points P, Q, R, and S are collinear. Point Q is between P and R, R is between Q and S, and . and PQ = RS . If PS = 33 and PR 25, what is the value of QR?

Answer: x=5.6

Step-by-step explanation:

Answer:

4-12x

Step-by-step explanation:

Answer:

X = S-R

Step-by-step explanation:

I don't really know what it means, maybe what makes sense is X = S-R?

Answer:

X = S-R

Step-by-step explanation:

We need to change the equation so that it shows X = .....

Thus, we move R to the opposite side of the equation, and we get...

X = S-R

(Since Positive R becomes negative after swapping sides)

Answer:

3 is the rate of change because it is the you go u p 3 and over 1. and 6 i the initial value because that is the number you start at.

Answer:

Step-by-step explanation:

0.2(20)+6-4(1/2)=4+6-2=8

Answer:

0.2(20)+6-4(112)=4+6-2=8

Answer:

10,000,000

Step-by-step explanation:

log10 x = 7

10^7 = 10,000,000

-6.75  is a rational number.

Let us understand about natural, whole, integer, rational, and irrational numbers one by one.

Natural number:

Natural numbers are numbers that start from 1 and end at infinity. These are non-negative numbers.

Whole number:

Whole numbers are numbers that start from 0 and end at infinity.

We can also natural numbers including 0 is known as whole numbers.

These are non-negative numbers.

Integer:

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

Rational number:

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p, and a non-zero denominator q.

Also, the decimal representation of the rational number is terminating and recurring.

Irrational number:

An irrational number is a number that can not be expressed as the quotient or fraction p/q of two integers, a numerator p, and a non-zero denominator q.

Also, the decimal representation of the irrational number is non-terminating and non-recurring.

The given number is -6.75.

The decimal form is terminating.

So, it is a rational number.

Thus, -6.75  is a rational number.

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Answer:

Step-by-step explanation:

ran 2 3/4 miles in 1/3 of an hour

2 3/4 miles =11/4 miles in 1/3 of hour

11/4 miles   divided by 1/3 hr

11/4 ÷ 1/3

11/4 * 3/1 =33/4 =8 1/4 miles in 1 hr

a^6 + b^6= (a^2 +b^2)(a^4-a^2b^2+b^2) is an identity. The reasoning is done below.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given an expression  a^6 + b^6= (a^2 +b^2)(a^4-a^2b^2+b^2) we need to assure if its right or not

Let "x" = a² and "y" = b² thus the equation

x³ + y ³ = ( x + y)(x² + y² - xy)

Take L.H.S.

=> x³ + y³ = (x + y)³ - 3xy (x + y)

» Take (x + y) common

=> (x + y) [(x + y)² - 3xy (1)]

=> (x + y) [(x² + 2xy + y²) - 3xy]

Because (a + b)² = a² + 2ab + b²

=> (x + y) (x² + y² + 2xy - 3xy)

=> (x + y) (x² + y² - xy)

L.H.S. = R.H.S.

Take R.H.S.

=> (x + y) (x² - xy + y²)

=> x(x² - xy + y²) + y(x² - xy + y²)

=> x³ - x²y +xy² + x²y - xy² + y³

=> x³ + y³

L.H.S. = R.H.S.

therefore, a^6 + b^6= (a^2 +b^2)(a^4-a^2b^2+b^2) is an identity .

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The equation to relate the flow of water from the 8-inch pipe (1600) to the flow of water from the 4-inch pipe (2400) is 2400.

To relate the flow of water from the 8-inch pipe to the flow of water from the 4-inch pipe, we can use the equation of continuity, which states that the product of the cross-sectional area of a pipe and the velocity of the fluid is constant.

Let's assume that the velocity of water flowing through the 8-inch pipe is V1 and the velocity of water flowing through the 4-inch pipe is V2. The cross-sectional area of the 8-inch pipe is A1 = π\((8/2)^2\) = 64π square inches, and the cross-sectional area of the 4-inch pipe is A2 = π\((4/2)^2\) = 4π square inches.

According to the equation of continuity, A1 * V1 = A2 * V2.

Substituting the given values, we have:

64π * V1 = 4π * V2

Simplifying, we get:

16V1 = V2

So, the equation to relate the flow of water from the 8-inch pipe (1600) to the flow of water from the 4-inch pipe (2400) is:

1600 * 16 = 2400

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2 x 10² kcal are in the serving report your answer to 2 significant figures.

According to the question

A serving of fish contains 50 g of protein and 4. 0 g of fat.

i.e. content of protein = 50 g

Content of fat = 4 g

kcal are in the serving report your answer to 2 significant figures:

As the serving of fish contains 50g of protein that is 4.0kcal/g

Calories in 50 g protein = (Content of protein) × (caloric value in protein)

50g × (4.0kcal/g) = 200kcal

That means the kcal of the serving is 200kcal

In 2 significant figures: 2 x 10² kcal

Hence,

2 x 10² kcal are in the serving report your answer to 2 significant figures.

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Answer:

Sue has 8 marbles

Molly has 8 marbles

Step-by-step explanation:

m = number of marbles Molly has

s =  number of marbles that sue has

m+s =32

m = 3s

Substitute the second equation into the first  equation

3s+s =32

4s = 32

Divide by 4

4s/4 =32/4

s = 8

Sue has 8 marbles

m = 32 = 3*8 = 24

Molly has 8 marbles

Answer:

A) \(\frac{x}{11} < -21\)

Step-by-step explanation:

Let "a number" be denoted by the variable, x. Set the equation:

"A number divided by 11": x/11

"is less than": <

"-21": -21

Put all the parts together:

"A number divided by 11 is less than -21": x/11 < -21

A) \(\frac{x}{11} < -21\) is your answer.

~

In the absence of price discrimination, the profit-maximizing conditions would be different, and the resulting prices, quantities, total revenue, total cost, and profit would also be different.

To find the profit-maximizing conditions with third-degree price discrimination, we need to equate the marginal revenue (MR) to the marginal cost (MC) for each market segment.

Given the demand equations and the total cost function:

Market 1: Q1 = 160 - 10P1 or P1 = 16 - 0.1Q1

Market 2: Q2 = 200 - 20P2 or P2 = 10 - 0.05Q2

Total Cost: TC = 120 + 4Q

To find the profit-maximizing prices and quantities, we equate MR to MC for each market segment:

MR1 = MC:

16 - 0.2Q1 = 4

0.2Q1 = 12

Q1 = 60

MR2 = MC:

10 - 0.1Q2 = 4

0.1Q2 = 6

Q2 = 60

Substituting the quantities back into the demand equations, we find:

P1 = 16 - 0.1(60) = 10

P2 = 10 - 0.05(60) = 7

The total revenue (TR) can be calculated by multiplying the price by the quantity for each market segment:

TR = P1 * Q1 + P2 * Q2

TR = (10 * 60) + (7 * 60)

TR = 600 + 420

TR = 1020

The total cost (TC) is given by the total cost function:

TC = 120 + 4Q

TC = 120 + 4(60 + 60)

TC = 120 + 480

TC = 600

Finally, the profit (π) can be calculated by subtracting total cost from total revenue:

π = TR - TC

π = 1020 - 600

π = 420

In the absence of price discrimination, the profit-maximizing conditions would be different, and the resulting prices, quantities, total revenue, total cost, and profit would also be different.

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The time that will elapse before the concentration of dye in the tank reaches 1% of its original value is 460.52minutes by using differential equation.

Let t denote the time in minutes, V = V (t) denote the amount of liquid in liters, and m = m(t) denote the amount of dye in grams. The tank initially has a capacity of 200 L and a concentration of 1\(\frac{g}{L}\), or mass of dye per unit volume.

P(t)=quantity of dye in tank after t min

P(0)=200

by using differential equation

\(\frac{dQ(t)}{dt}\)= rate in and rate out

\(\frac{dQ(t)}{dt}\)=-2\(\times \frac{Q(t)}{200} =- \frac{Q(t)}{100}\)

Q(t)=c×\(e^{\frac{-t}{100}}\)

200=Q(0)=c×\(e^0\)\(\rightarrow c=200\)

Q(t)=200×\(e^{\frac{-t}{100}}\)

1% of 200 is 2 grams

2=200×\(e^{\frac{-t}{100}}\)

\(e^{\frac{t}{100}}\)=100

t=100ln(100)

t=460.52minutes

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Answer:

14

Step-by-step explanation:

below is 12+2 which is the same size as the top one

The project completion time is output of the simulations, option A, the EXCEL function used is (c) 1+4*RAND() and the standard deviation is

(b) 1.47.

1) In this simulation, we enter commands based on the way that activity durations are distributed (here uniformly with predetermined intervals). We determine the project completion time as an output based on the command we used and our calculations. This value will fluctuate (slightly) when the simulation is run, hence it is not fixed.

Hence, the "project completion time" is an (a) Output of the simulation.

2) Here, it is given that time required to complete activity A is uniformly distributed in an interval [1, 5].

So, we require random numbers starting from 1 with an interval of length 5-1=4.

We know, during simulation using usual Excel function RAND() we obtain random numbers in an interval [0, 1].

Thus if we multiply usual Excel function RAND() by 4 and thus use 4*RAND(), then we obtain random numbers in an interval [0*4, 1*4] i.e

[0, 4].

Adding 1 to this Excel function i.e. using Excel function 1+4*RAND() we obtain random numbers in an interval [0+1, 4+1] i.e [1, 5].

Hence, the Excel function to be used to generate random numbers for the duration of activity A is (c) 1+4*RAND().

3) For \(\tiny X\sim Unif\left ( a,b \right )\), variance is given by

\(\tiny Var\left ( X \right )=\frac{\left ( b-a \right )^2}{12}\)

Variance for activity A is given by

\(\tiny \frac{\left ( 5-1 \right )^2}{12}=\frac{4^2}{12}=1.333333\)

Variance for activity B is given by

\(\tiny \frac{\left ( 3-2 \right )^2}{12}=\frac{1^2}{12}=0.083333\)

Variance for activity C is given by

\(\tiny \frac{\left ( 6-3 \right )^2}{12}=\frac{3^2}{12}=0.75\)

Variance of project completion time in the project is \tiny \(1.333333+0.083333+0.75= 2.166666\)

So, standard deviation of project completion time in the project is \(\tiny \sqrt {2.166666}=1.47196\approx 1.47\)

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Complete question:

A project has three activities A, B, and C that must be carried out sequentially. The probability distributions of the times required to complete each of the activities A, B, and C are uniformly distributed in intervals (1,5), (2,3) and (3,6) respectively. Find the total project completion time and run 1000 simulation trials in Excel. 7. The "project completion time" is a(n)... a. Output of the simulation b. Input of the simulation c. Decision variable in the simulation d. A fixed value in the simulation 8. Which of the following Excel functions would properly generate a random number for the duration of activity A in the project described above? a. 5* RANDO b. 1+5 * RANDO c. 1+4* RANDO d. NORM.INV(RAND(),1,5) e. NORM.INV(RAND(0,5,1) 9. The standard deviation of the project completion time in the project described above is cl a 2.83 b. 1.47 c. 1.15 d. 1.82 e. 1.63

Miriam needs 8 consecutive throws to win

Here, we want to calculate the number of throws consecutively that Miriam must make into the cup to beat Ishak

Since Ishak made 48% already, Miriam must make 52%

Out of 30, she made 12;

This represents a percentage of;

Let the number of throws needed be x;

So;

So what this mean is that, out of 38 throws, 20 would enter, with the last 8 being consecutive

Since calculating volume is multiplying the side lengths together we first have:

b x b x 4

Then we can simplify b x b to b ²

And when you multiply b² by 4 you get 4b²

Answer: 4b² is the volume of the fish tank.

Answer:

4b² is the volume of the fish tank.

Step-by-step explanation:

I think

The exact value of the given expression. sin 2 cos−1 12 13 is 240/169.

To find the exact value of the given expression, we need to use the identity sin(2θ) = 2sin(θ)cos(θ) and the information provided. The expression you want to find is sin(2 * cos^(-1)(12/13)).

First, let's find the angle θ, which is cos^(-1)(12/13). In a right triangle with the adjacent side = 12 and hypotenuse = 13, we can use the Pythagorean theorem to find the opposite side: Opposite side = √(13^2 - 12^2) = √(169 - 144) = √25 = 5

Now, we can find sin(θ) and cos(θ): sin(θ) = opposite/hypotenuse = 5/13 cos(θ) = adjacent/hypotenuse = 12/13 Next, use the sin(2θ) identity: sin(2θ) = 2sin(θ)cos(θ) = 2(5/13)(12/13) = (10/169)(24) = 240/169 So, the exact value of the given expression is 240/169.

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Answer:

182 songs

Step-by-step explanation:

Given :

Celtic Thunder albums = 5

Irish Tenor albums = 3

Frank Patterson album = 6

Number of songs per album = 12

Number of repeat songs = 14

Total number of songs in playlist :

(Σ(Number of albums * number of songs ​per album)) + number of repeat songs

(12 * 5) + (12 * 3) + (12 * 6) + 14

60 + 36 + 72 + 14 = 182 songs

The perimeter of triangle is 66.24 units.

What is triangle?

In Euclidean geometry, any 3 points, once non-collinear, verify a unique triangle and at the same time, a unique plane

Main body:

according to question :

c = 28

let the vertices be A,B,C

∠A= 30°

by using trigonometric ratios,

BC/ AB = sin30°

AB = C = 28

BC/28 = sin30°

BC = 28*sin30°

BC= 28*(1/2)

BC = 14

similarly

AB /CA = cos 30°

28/CA = √3/2

CA = 28*√3/2

CA = 14/√3

CA = 24.24

Hence , perimeter = AB +BC +CA = 28+14+24.24

                              =66.24 units

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Answer:

cosPcosQ - sinPsinQ

Step-by-step explanation:

using the addition identity

• cos(x + y) = cosxcosy - sinxsiny

then

cos(P + Q) = cosPcosQ - sinPsinQ

Answer:

A.

Monna marries Federigo in the end, although she is not in love with him.

Step-by-step explanation:

Answer:

The answer is C C.The only time Monna asks Federigo for something, he can't give it to her.

Answer:

  x - y = 2

Step-by-step explanation:

You want an equation for the tangent to (x^2+y^2)^3−8x^2y^2=0 at the point (x, y) = (1, -1).

A graph of the curve shows it has a slope of +1 at (x, y) = (1, -1).

In point-slope form the equation of the line is ...

  y -k = m(x -h) . . . . . . . . line with slope m through point (h, k)

  y -(-1) = 1(x -1) . . . . . . substituting known values

  x - y = 2 . . . . . . . . rearranging to standard form

__

Additional comment

Differentiating implicitly, you get ...

  3(x^2 +y^2)^2(2x·dx +2y·dy) -16xy^2·dx -16x^2y·dy = 0

at (1, -1), this is ...

  3(1 +1)^2(2·dx -2·dy) -16·dx +16·dy = 0

  8dx -8dy = 0 . . . . simplified

  dy/dx = 1

Then we can proceed with the point-slope equation as above.

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Answer:

21440

Step-by-step explanation:

Start by multiplying 7x³ by x² and -5.

Multiply 8x² by x² and -5.

Multiply -3 by x² and -5.

Combine like terms together.

Rearrange the terms in descending power order.

Substitute x = 5 into the above polynomial.

Evaluate the exponents first.

Multiply the terms together.

Combine the terms together.

This is the answer when substituting x = 5 into the simplified expression.

Substitute x = 5 into the expression.

Evaluate the exponents first.

Multiply the terms in the first bracket next.

Evaluate the expressions inside the brackets.

Multiply these two terms together.

This is the answer when substituting x = 5 into the original (unsimplified) expression.

The total surface area of the cuboid is 2 (lh + lw+ hw) square units.

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A series is convergent when the sequence of partial sums, which are the sums of the first n terms in the series, approaches a finite limit as n approaches infinity. In other words, the series has a sum that can be found. On the other hand, a series is divergent if the sequence of partial sums does not approach a finite limit. This means the series does not have a sum. So, to determine if a series is convergent or divergent, analyze the behavior of its sequence of partial sums.

A series is a sum of the terms in a sequence. A convergent sequence is one that has a limit as n approaches infinity, meaning that the sequence approaches a specific value. Similarly, a sequence of partial sums is the sum of the first n terms of the series. If this sequence of partial sums converges to a specific value, then the series is convergent. However, if the sequence of partial sums diverges, meaning it does not approach a specific value, then the series is divergent. Understanding whether a series is convergent or divergent is important in various fields such as physics and engineering.
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Answer:

Step-by-step explanation:

i am sorry im in geomatry now and i don'teven know this

Answer:

angle TEA = 58 (which is 29 times 2) degrees

angle TEF = 37 (which is 74 divided by two 2) degrees

Step-by-step explanation:

The angle bisector divides a given angle into two equal parts