A furnace operates at 2,300°F. Before it can be used to extract metal from an ore, the temperature must be raised to 3,600°F. This takes place at a rate of 250°F per quarter-hour. Identify the slope and y-intercept in an equation for the temperature in terms of x quarter hours.

Enter your answer using the equation y=mx+b

Answer:

x=y-44 and x+y=410

Step-by-step explanation:

So, you want to use the equations x=y-44 and  x+y=410 when x is Ann's score and y is Ruth's score. This is because x (Ann's score) is Ruth's score (y) but 44 less, so you subtract y-44 to get x. Then x+y would also have to equal 410 so that's the other equation. Graphing the 2 equations gets you to the point  (183,227) in which Ann's score is 183 points and Ruth's score is 227 points.

Rotation is the rigid type of transformation which is equivalent to the two reflections across intersecting lines.

Therefore, the rigid type transformation which is equivalent to two reflection across the intersecting lines is called rotation.

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We know that,

\( \bf{average \: speed \: = \: \frac{total \: distance \: travelled}{total \: time \: taken} }\)

Put the values according to the formula :

\( \bf{\frac{220km}{3hr} = 73.3 km/hr}\)

Answer:

  (5.4)^9

Step-by-step explanation:

You want the simplified form of (5.4)(5.4^2)^4.

It can be useful to think of integer exponents as telling you how many times the base is a factor in the product.

  (5.4)(5.4^2)^4 = (5.4)·((5.4)(5.4))^4

  = (5.4)·((5.4)(5.4))·((5.4)(5.4))·((5.4)(5.4))·((5.4)(5.4))

Eliminating excess parentheses, we see the product is ...

  = (5.4)(5.4)(5.4)(5.4)(5.4)(5.4)(5.4)(5.4)(5.4)

This has 9 factors of 5.4, so ...

  = (5.4)^9

Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:

v = d/t.

The parameters for the trip are given as follows:

Hence the velocity is obtained as follows:

230/7 = 32.86 miles per hour.

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Step-by-step explanation:

x^2-25=

\( {x}^{2} - 25 = (x - 5)(x + 5) \)

The area enclosed by the ellipse is 20π square units.

The parametric equations of the ellipse are given as z = 5 cos(θ) and y = 4 sin(θ), where θ represents the angle parameter in the range 0 ≤ θ < 2π. To find the area enclosed by the ellipse, we need to integrate over the parameter θ. The area of an infinitesimally small element of the ellipse is given by dA = z dy, which can be calculated using the parametric equations. Integrating this expression from 0 to 2π will yield the total area enclosed by the ellipse.

Parametric equations allow us to express the coordinates of points on a curve in terms of one or more parameters. By using these equations, we can determine various properties of curves, including the area they enclose. In this case, the parametric equations for the ellipse are z = 5 cos(θ) and y = 4 sin(θ). These equations represent the height and width of the ellipse at each point along the curve. By integrating the product of these values, we can find the area enclosed by the ellipse. The integral limits, 0 to 2π, ensure that we consider the entire curve.

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Answer:

There are 78 plums and 42 peaches.

Step-by-step explanation:

Let p = number of plums.

Let e = number of peaches.

The value of the plums is 2p.

The value of the peaches is 3e.

"total cost of plims was 30$ more than the cost of peaches"

2p = 3e + 30

"there are 120 fruits some are plums [...] others are peaches"

p + e = 120

We have a system of simultaneous equations.

2p = 3e + 30

p + e = 120

2p = 3e + 30

p = -e + 120

     2p = 3e + 30

+   3p = -3e + 360

------------------------------

     5p =         390

p = 78

p + e = 120

78 + e = 120

e = 42

Answer: There are 78 plums and 42 peaches.

Check:

78 plums cost 78 × $2 = $156

42 peaches cost 42 × $3 = 126

$156 - $126 = $30

The plums do cost $30 more than the peaches.

78 + 42 = 120

The total is indeed 120.

The answer above is correct.

Answer:

no question

Step-by-step explanation:

Answer:

4^-3

Step-by-step explanation:

Formula : -

a^m x a^n x a^k = a^( m + n + k )

Here,

a = 4

m = - 8

n = - 1

k = 6

4^-8 x 4^-1 x 4^6

= 4^( - 8 + ( - 1 ) + 6 )

= 4^( - 8 - 1 + 6 )

= 4^( - 9 + 6 )

= 4^-3

The probability of obtaining a sum of 7 when rolling two number cubes is 1/6 or approximately 0.1667.

To find the probability, we need to determine the number of favorable outcomes (sum of 7) and the total number of possible outcomes when rolling two number cubes. Each cube has six faces, numbered from 1 to 6.

To obtain a sum of 7, we can have the following combinations: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). There are six favorable outcomes.

The total number of possible outcomes when rolling two number cubes is the product of the number of outcomes for each cube, which is 6 * 6 = 36.

Therefore, the probability of obtaining a sum of 7 is given by:

Number of favorable outcomes / Total number of possible outcomes = 6 / 36 = 1/6 ≈ 0.1667.

Thus, the probability that the sum of the two numbers rolled on the number cubes will be 7 is approximately 0.1667, or 1/6 when expressed as a fraction.

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The optimal solution for the amount of cash to withdraw each time to minimize transportation costs and maximize interest earnings is determined by calculating the Economic Order Quantity (EOQ) using the formula Q = √((2 * C * T) / r), and rounding the result to a convenient amount.

The Economic Order Quantity (EOQ) model is typically used for inventory management, not for optimizing cash withdrawals. However, if we assume that the question is seeking an optimal withdrawal strategy to minimize transportation costs and maximize interest earnings, we can approach it as follows:

Let's denote:

C = Annual cash need ($5,000)

T = Transportation cost per visit ($5)

r = Annual interest rate (5%)

To find the optimal solution for the amount of cash to withdraw each time, we can consider the trade-off between transportation costs and interest earnings. The objective is to minimize the total cost.

Calculate the optimal order quantity (Q) using the EOQ formula:

Q = √((2 * C * T) / r)

Round the calculated Q to the nearest convenient amount, such as multiples of $100 or $500.

The optimal solution would be to withdraw the rounded Q amount each time to minimize transportation costs while still meeting the annual cash need.

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Answer:

2

Step-by-step explanation:

The amplitude is the height of the wave. Notice the bottom of the wave is at 1 and the top of the wave is at 3.

The amplitude of the given graph is 2 unit.

Amplitude:

It is the height of the wave measures by the distance between highest and lowest position of the wave.

Here the lowest position of the wave is = 1

And the highest position of the wave that is peak = 3

The amplitude = 3 - 1 = 2

hence the final answer is 2 unit.

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A) D = 1/2[C]  = 1/2[-16]

B) Elevation of city D is -8 feet.

Answer is negative due to -8 feet below sea level.

What is elevation?

The elevation is the height above sea level. Typically, elevations are expressed in feet or meters. Maps can depict them using contour lines, which link points of the same elevation, color bands, or numbers that indicate the precise elevations of specific points on the surface of the Earth.

The elevation of city A is 60 feet below sea level
⇒ A = -60
The elevation of city C is 16 feet below sea level
⇒ C = -16                        

The elevation of city D is 1 over 2 of the elevation of city C.
⇒  D = 1/2[C]

Part A: Write an expression to represent the elevation, in feet, of city D.
⇒ D = 1/2[C]  = 1/2[-16]

Part B: Solve the expression and explain why the answer is negative or positive.              
⇒  D = 1/2[-16]
     D = -8
As a result Elevation of city D is -8 feet.
Here founded answer is negative due to -8 feet below sea level.

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Answer:

25 × 60 (1 minute) × 60 (1 hour) = 90,000 meters/hour

90,000 converted into miles is 55.923

Answer:

A = 160

Step-by-step explanation:

Formula 1/2 d1d2

1/2 (16 x 20)

320 x 1/2 OR 320/2

=160

Hope this helps :)

The value of f left parenthesis 3 right parenthesis is 45.

According to the statement

We have given that the F(x) = 5(x)^2

and we have to find the value when Sophia have a 3 right parenthesis.

So, Parenthesis are used in mathematical expressions to denote modifications to normal order of operations.

And now we have to find the value for 3 right parenthesis

And for this purpose we have to put the value X= 3 in the f(x) then

F(x) = 5(x)^2

F(3) = 5(3)^2

F(3) = 5*9

F(3) = 45.

here the value of 3 right parenthesis is 45.

So, The value of f left parenthesis 3 right parenthesis is 45.

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Between 20 and 40 units per hour, the long-run average cost curve exhibits constant returns to scale. The statement that indicates between 20 and 40 units per hour, the long-run average cost curve exhibits constant returns to scale. This is option B.

In microeconomics, the long-run average cost (LRAC) is a method of showing the average expense per unit for a given level of production input. It is the cost of producing goods per unit using a specified number of inputs, such as labor and capital.

Long-run average cost is the average cost per unit of production after the company has adapted its production scale fully. As a result, the term "long-run" denotes a period in which all of the firm's inputs are variable.

The cost structure's shape is represented by the long-run average cost curve. The curve is determined by dividing the cost of producing goods by the number of goods produced. It aids in identifying the production rate at which a firm may generate the most output at the lowest cost.The long-run average cost curve depicts how the average cost of production varies with scale.

The curve might be downward-sloping, indicating economies of scale, flat, implying constant returns to scale, or upward-sloping, indicating diseconomies of scale, based on the company's production methods.

Hence, the answer is B.

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Answer:

20y-14y+4=16

20y+(-14y) -4   -4

6y=12

y=2

Step-by-step explanation:

Combine like terms

subtrate 4 from each side

Divide 6 by 6 and 12 by 6

There for y=2

Answer:

True.

Explanation:

When solving equations with unknowns on both sides, it is generally recommended to first deal with the variable terms before dealing with the constant terms. This involves simplifying the equation by combining like terms and isolating the variable on one side of the equation. Once the variable is isolated, you can then solve for its value.\(\)

Answer: -32+5√6

Step-by-step explanation:

(3√3 - 5√2) (2√3 + 5√2)=

(3√3 * 2√3) + (3√3 * 5√2) - (5√2 * 2√3) - (5√2 * 5√2) =

(3*2*√3*√3) + (3*5*√3*√2) - (5*2*√2*√3) - (5*5*√2*√2)=

6*3 + 15*√(3*2) - 10*√(2*3) - 25*2=

18+15√6-10√6-50=

18-50+(15-10)*√6=-32+5√6

Answer:

124 is the total

Step-by-step explanation:

100 * .09 = 9

100 * .15 = 15

15+ 9 + 100 = 124

Hope it helps!

(1) The number of pairs (r, y) satisfying the equation x + 2y = 25 is 12.

(2) The number of triples (x, y, z) satisfying x + y + 2z = 25 is 12.

We have,

(1)

The number of pairs (r, y) of positive integers satisfying the equation

x + 2y = n can be found by dividing n by 2 and taking the floor value.

In this case,

n = 25, so the number of pairs is floor(25/2) = 12.

(2)

To find the number of triples (x, y, z) of positive integers satisfying the equation x + y + 2z = n, we can use a similar approach.

Since n is odd, we can set x = 1 and consider the remaining part of the equation: y + 2z = n - 1.

The number of solutions to this equation is floor((n - 1)/2).

In this case, n = 25, so the number of triples is floor(24/2) = 12.

Thus,

(1) The number of pairs (r, y) satisfying x + 2y = 25 is 12.

(2) The number of triples (x, y, z) satisfying x + y + 2z = 25 is 12.

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Answer:

You can use Protector' but dint have use this method:

Acute. Draw a vertical line connecting the 2 rays of the angle. To determine the number of degrees in an acute angle, connect the 2 rays to form a triangle. Line up the short end of your ruler with the bottom ray, then draw a vertical line intersecting the other ray using the long side of your ruler.

Answer:

28.26 miles

Step-by-step explanation:

Area= pi times radius squared

diameter is twice the radius so 6÷2=3miles

3 miles is the radius

So A= 3.14 × 3²

= 28.26

Formula: A = πr²

Divide to find the radius.

6 / 2 = 3

Solve using the values we are given and solved for.

A = π(3)²

A = 9π

A ≈ 28.26

Best of Luck!

x + 3, x > -3 is the piece which will be included in the given function          f(x) = [ x + 3 ]. This can be obtained by removing modulus and finding the value for x.

Each element of a non-empty set A has a function connecting it to at least one element of a second non-empty set B. A function f between two sets, A and B, is said to have a "domain" and a "co-domain" in mathematics. For any value of an or b, F = (a,b)| holds true.

Which piece will the function include?

Given that,  

f(x) = [ x + 3] which is an absolute value function.

Therefore,

| x+3 | > 0

By removing the modulus,

x+3 > 0

x > - 3

Hence x + 3, x > -3 is the piece which will be included in the given function:

f(x) = [ x + 3].

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Answer:

21/18 or 1 and 3/18

Step-by-step explanation:

6/9 = 12/18

3/6 = 9/18

12/18 + 9/18 = 21/18 or 1 3/18

Answer:

The dimensions of the playground that maximize the total enclosed area is 100 feet.

Let,

L= length of entire playground

W = width of entire playground

Assume the dividing fence is parallel to the width.

Total fencing required

2L + 3W = 400

L= (400 − 3W)2

Area of entire playground,

A= L × W

= (400−3W)/2⋅W

= −3/2W^2 + 200W

Maximum area will occur at a point where the derivative of the area is equal to zero.

dA/dW = −3W+  200 = 0

W = 66 2/3

Substituting 91 1/3 for W in 2L + 3W = 400

gives

2L = 200

L = 100

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The probability of getting a lemon-lime drink on the first draw and a fruit-punch drink on the second draw is A. 0. 139.

The probability of getting a lemon-lime drink on the first draw is 5/12. The probability of getting a fruit-punch drink on the second draw is 4/12. Since the bottles are returned to the cooler and mixed up between draws, the events are independent.

Therefore, the probability of getting a lemon-lime drink on the first draw and a fruit-punch drink on the second draw is :

= 5 / 12 x 4 / 12

= 0. 139

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The question is:

What is the probability of getting a lemon-lime drink on the first draw and a fruit-punch drink on the second draw?

Answer:

7/10 is the answer as a fractions