Point Tis on line segment SU. Given SU = 18 and TU = 10, determine the
length ST.

The macrostate s of two six-sided dice can be defined as the sum of the top faces of the dice.

The macrostate of a system refers to a comprehensive description of the system in terms of its properties and variables that are used to characterize it. In the case of two six-sided dice, the macrostate is described by the sum of the numbers on the top faces of the two dice, which determines the total score or outcome. This macrostate, represented by the variable "s", is a measurable quantity that summarizes the state of the system, providing information about the distribution of the outcomes over all possible configurations of the two dice.

It's important to note that a macrostate does not specify the exact configuration of the system, but rather provides a probabilistic description of it. In other words, the macrostate "s" only describes the sum of the two dice and does not specify which number is on each die. In thermodynamics, macrostates are used to characterize the thermodynamic properties of a system, such as its temperature, pressure, and entropy. The study of macrostates and their distributions helps us to understand the behavior of complex systems and make predictions about their future behavior.

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The perimeter of the rectangle 48.48 inches and the expression of the new perimeter of the rectangle is 48.48 - (1.57/a) inches

In this question, we have

Area = 144 square inches

Length = 4 * Width

The area of a rectangle is represented as

A = lw

So, we have

A = (w + 4) * w

This gives

(w + 4) * w = 144

Expand

w² + 4w = 144

So, we have

w² + 4w - 144 = 0

Using a graphing calculator, we have

w = 10.12

Recall that

l = w + 4

So, we have

l = 10.12 + 4

Evaluate

l = 14.12

The perimeter is then calculated as

P = 2 * (l + w)

So, we have

P = 2 * (10.12 + 14.12)

Evaluate

P = 48.48

So, the perimeter is 48.48 inches

Here, we have

Value subtracted = (4/a) cm

Converted to inches

Value subtracted = (1.57/a) inches

So, we have

New perimeter = 48.48 - (1.57/a) inches

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Complete question

The length of a rectangle is four times its width. If the area of the rectangle is 144 square inches find its perimeter.

if the perimeter of the given rectangle is subtracted by (4/a)cm, what will be its new perimeter?;

EXPLANATION

Given that we have the rate of 17cm/min we can apply the unitary method in order to get the number of feet per hour as shown as follows:

Simplifying:

Hence, the solution is 33.46 feet/hour

In summary, the difference between these two regression equations is mainly in the notation used to represent the regression coefficients, with lowercase letters used in simple linear regression models and uppercase letters used in multiple linear regression models.

In mathematics, an equation is a statement that asserts that two mathematical expressions are equal to each other. It usually contains one or more variables, which are placeholders for values that can vary. Equations are used to describe mathematical relationships and to solve problems. They can take many forms, such as linear equations, quadratic equations, polynomial equations, exponential equations, and so on. The specific form of an equation depends on the type of problem being solved and the mathematical relationships involved.

Here,

Both the regression equations ^y = b0 + b1x and Y = B0 + B1x are used to model the relationship between a dependent variable (y or Y) and an independent variable (x). However, the key difference between these two equations lies in the notation used to represent the regression coefficients.

In the first equation ^y = b0 + b1x, the regression coefficients are represented with lowercase letters (b0 and b1). This notation is typically used in simple linear regression models where there is only one independent variable. The hat symbol (^) over the y indicates that this is an estimated value of y based on the model.

In the second equation Y = B0 + B1x, the regression coefficients are represented with uppercase letters (B0 and B1). This notation is typically used in multiple linear regression models where there are two or more independent variables. The capitalization of the letters helps to distinguish them from the coefficients in the simple linear regression model.

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Value of m and b of the straight line in the graph is 0 and 2 respectively.

In mathematics, slope refers to the steepness or inclination of a line, and is defined as the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line. It is often represented by the letter m. The slope of a line can be positive, negative, zero, or undefined.

Let us assume that the equation of line be y=mx+b.

where m is the slope

and b is the intercept

The line in the graph is parallel to x axis

so, slope is 0

m=0

the line passes through(0,2)

Putting the value in the equation, we get

b=2

Hence, the equation of line be y=2

Therefore, value of m=0 and b=2.

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The complete question is:

The graph is showing the equation of straight line y=mx+b, find the value of m and b.

Image is attached below:

hello. Let's develop the equation and see if this is true or false:

So, this is false.

Answer: There were 51 students

Step-by-step explanation: Divide 362 by 7 which equals 51 with 5 students remaining! Hope this helps!

Answer:

0.88

Step-by-step explanation:

Given data

Rate of depreciation = 12%

The expression for the exponential function is given as

A= P(1-r)^t

r= 0.12

A= P(1-0.12)^t

A= P(0.88)^t

Hence as seen from the expression, the multiplier is 0.88

For each variable, the possible values are:

a) T = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

b) X = {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6}

c) U = {0, 1, 2, 3, 4, 5, 6}

d) Z = {0, 1, 2}

Item a:

In total, there are 10 pumps, hence the possible values are all integers from 0 to 10, that is:

T = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Item b:

In the first, there are 6 pumps, and in the second 4, hence, the difference ranges from -4 to 6, that is:

X = {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6}

Item c:

The maximum number in a station is 6 pumps, hence this variable ranges from 0 to 6.

U = {0, 1, 2, 3, 4, 5, 6}

Item d:

Either none of the stations has exactly two pumps in use, or one has or both, hence the variable ranges from 0 to 2.

Z = {0, 1, 2}

The question is incomplete. The complete question is:

"The number of pumps in use at both a six-pump station and a four-pump station will be determined. Give the possible values for each of the following random variables. (Enter your answers in set notation.)

a. T = the total number of pumps in use

b. X = the difference between the numbers in use at stations 1 and 2.

c. U = the maximum number of pumps in use at either station

d. Z = the number of stations having exactly two pumps in use"

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Answer:

B) Fifth Grade Boys

Step-by-step explanation:

The far right green line represents the fifth grade boys, and you can see that this lines up right in the middle of 50 and 60.

Answer:

A: You plot these points (-3,4) (-3,6) (-5,6) (-7,4)

B: The transformation would be described as a reflection over the y axis

C:  The transformation does result in a congruent figure because the shape doesn't change in size or shape and in length or width

Step-by-step explanation:

So our plots from the figure are: (3,4)  (3,6)  (5,6)  (7,4)

So using the rule (x, y) → (-x, y) are new points would be:

(-3,4)

(-3,6)

(-5,6)

(-7,4)

This rule (x, y) → (-x, y) is used for the type of transformation that is a reflection but over the y axis.

The equation of the circle with radius 9 and center ( -1,-8 ) is( x + 1 )² + ( y + 8  )² = 81.

The standard form equation of a circle with center (h, k) and radius r is:

( x - h )² + ( y - k )² = r²

Given that the circle has a center of (-1, -8) and the radius is 9.

Hence; from the standard form of the equation of the circle:

Center ( h , k ) = ( -1, -8 )

h = -1

k = -8

And radius r = 9

Plug these values into the above formula and simplify.

( x - h )² + ( y - k )² = r²

( x - ( -1 ) )² + ( y - ( -8 ) )² = 9²

Simplify

( x + 1 )² + ( y + 8  )² = 81

Therefore, the equation of the circle is ( x + 1 )² + ( y + 8  )² = 81.

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Answer:

20.

Step-by-step explanation:

60 - 40 = 20

Answer:

There are 5 prime numbers between 40 and 60.

Step-by-step explanation:

A prime number is a number that is ONLY divisible by itself and 1 with no remainder. For example 3 can only be divided by 1 or 3 without a remainder left.

Between 40 and 60 there are 5 prime numbers: 41, 43, 47, 53, and 59.

Answer:

\(3w + 6 = 21 \\ 3w = 15 \\ w = 5\)

Hey there!

\(\mathsf{3w + 6 = 21}\)

\(\mathsf{3w + 6 - 6 = 21 - 6}\)

\(\mathsf{21 - 6 = \boxed{\bf 15}}\)

\(\mathsf{\dfrac{3w}{3}=\dfrac{15}{3}}\)

\(\mathsf{\dfrac{15}{3}=\boxed{\bf 5}}\)

\(\boxed{\boxed{\large\textsf{Therefore, your answer: \huge \bf w = 5}}}\huge\checkmark\)

\(\large\text{Good luck on your assignment and enjoy your day!}\)

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Answer:

36

Step-by-step explanation:

calculate the 6+the Other 6 together

Answer:

36

Answer:

He has $9.24 left of his gift certificate

Step-by-step explanation:

Given that,

He bought two baseballs for $1.79

Baseball= 1.79+1.79 or 1.79 × 2 (because there are two baseballs.

= $3.58

Baseball Glove = $49.99

Baseball Bat = $12.19

Altogether = $3.58 + $49.99 + $12.19

= $65.76

So you subtract $65.76 from the Original amount in the gift certificate,

=> $75 - $65.76

= $9.24

Answer:

1. Multiply the area by 2 and divide the result by the central angle in radians.

2. Find the square root of this division.

3. Multiply this root by the central angle again to get the arc length.

Step-by-step explanation:

Answer:

1-10.5

2-8.8

3-1.1

4-9.3

Answer:

2/5

Step-by-step explanation:

She earned 0.91 pounds for every $1 US dollar when a visitor traded $1,000 US dollars for 910 British pounds.

A proportion is an equation that sets two ratios equal to each other. For example, if there is one guy and three girls, the ratio may be written as 1: 3. (for every one boy there are 3 girls) One-quarter are males and three-quarters are girls. 0.25 are males (by dividing 1 by 4). According to the notion of proportion, two ratios are in proportion when they are equivalent. It is a formula or statement that shows that two ratios or fractions are equivalent.

Here,

For 910 pounds, she spent $1000 US dollars.

For $1,

=910/1000 pound

=0.91 pounds

For each $1 US dollar, she received 0.91 pounds as tourist exchanged $1,000 US dollars for 910 British pounds.

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Let's assume David's average speed is S km/h.

A) To find David's average speed, we can use the formula: Speed = Distance / Time.

David completed the race in 5 hours, so his speed is S km/h. Therefore, we have:

S = Distance / 5

B) Ken's average speed is 9.8 km/h less than David's average speed, which means Ken's average speed is (S - 9.8) km/h.

Ken took 7 hours to complete the race, so we have:

S - 9.8 = Distance / 7

Now, we can solve the system of equations to find the values of S and Distance.

From equation (1): S = Distance / 5

Substitute this into equation (2):

Distance / 5 - 9.8 = Distance / 7

Multiply both sides of the equation by 35 to eliminate the denominators:

7 * Distance - 35 * 9.8 = 5 * Distance

7 * Distance - 343 = 5 * Distance

Subtract 5 * Distance from both sides:

2 * Distance - 343 = 0

Add 343 to both sides:

2 * Distance = 343

Divide both sides by 2:

Distance = 343 / 2 = 171.5 km

Therefore, the distance of the cycling race is 171.5 kilometers.

To find David's average speed, substitute the distance into equation (1):

S = Distance / 5 = 171.5 / 5 = 34.3 km/h

So, David's average speed was 34.3 km/h.\(\)

Answer:

A) 34.3 km/h

B) 171.5 km

Step-by-step explanation:

Since Ken's average speed is said to be 9.8km/h less than David's average speed, and we know that Ken's average speed is dependent on him traveling for 7 hours, then we have our equation to get the distance of the cycling race:

\(\text{Ken's Avg. Speed}=\text{David's Avg. Speed}\,-\,9.8\\\\\frac{\text{Distance}}{7}=\frac{\text{Distance}}{5}-9.8\\\\\frac{5(\text{Distance})}{7}=\text{Distance}-49\\\\5(\text{Distance})=7(\text{Distance})-343\\\\-2(\text{Distance})=-343\\\\\text{Distance}=171.5\text{ km}\)

This distance for the cycling race can now be used to determine David's average speed:

\(\text{David's Avg. Speed}=\frac{\text{Distance}}{5}=\frac{171.5}{5}=34.3\text{ km/h}\)

Therefore, David's average speed was 34.3 km/h and the distance of the cycling race was 171.5 km.

The missing variables on item 2 are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:

For the angle of 60º, we have that:

Hence the length o is given as follows:

tan(60º) = o/12.

\(\sqrt{3} = \frac{o}{12}\)

\(o = 12\sqrt{3}\)

Applying the Pythagorean Theorem, the length i is given as follows:

i² = 12² + \((12\sqrt{3})^2\)

i² = 576

i² = 24²

i = 24.

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Answer:

o = 12√3

i = 24

Step-by-step explanation:

From observation of the given right triangle, we can see that two of its interior angles measure 60° and 90°. As the interior angles of a triangle sum to 180°, this means that the remaining interior angle must be 30°, since 30° + 60° + 90° = 180°. Therefore, the triangle is a special 30-60-90 triangle.

The side lengths in a 30-60-90 triangle have a special relationship, which can be represented by the ratio formula a : a√3 : 2a, where "a" represents a scaling factor that can be any positive real number.

In triangle #2, the shortest leg is 12 units.

As "a" is the shortest leg, the scale factor "a" is 12.

The side labelled "o" is the longest leg opposite the 60° angle. Therefore:

\(o = a\sqrt{3}=12\sqrt{3}\)

The side labelled "i" is the hypotenuse of the triangle. Therefore:

\(i= 2a = 2 \cdot 12=24\)

Therefore:

Answer:

0.03323

BRAINLIEST, PLEASE!

Step-by-step explanation:

Move the decimal place 3 places to the left.

33.23 becomes 0.03323.

Answer:

x = -1

Step-by-step explanation:

6+4 = 10

14-10 = 4

2x + 6 = 4

2x (-2) = -2

-2 + 6 = 4

Step-by-step explanation:

To find the profit of the firm, we need to first determine the quantity Q that maximizes the profit, and then use that quantity to find the price and profit.

The profit function can be written as:

π(Q) = TR(Q) - TC(Q)

where TR(Q) is the total revenue function and TC(Q) is the total cost function. We can write TR(Q) as:

TR(Q) = P(Q) * Q

where P(Q) is the price function, which is given as:

P(Q) = 240 - 20Q

So, the profit function becomes:

π(Q) = (240 - 20Q) * Q - (120 + 45Q - Q^2 + 0.4Q^3)

Simplifying this expression, we get:

π(Q) = -0.4Q^3 + 24.6Q^2 - 195Q + 120

To maximize the profit, we take the derivative of the profit function with respect to Q and set it equal to zero:

π'(Q) = -1.2Q^2 + 49.2Q - 195 = 0

Solving for Q using the quadratic formula, we get:

Q = (49.2 ± sqrt(49.2^2 - 4*(-1.2)(-195))) / (2(-1.2))

Q = 21 or Q = 32.5

Since the coefficient of the Q^3 term in the profit function is negative, the profit function has a maximum at Q = 32.5. Therefore, the firm should produce and sell 32.5 units of output.

To find the price that the firm should charge, we substitute Q = 32.5 into the demand function:

P = 240 - 20Q

P = 240 - 20(32.5)

P = 160

Therefore, the firm should charge a price of $160 per unit.

To find the profit at the optimal level of output, we substitute Q = 32.5 and P = 160 into the profit function:

π(Q) = -0.4Q^3 + 24.6Q^2 - 195Q + 120

π(32.5) = -0.4(32.5)^3 + 24.6(32.5)^2 - 195(32.5) + 120

π(32.5) = $1,722.81

Therefore, the profit at the optimal level of output is $1,722.81

Answer:

-4.8h + 2

Step-by-step explanation:

Use the distributive property to expand the expression.

-4(1.2h - 0.5)

-4 · 1.2h = -4.8h

-4 · -0.5 = 2

Therefore, the expanded expression is -4.8h + 2.

To solve the savings plan balance, we have to calculate the interest for 19 months. The formula for calculating interest for compound interest is given below:$$A = P \left(1 + \frac{r}{n} \right)^{nt}$$where A is the amount, P is the principal, r is the rate of interest, t is the time period and n is the number of times interest compounded in a year.

The given interest rate is 11% per annum, which will be converted into monthly rate and then used in the above formula. Therefore, the monthly rate is $r = \frac{11\%}{12} = 0.0091667$.

The monthly payment is $PMT = $250. We need to find out the amount after 19 months. Therefore, we will use the formula of annuity.

$$A = PMT \frac{(1+r)^t - 1}{r}$$where t is the number of months of the plan and PMT is the monthly payment. Putting all the values in the above equation, we get:

$$A = 250 \times \frac{(1 + 0.0091667)^{19} - 1}{0.0091667}$$$$\Rightarrow

A = 250 \times \frac{1.0091667^{19} - 1}{0.0091667}$$$$\Rightarrow

A =250 \times 14.398$$$$\Rightarrow A = 3599.99$$

Therefore, the savings plan balance after 19 months with an APR of 11% and monthly payments of $250 is $3599.99 (approx).

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Hi there!

For this, we would be using PEMDAS:

Parentheses

Exponents

Multiplication (from left to right)

Division (from left to right)

Addition (from left to right)

Subtraction (from left to right)

1.Multiply all terms:

\(3\)·\(4\)·\(5\)\(-8\)·\(9\)·\(10\)·\(11=60\)

2.Multiply the terms again:

\(60-8\)·\(9\)·\(10\)·\(11=\)\(60-7920\)

3.Subtract the terms:

\(60-7920=-7860\)

Therefore, the answer would be -7860.