9.8%

Answer:

9.8 is your answer

the percentage decrease from 133 to 120 is 9.7744

but rounded to the nearest tenth is 9.8

Answer:

in step 2, she calculated 2.5^2 incorrectly.

Step-by-step explanation:

its right tho

Answer:

b.

Source:

trust me bro

Answer:

n= 36

Step-by-step explanation:

18=n-18 (add 18 to both sides of the equation, 18 and -18 cancel out)

36=n

The solution for n in equation 18 = n - 18 is 36.

To solve the equation 18 = n - 18, we need to isolate the variable n. Here's how:

Start with the equation: 18 = n - 18.

Add 18 to both sides of the equation to move the constant term to the other side: 18 + 18 = n - 18 + 18.

Simplify 36 = n.

Therefore, the solution for n is 36.

By adding 18 to both sides of the equation, we eliminate the -18 on the right side, leaving n isolated on the right side. Thus, the value of n that satisfies the equation is 36.

To check the solution, we substitute n = 36 back into the original equation: 18 = 36 - 18. Simplifying this equation results in 18 = 18, which confirms that n = 36 is indeed the solution to the equation.

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Answer:

Option 4

Step-by-step explanation:

"Angle formed between a secant and a tangent at a point outside a circle is equal to half of the difference of the measure of the intercepted arcs"

By applying this theorem in the figure given in the picture,

m∠RST = [tex]\frac{1}{2}[\text{m(arc TU - m(arc RT))}][/tex]

[tex]x=\frac{1}{2}(155-65)[/tex]

[tex]x=\frac{1}{2}(90^0)[/tex]

[tex]x=45^0[/tex]

Therefore, Option 4 is the correct option.

Answer:

g(f(x)) means that the x of the g function is the f(x) function, if that makes sense.

so you do 8(x-10)-5

8x-80-5

8x-85

hope that answers your question

Don't hesitate to comment if you don't understand something.

Step-by-step explanation:

Square bases is not an attribute of a right rectangular prism. Option D

A right rectangular prism can be described as a three-dimensional solid shape with 6 faces, 12 edges, and 8 vertices.

It is sometimes called a cuboid.

All the faces of the right rectangular prism are rectangular in shape.

Examples of  right rectangular prisms are books, bricks and aquarium.

Some properties of a right rectangular prism include;

These prisms have no square base(s)

Hence, the right option is square bases.

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