A bee colony produced 0.4 pounds of honey, but bears ate 0.2 pounds of it. How much
honey remains?

The length of the curve x = 1/3 √y (y − 3)  is 64/3.

The distance between two point along a segment of a curve is known as the arc length.

The equation of the curve is given by:

x = 1/3 √y (y − 3), 16 ≤ y ≤ 25

Length of the curve y = f(x) between point  x =a to x = b is given by:  

\(\int\limits^b_a {\sqrt{1+[f'(x)]^2} } \, dx\)

 √1 + [f′(x)]2 dx.

x = 1/3 √y (y − 3)

x = 1/3 * \(y^\frac{3}{2}\) - \(y^\frac{1}{2}\)

Let's find the first derivative of x.

dx/dy = 1/3. 3/2.  \(y^\frac{1}{2}\)- 1/2 .  \(y^\frac{1}{2}\)

dx/ dy = 1/2 ( \(y^\frac{1}{2}\) - \(y^\frac{-1}{2}\))

(dx/dy)^2= 1/4 (  \(y^\frac{1}{2}\) - \(y^\frac{-1}{2}\))^2

= 1/4(y + \(y^-^1\)-2)

1 + {f′(x)}2 = 1 + 1/4(y +\(y^-^1\)-2)

= 1/4 y + 1/4\(y^-^1\)+ 1/2

1 + {f′(x)}2= 1/4 (y + \(y^-^1\) + 2)

√[1 + {f′(x)}2] = 1/2 (  \(y^\frac{1}{2}\) +  \(y^\frac{-1}{2}\))

Length of curve  is given by:  

25

∫   \(\frac{\sqrt{y} }{2} +\frac{1}{2\sqrt{y} }\) dy

16

= \(\left \{ {{y=25} \atop {x=16}} \right.\) [\(y^\frac{3}{2}\)/3 + √y]

= [(25)3/2 /3 + √25] - [(16)3/2 /3 + √16]

= [125/3 + 5] - [64/3 + 4]

= 140/3 - 76/3

= (140 - 76)/3

= 64/3

So the length of the curve is 64/3

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Answer:

your ansawer 2.55 i sorry if i am worng

Step-by-step explanation:

The total materials cost before sales tax is $297.21.

The total materials cost is the result of the addition of the total cost of posts, wire mesh, gate, and staples, as follows.

The length of the rectangular space = 6 meters

The width of the space = 10.5 meters'

The perimeter of the space = 33 meters [2(6 + 10.5)]

The space between posts = 1.5 meters

The number of posts = 22 (33 ÷ 1.5)

The cost per post = $2.69

a) The cost of the posts = $59.18 ($2.69 x 22)

The cost of wire mesh:

Cost per meter = $5.96

The number of meters of wire mesh = 33 meters

b) Total cost of the wire mesh = $196.68 ($5.96 x 33)

c) Cost of the gate = $25.39

Cost of Staples:

The number of staples per post = 7

The total number of staples required = 154 (22 x 7)

The number of boxes of staples = 4

The cost per box = $3.99

d) The total cost of staples = $15.96 (4 x $3.99)

The total cost of materials = $297.21 ($59.18 + $196.68 + $25.39 + $15.96)

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Answer:

Step-by-step explanation:

each pencil costs $8.33.

12÷$1.44=$8.33.

hope this helps!

mark me brainliest as well please.

Answer:

:let x = the number

then 8x + 9 = 9x

solving, x = 9

Proof: (8 x 9) + 9 = 9 x 9; 72 + 9 = 81, and 81 = 81

Answer:

21 miles

Step-by-step explanation:

s=vt

Vt = 3.5mi/h + 7mi/h

= 10.5mi/h

Tt = 0.5 hr + 1.5hr

= 2 hr

St = 10.5(2hr)

= 21 miles

Equation for a linear line is y=5x-5

What is linear line?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

slope of line passing through two points (-2,-15) and (2,5) is

\(m= (5-(-15))/(2-(-2))\\m=20/4\\m=5\)

Therefore, the slope of the line is 5

Now,finding the y-intercept now by using the slope and one of the two points.

\(y=m*x+b\\5=5*2+b\\b=-5\)

putting this value of b to find equation,

\(y=m*x+b\\y=5x-5\\\)

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The cost of the small needlepoint pillows is $20.

The cost of the large needlepoint pillows is $45.

The first step is to set up a system of equations that describe the question.

The system of equations are:

2s + 5l = 265 equation 1

7s + 11l = 635 equation 2

Where:

s = cost of the small needlepoint pillows

l = cost of the large needlepoint pillows

The elimination method would be used to solve the equations.

Multiply equation 1 by 7 and equation 2 by 2

14s + 35l = 1855 equation 3

14s + 22l = 1270 equation 4

Subtract equation 4 from equation 3

13l = 585

Divide both sides of the equation by 13

l = 585 / 13

l = $45

Substitute for l in equation 1:

2s + 5(45) = 265

2s + 225 = 265

2s = 265 - 225

2s = 40

s = 20

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Step-by-step explanation:

Probabibility = 1/6 * 1/6 = 1/36 = 2.77%.

Answer:

B

Step-by-step explanation:

Not A cause the ratios are different, as the first ratio is -1/3 and the rest are 1/3

B is correct cause the ratio is 1/3 and the first term is 1

Not C cause the ratio is not 1/3

Not D cause the ratio is 3

Have a nice day! :)

-Vana

hope you'll understand

Answer:

1626.02

Step-by-step explanation:

1 gram is 0.001 kilograms. The bag weighs 2 kilograms and each popcorn is 1.23 grams. 2 kilograms weigh 2000 grams.

The domain of the graphed function in this problem is given as follows:

2 <= x <= 5.

The domain of a function is the set composed by all the input values that the function accepts.

On the graph, the domain of the function is given by the values of x.

For this problem, the values of x are a closed interval between x = 2 and x = 5, hence the domain of the function is defined by the interval presented as follows:

2 <= x <= 5.

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Answer:

True

Step-by-step explanation:

expression

3x+5

equation

3x+5 =0

Reserve Requirement

Took the test got 100

Answer:

Its D

Step-by-step explanation:

Reserve Requirement I got it right on my test

The person incurred a loss of: ₹8 in the bargain.

The person purchased 10 eggs for ₹4 each, so the total cost of the eggs is:

This is the money they spent on buying the eggs.

They then sold 8 eggs for ₹4 each,

so the revenue from the sale is:

This is the money they received from selling the eggs.

To calculate the profit or loss in the transaction, we subtract the cost from the revenue:

A negative result indicates a loss. So, in this case, the person incurred a loss of ₹8 in the bargain. This means they received less money from selling the eggs than what they spent on buying them.

Complete Question:

"A person purchased 10 eggs for ₹4 and sold 8 eggs for ₹4. The profit or loss in the bargain will be?"

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(a) The 99% confidence interval for the selling price-list price difference is approximately -$16,636 to $9,889.

(b) This suggests that housing prices can vary significantly, with potential discounts or premiums compared to the listed price.

(a) Based on the provided data, the 99% confidence interval for the difference between the selling price and list price (selling price - list price) is approximately (-$16,636 to $9,889) rounded to the nearest dollar. This interval notation represents the range within which we can estimate the true difference to fall with 99% confidence.

(b) Interpreting the confidence interval in terms of the housing market, it means that we can be 99% confident that the actual difference between the selling price and list price of homes lies within the range of approximately -$16,636 to $9,889. This interval reflects the inherent variability in housing prices and the uncertainty associated with estimating the exact difference.

In the housing market, the confidence interval suggests that while the selling price can be lower than the list price by as much as $16,636, it can also exceed the list price by up to $9,889. This indicates that negotiations and market factors can influence the final selling price of a property. The wide range of the confidence interval highlights the potential variability and fluctuation in housing prices.

It is important for buyers and sellers to be aware of this uncertainty when pricing properties and engaging in real estate transactions. The confidence interval provides a statistical measure of the range within which the true difference between selling price and list price is likely to fall, helping stakeholders make informed decisions and consider the potential variation in housing market prices.

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The probability that the date sara chose is a prime number is 0.2.

Given that, sara chose a date from the calendar.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

Here, total number of outcomes = 30

Number of favourable outcomes = 6

Now, probability = 6/30

= 1/5

= 0.2

Therefore, the probability that the date sara chose is a prime number is 0.2.

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Answer:

Step-by-step explanation:

As given in the picture attached,

Coordinates of W → (-1, 1)

Coordinates of X → (2, -3)

Coordinates of Y → (0, -6)

Coordinates of Z → (-2, -5)

By reflecting these points across x = -3, distance between original points to the line of reflection and distance between the image points and line of reflection will be equal.

Coordinates of W' → (-5, 1)

Coordinates of Y' → (0, 0)

Coordinates of Z' → (-4, -5)

Coordinates of X' → (-8, -3)

Answer:

square tables

round tables

12

Step-by-step explanation:

is this really that difficult ?

just think logically.

a square table sits 8 people. that means every square table "stands" for 8 people present.

a round table sits 6 people. so, every round table "stands" for 6 people present.

now, the whole party has 150 people.

that means the sum of all people on all tables is 150.

so, if we count all square tables, we know how many people are sitting at square tables, as each table "stands" for 8 people (we multiply the number of square tables by 8).

similar for the round tables.

so, we say we have x square tables and y round tables.

therefore the equation is

150 = 8×x + 6×y

the variable with the factor 8 must be describing the square tables (due to the reasons above).

that is x.

and the variable with the factor 6 must describe the round tables.

that is y.

now we are told that there are 9 round tables (y=9).

using the equation from above

150 = 8×x + 6×9 = 8×x + 54

96 = 8×x

x = 12

so, we must have 12 square tables to satisfy the condition that we have in total 150 people present.

Answer:

John

Step-by-step explanation:

To get from a percent to a decimal, you move the decimal point two places to the left, so John is correct.

7.7 in

Explanation

Step 1

Let

AB=5.1( black)

BC=2.6(red)

AC=?

AC is the line that goes from A to C, (blue)

Also

Step 2

replace

so, the answer is 7.7

The expressions ((p ∨ r) ∧ (q ∨ ¬r)) and (p ∨ q) are logically equivalent.

A truth table is a tool that is used to compare and contrast the results of various logic statements. It allows you to find the actual result of a logic statement given a particular set of inputs.

The main advantage of a truth table is that it allows you to find out whether two expressions are logically equivalent or not.

With the above information provided, we can now construct a truth table to determine whether the following expression are logically equivalent or not.

Let's start by constructing the truth table:

Truth table

pqr¬rq ∨ rp ∨ rq ∨ ¬r(p ∨ r) ∧ (q ∨ ¬r)(p ∨ r) ∧ (q ∨ ¬r)

⇔ p ∨ qq ∨ ¬rq ∨ qq ∨ ¬rp ∨ ¬r

TTFTRTTFTTFFFTTTTTFFFTFTFFTTFFTFFTT

As you can see from the truth table, the last two columns are identical.

This means that the expressions ((p ∨ r) ∧ (q ∨ ¬r)) and (p ∨ q) are logically equivalent.

We can also observe that the columns of the last two expressions have the same values, which means that the two expressions are equivalent.

Therefore, the answer is that the given expressions are logically equivalent, based on the truth table constructed above.

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In the given time interval [0,7]:

(a) the maximum speed is 1096.63 units at t = 7 and

(b) the minimum speed is 0.91 units at time t = ln2/4.

Parametric equations of the curve

x(t) = \(e^t + e^{-t}\)

y(t) = \(e^{-t}\)

so, dx/dt = \(e^t - e^{-t}\)

dy/dt = \(-e^{-t}\)

So, speed: v(t) = \(\sqrt{(dx/dt)^2 + (dy/dt)^2}\) = \(\sqrt{(e^t-e^{-t})^2 + (-e^{-t})^2}\)

When v(t) is maximized or minimized, evidently v² is also maximized or minimized because speed is a positive quantity.

or (speed)² = v² = \((e^t-e^{-t})^2 + (-e^{-t})^2\) = \((e^{2t} + 2e^{-2t} -2)\)

Now, to get the maxima or minima of a curve we have to derivate function

d/dt(v²) = 0 or d/dt\((e^{2t} + 2 e^{-2t} -2)\)

or \(2e^{2t} -4 e^{-2t} = 0\) or \(e^{2t} = 2 e^{-2t}\)

taking logs on both sides

4t lne = ln2 or 4t = ln2 or t = ln2/4

so, the only critical point is t = ln2/4 ∈ [0,7]

To calculate the maxima/minima of v, we will find functional values at the critical point and boundary values of the given interval [0,7].

At t = 0 : v(0) = \(\sqrt{e^0 + 2e^0 - 2} = \sqrt{1+2-2}\) = 1

At t = ln2/4: v(ln2/4) = \(\sqrt{e^{2ln2/4} + 2e^{-2ln2/4} - 2} = \sqrt{2\sqrt{2} -2 }\) = 0.91

At t = 7: v(7) = \(\sqrt{e^{14} + 2e^{-14} - 2}\) = 1096.63

Therefore, in the given time interval [0,7]: (a) the maximum speed is 1096.63 units at t = 7 and (b) the minimum speed is 0.91 units at time t = ln2/4.

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Answer:

A

Step-by-step explanation:

The graph is not a function because two outputs have exactly one input.

From the question, we have the following parameters that can be used in our computation:

The graph

The graph can be represented as

x  g(x)

0  2

1  3

1   4

2  5

3  5

The above table of values is not a function

This is so because the input value 1 has different output values. i.e. it would fail the vertical line test when represented on a graph

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a) 2-year subscriptions is approximately 20%.

b) 3-year subscriptions is approximately 29.56%.

c) 5-year subscriptions is approximately 41.33%.

To compute the rate of return on the investment for purchasers of different subscription lengths, we need to calculate the average annual cost of each subscription option.

a) 2-year subscriptions:

The cost of a 2-year subscription is $12.00. To find the average annual cost, we divide the total cost by the number of years:

Average annual cost = $12.00 / 2 = $6.00

b) 3-year subscriptions:

The cost of a 3-year subscription is $16.00. To find the average annual cost, we divide the total cost by the number of years:

Average annual cost = $16.00 / 3 = $5.33 (rounded to two decimal places)

c) 5-year subscriptions:

The cost of a 5-year subscription is $22.00. To find the average annual cost, we divide the total cost by the number of years:

Average annual cost = $22.00 / 5 = $4.40

Now, to calculate the rate of return on the investment, we need to compare the average annual cost to the regular 1-year subscription rate of $7.50.

a) For 2-year subscriptions:

Rate of return = (1 - Average annual cost / 1-year subscription rate) * 100%

Rate of return = (1 - $6.00 / $7.50) * 100% ≈ 20%

b) For 3-year subscriptions:

Rate of return = (1 - Average annual cost / 1-year subscription rate) * 100%

Rate of return = (1 - $5.33 / $7.50) * 100% ≈ 29.56%

c) For 5-year subscriptions:

Rate of return = (1 - Average annual cost / 1-year subscription rate) * 100%

Rate of return = (1 - $4.40 / $7.50) * 100% ≈ 41.33%

Therefore, the rate of return on the investment for purchasers of:

a) 2-year subscriptions is approximately 20%.

b) 3-year subscriptions is approximately 29.56%.

c) 5-year subscriptions is approximately 41.33%.

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Answer:

Step-by-step explanation:

its (x+1,y+-3)

Answer:

The new width is 3 in.

Step-by-step explanation:

We can use the ratio of w/h, the origal width and height should have the same ratio as the new width and height.

12 = x

16    4

Then solve for x:

x = 4 (12/16)

x = 3

To check:

12/16 = 3/4

3/4 = 3/4

Answer:

B

Step-by-step explanation: