Which one is the correct Pascal's identity?

As per the given question;

Let the amount of water in the tank before the drainage be V.

The time for which the drainage occurred is 't'.

The change of volume of water with respect to time is;

Rate = Change in volume/total time

Rate = ΔV/Δt

ΔV = rate×Δt

Rate = 10 cubic feet/min

time = 7 min

Put the values;

ΔV = 10×7 = 70 cubic feet.

The volume of drained water in 7 minutes is 70 cubic feet.

If the volume left in tank after discharge is W.

Then,

W = V - 70 cubic feet.

As, the initial amount of water was 1000 cubic feet.

V = 1000 cubic feet.

The water left in tank is;

W = V - 70 cubic feet.

Put the values;

W = 1000 - 70

W = 930 cubic feet.

Thus. the value of water left in water tank after 7 minutes is 930 cubic feet.

To know more about rate of change, here

https://brainly.com/question/18438069

#SPJ9

Answer:

100 lol thanks

Step-by-step explanation:

25+25=50 50+25=75 75+25+100

9514 1404 393

Answer:

  u'(1) = 0

  v'(5) = -2/3

Step-by-step explanation:

There are several ways to go at this. One is to write the function composition, then differentiate that. Another is to make use of the derivative relations only at the point of interest. (The first method is used in the graph.)

At x=1

u(x) = f(x)g(x)

u'(1) = f'(1)g(1) +f(1)g'(1)

The derivatives of the functions will be their slopes at the point of interest.

  f(1) = 2, f'(1) = 2

  g(1) = 1, g'(1) = -1

u'(1) = (2)(1) +(2)(-1)

u'(1) = 0

__

At x=5

v(x) = f(x)/g(x)

v'(5) = (g(5)f'(5) -f(5)g'(5))/g(5)²

The relevant function values are ...

  f(5) = 3, f'(5) = -1/3

  g(5) = 2, g'(5) = 2/3

v'(5) = ((2)(-1/3) -(3)(2/3))/(2²) = (-2/3 -2)/4 = (-8/3)/4

v'(5) = -2/3

_____

Additional comment

The functions used in each of the compositions are only defined on the relevant interval [0, 2] or (2, ∞).

Answer:

1/9

Step-by-step explanation:

(1/3)/3 = 1/9

There will be 524,288 bacteria in petri dish after 4 hours.

Given the function that modeled the number of bacteria in a petri dish, after t hours expressed as:

The value of p(4) is expressed as:

Hence there will be 524,288 bacteria in petri dish after 4 hours.

Answer:

Answers are below

Step-by-step explanation:

1.) No solution

2.) Unique solution

3.) Unique solution

4.) No solution

I graphed the equation that had a unique solution on the graph below.

If these answers are correct, please make me Brainliest!

For the given figure,   x = 23°  and      y = 129°

Parallel lines:

                        Parallel lines are lines that always stay the same distance apart and never meet.

Transversal line :

                             A transversal is a line that crosses two or more other lines.

given,

     ∠TLN = (3x - 18)°

    ∠MZQ = (5x + 14)°

    ∠NLM = y°

Now,

         ∠MZP + ∠MZQ = 180°  (Linear Pair)

        ∠MZP  = 180° - ∠MZQ  ...........(I)

again,

          ∠NLM + ∠TLN  =180°  ...........(II)      (Linear Pair)

  As,         ∠TLN = ∠MZP  (Corresponding Angle)

             (3x - 18)° =  180° - ∠MZQ  

           (3x - 18)° = 180° - (5x + 14)°

         3x + 5x  = 180° - 14° + 18°

           8x = 184°

           x = 184 / 8

          x = 23°

      From (II),

      ∠NLM + ∠TLN  =180°

    y° + 3x - 18° = 180°

 y = 180 - 3x + 18

     = 180 - 3* 23 + 18

      = 180 - 69 +18

     y = 129°

For the given figure,

                                     x = 23°  and      y = 129°

To learn more about Parallel line visit:

https://brainly.com/question/17432060

#SPJ9

\( \sf \longrightarrow \: 5 \bigg( \: n - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{n}{1} - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10 \times n - 1 \times 1}{1 \times 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10n - 1}{ 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: \frac{50n - 5}{ 10} = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =1(10) \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =10 \\ \)

\( \sf \longrightarrow \: \: 100n - 10=10 \\ \)

\( \sf \longrightarrow \: \: 100n =10 + 10\\ \)

\( \sf \longrightarrow \: \: 100n =20\\ \)

\( \sf \longrightarrow \: \:n = \frac{2 \cancel{0}}{10 \cancel{0}} \\ \)

\( \sf \longrightarrow \: \:n = \frac{1}{5} \\ \)

Answer:-

To solve the equation \(\sf 5(n - \frac{1}{10}) = \frac{1}{2} \\\) for \(\sf n \\\), we can follow these steps:

Step 1: Distribute the 5 on the left side:

\(\sf 5n - \frac{1}{2} = \frac{1}{2} \\\)

Step 2: Add \(\sf \frac{1}{2} \\\) to both sides of the equation:

\(\sf 5n = \frac{1}{2} + \frac{1}{2} \\\)

\(\sf 5n = 1 \\\)

Step 3: Divide both sides of the equation by 5 to isolate \(\sf n \\\):

\(\sf \frac{5n}{5} = \frac{1}{5} \\\)

\(\sf n = \frac{1}{5} \\\)

Therefore, the solution to the equation \(\sf 5(n - \frac{1}{10})\ = \frac{1}{2} \\\) is \(\sf n = \frac{1}{5} \\\), which corresponds to option (d).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The equation solved for the variable h is h = \(\sqrt[]{\frac{2A -b^2}{b} }\)

To solve for a variable in a given equation is to make it the subject of formula.

The variable is made to stand alone on one end of the equality sign.

We have the equation given as;

A=1/2bh(h+b)

First, cross multiply

2A = bh(h+b)

2A = bh² + b²

collect like terms

2A - b² = bh²

Now divide by the coefficient of h²

h² = 2A - b²/b

Find the square root of both sides

h = \(\sqrt[]{\frac{2A -b^2}{b} }\)

Hence, the equation is h = \(\sqrt[]{\frac{2A -b^2}{b} }\)

Learn about subject of formula at: https://brainly.com/question/10643782

#SPJ1

The order of calculate the confidence interval for the mean are as follows:

1. Select sample stat

2. select desired confidence

3. determine margin of error

4. specify upper and lower limits

Now, According to the question:

The order of calculate the confidence interval for the mean are as follows:

1. Select sample stat

2. select desired confidence

3. determine margin of error

4. specify upper and lower limits

Let's know:

What is Confidence Interval?

A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data.

The common notation for the parameter in question is θ. Often, this parameter is the population mean μ , which is estimated through the sample mean bar x.

The level C of a confidence interval gives the probability that the interval produced by the method employed includes the true value of the parameter θ.

Learn more about Confidence Interval at:

https://brainly.com/question/16256721

#SPJ4

Answer:

At 9 a.m., the temperature was 11 ˚F or -5 ˚F.

Step-by-step explanation:

Temperature at noon: 3 ˚F

Temperature at 9 a.m.: 8 ˚F higher or lower than 3 ˚F

Temperature at 9 a.m.:

3 ˚F + 8 ˚F = 11 ˚F

or

3 ˚F - 8 ˚F = -5 ˚F

Answer: At 9 a.m., the temperature was 11 ˚F or -5 ˚F.

on this one, we proceed the same as the other, we start off by graphing them, Check the picture below.  Now, we have a solid horizontal line at y = 7, that'd be our boundary, and a parabola that has a vertex at the origin, that's our other boundary, from 0 to 7.

In this case, is a solid area from the curve to the axis of rotation, so we can simply use the "disk" method to get the volume, lemme do it in the same way as "area under the curve", assuming h(y) = 0 for the axis of rotation

\(\textit{area under the curve}\\ \stackrel{f(y)}{2\sqrt{3y}}~~ - ~~\stackrel{h(y)}{0}\qquad \implies 2\sqrt{3y} \\\\\\ \displaystyle\int_{0}^7\pi \left( 2\sqrt{3y} \right)^2 dy\implies \int_{0}^7\pi(12y)dy\implies 12\pi \int_{0}^7 y\cdot dy \\\\\\ 12\pi \cdot \left. \cfrac{y^2}{2} \right]_{0}^7\implies12\pi \cdot \cfrac{49}{2}\implies 294\pi\)

To estimate the total money raised by the school, we have to round off each number to the nearest hundred place before multiplying. Let’s first understand how to round off numbers to the nearest hundred.Rounding off a number to the nearest hundred means to keep the digit in the tens place and leave out the digits in ones and tens places.

For example, if we have a number 768 and we want to round it off to the nearest hundred, we will keep the digit in the tens place and leave out the digits in the ones and tens place.

We get 800 when rounding off 768 to the nearest hundred.Let’s round off 827 and 143 to the nearest hundred.827 rounded off to the nearest hundred is 800143 rounded off to the nearest hundred is 100 Now, we have to multiply these two numbers to get the estimated total money raised by the school.

800 × 100 = 80000

Therefore, we can estimate that the school raised about $80,000 at the fundraiser.

To answer whether this estimate is very good or not, we need to compare it to the actual amount of money raised by the school.

If the actual amount is close to $80,000, then our estimate is good. However, if the actual amount is significantly different, then our estimate is not very good.

Unfortunately, we don’t have any information about the actual amount of money raised by the school. So, we cannot determine whether this estimate is very good or not.

For such more question on multiplying

https://brainly.com/question/29793687

#SPJ8

If n is an integer and m + 5 is odd, then n must be even.

To prove this statement using contraposition, we need to show that if n is odd, then m + 5 must be even. Assume that n is odd, which means we can write n = 2k + 1 for some integer k.

Then, we can rewrite m + 5 as (2k + 1) + 5 = 2k + 6 = 2(k + 3), which is even.

Therefore, we have shown that if n is odd, then m + 5 is even.

By contraposition, we can conclude that if m + 5 is odd, then n must be even. Overall, the proof uses the fact that odd + odd = even and even + odd = odd, along with the definition of even and odd integers.

For more questions like Contraposition click the link below:

https://brainly.com/question/5306301

#SPJ4

Answer:

slope is -3

Step-by-step explanation:

use slope equation, shown in picture hope this helps

The total price of the vehicle would be $18,192.88.

The total deferred price of the car would be $11,191.60.

The length of the financing agreement is 68 months .

The total deferred price after the payments was $19,601.84.

The monthly payments would be $516.92.

Subtotal = Base price + Options + Destination charges

Subtotal = $14,500 + $982 + $592 = $16,074

Dealer preparation = 5% of subtotal

Dealer preparation = 0.05 x $16,074 = $803.70

Sales tax = 7% of subtotal

Sales tax = 0.07 x $16,074 = $1,125.18

Total price = Subtotal + Dealer preparation + Sales tax + Tag fee + Title fee

Total price = $16,074 + $803.70 + $1,125.18 + $145 + $45 = $18,192.88

Tax = 8% of selling price = 0.08 x $8,850 = $708

Tag fee = $130

Title fee = $35

Total amount financed = Amount financed + Tax + Tag fee + Title fee = $7,350 + $708 + $130 + $35 = $8,223

Annual interest rate = 9.5%

Number of years financed = 3

Total finance charges = $8,223 x 0.095 x 3 = $2,341.595

Total financed amount = $8,223 + $2,341.595 = $10,564.595

Monthly payments = Total financed amount / (Number of years financed x 12 months) = $10,564.595 / (3 x 12) = $293.4615

Total deferred price = Selling price + Total finance charges = $8,850 + $2,341.595 = $11,191.595

Total deferred price = $28,000

Down payment = $2,100

Total amount financed = Total deferred price - Down payment = $28,000 - $2,100 = $25,900

Monthly payments = $380

Number of months = Total amount financed / Monthly payments = $25,900 / $380 = 68.16

The financing agreement is approximately 68 months long.

Sticker price = $19,200

Discount = 6% of sticker price = 0.06 x $19,200 = $1,152

Selling price = Sticker price - Discount = $19,200 - $1,152 = $18,048

Sales tax = 8% of selling price = 0.08 x $18,048 = $1,443.84

Total price = Selling price + Sales tax + Tag fee + Title fee = $18,048 + $1,443.84 + $65 + $45 = $19,601.84

Using the formula for monthly payments on a loan:

P = (PV x r x (1 + r)^ n) / ((1 + r) ^ n - 1)

= ($26,515.80 x 0.005265 x (1 + 0.005265) ^ 60 ) / ((1 + 0.005265) ^ 60 - 1) = $516.92

Find out more on monthly payments at https://brainly.com/question/27926261

#SPJ1

The interest rate of the account that Steve invested in after the given number of years would be = 16%

The total amount of money invested (p) = $2,807

The time of investment= 13 years

The interest generated at the end of the given years = 9,044.13-2807 = $6,237.13

Therefore the rate = ?

The formula for simple interest:

= P×T×R/100

6,237.13= 2,807× 14 ×r/100

Make r the subject of formula;

r= 6,237.14×100/2807×14

r = 623714/39298

r= 15.87139294

r= 16%

Learn more about simple interest here:

https://brainly.com/question/25793394

#SPJ1

The taxi ride was 7 miles

Mia took a taxi from her house to the airport

The taxi charged a pick up fee of $1.30

They also charged $4.25 per mile

The total fare was $31.05

The number of miles can be calculated as follows

31.05 - 1.30 = 4.25x

29.75= 4.25x

Divide both sides by the coefficient of x which is 4.25

29.75/4.25= 4.25x/4.25

x= 7

Hence the taxi ride was 7 miles

Read more on miles here

https://brainly.com/question/28408182?referrer=searchResults

#SPJ1

Answer:

\(\frac{5}{2}\)

Step-by-step explanation:

5a - 3a = 6a -10  On the left side of the equation, we will combine the like terms.  5a and -3a are like terms.  If I was on a number line and I started at 5 and went 3 spaces towards the negative numbers, where would I be?  2

2a = 6a - 10  I want to get the variable a on only one side of the equation.  I am trying to isolate the variable.  Right now, we have a's on the both the right and left side of the equation.  Let's subtract 6a from both sides of the equation

-4a = -10  The last step is to divide both sides by -4

a = \(\frac{10}{4}\)

\(\frac{10}{4}\)÷\(\frac{2}{2}\) = \(\frac{5}{2}\) or 2.5 or 2\(\frac{1}{2}\)

Answer:

 a = \(\frac{5}{2}\)

Step-by-step explanation:

Alright so i´ll explain

you are going to combine 5a and -3a to get 2a

2a= 6a -10

then you are going to subtract 6a from both sides

2a-6a= -10

then combine 2a and -6a to get -4a

-4a= -10

then divide both sides by -4

a=\(\frac{-10}{-4}\)

and last reduce the fraction to the lowest term, extract and cancel out -2

and the final answer is a = \(\frac{5}{2}\)

Let me know if you have any doubt, important to be aware of the positive and negative signs

A person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.

How to determine the amount of carpet needed for a rectangular room?

To determine the amount of carpet needed for a rectangular room, you need to convert the measurements to the same unit of measurement. Since the carpet is sold in square yards, we need to convert the dimensions of the room to yards.

The length of the room is given in yards, so we don't need to make any conversions for that dimension. However, the width of the room is given in feet, so we need to convert it to yards by dividing by 3 (since there are 3 feet in a yard),

18 feet ÷ 3 feet/yard = 6 yards

So the dimensions of the room in yards are 10 yards by 6 yards.

To find the total area of the room, we need to multiply the length and width,

10 yards × 6 yards = 60 square yards

Therefore, a person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.

Learn more about rectangle here,

https://brainly.com/question/25292087

#SPJ9

Answer:

34 weeks

Step-by-step explanation:

$824-$156=668

20×34=$680

2 is the initial amount, growth rate is (3ˣ - 1) × 100% , domain of the function is all real numbers and  range of the function is all positive real numbers

A relation is a function if it has only One y-value for each x-value.

The given function is:

f(x) = 2(3)ˣ

To find the initial amount, we need to find f(0):

f(0) = 2(3)⁰ = 2(1) = 2

So the initial amount is 2.

To find the growth rate, we can use the formula:

growth rate = (f(x) - f(0)) / f(0) × 100%

= (2(3)ˣ - 2) / 2 × 100%

= (3ˣ - 1) × 100%

So the growth rate is (3ˣ - 1)×100%.

The domain of the function is all real numbers because the function is defined for all values of x.

The range of the function is all positive real numbers because the function is always positive for any value of x.

Specifically, the range of the function is (0, infinity).

Hence, 2 is the initial amount, growth rate is (3ˣ - 1) × 100% , domain of the function is all real numbers and  range of the function is all positive real numbers

To learn more on Functions click:

https://brainly.com/question/30721594

#SPJ2

There were approximately 5,184 graduates in 2008.

The cubic model is a useful tool for estimating the number of graduates in a given year, as it takes into account the trend of the data points. This allows us to make an educated guess about the number of graduates in a given year, despite not having data points for that year.The cubic model for the number of graduates from an online university since 2002 can be expressed as y = -7.8x^3 + 74.4x^2 + 437x - 9,150. Here, x is the number of years since 2002, and y is the number of graduates in that year. To estimate the number of graduates in 2008, we can plug in x = 6 into the equation, giving us y = 5,184. That is, there were approximately 5,184 graduates in 2008.

Learn more about cubic model  here:

https://brainly.com/question/23134736

#SPJ4

Answer:

3.3

Step-by-step explanation:

You do 5.50 times .4o That will give you 2.2 Then you do 5.5-2.2 and that will give you a answer of 3.3

the smaller has a area of rectangle will have 12m²

What is a rectangle?

A rectangle is a quadrilateral with four right angles in Euclidean plane geometry. It can also be described as: an equiangular quadrilateral since equiangular denotes that all of its angles are equal; Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.

The area of a rectangle is A = a*b

The ratio of the corresponding sides of two rectangles is 1/3.

So the larger rectangle has x side and 108 area so the other side is

108/x

Now the smaller rectangle (108/A)  = (3/1)²

A = 108/9 = 12

Hence the smaller an area of rectangle will have 12m²

Learn more about rectangular by following the link below.

brainly.com/question/25292087

#SPJ1

Answer:

just add up the 2 numbers pretty simple

Step-by-step explanation:

53.2 plus 29.4

Answer: 82.6 lb

Step-by-step explanation:

Since the restaurant is buying the pounds given from the farmer, add the pounds together.

Add

53.2 + 29.4 = 82.6

Hence, the restaurant bought 82.6 pounds of vegetables.

Answer:

3%

Step-by-step explanation:

They made 97+3 total jars, 3 out of 100 is 3 percent.

The kind of evidence geologists use to make geological timelines of events in Earth's history is the fossil remains.

A geological timeline shows a calendar of events in Earth's history.

To develop geological timelines, scientists understudy physical objects or structures on the Earth.  These objects or structures enable them to prove a phenomenon of interest.

Generally, the best form of evidence for the study of the history of life on earth is fossils, as they give clues about geological events and past climates, including the ages of rocks.

Other kinds of evidence for developing geological timelines include the following:

Thus, fossils provide the best kind of evidence for geological timelines.

Learn more about geological timelines and fossils at https://brainly.com/question/24584907.

#SPJ1