A person’s weekly pay is directly proportional to the number of hours worked. Shawn’s pay is $123.00 for 20 hours of work. Find the amount of pay for 31 hours of work.

The number of miles that must be driven for the two-day rental from Company B to be less than Company A is 200 miles.

The equation that can be used to determine the total cost of renting from Company A is:

Total cost = (cost per day x number of days) + (cost per mile x number of miles)

($25 x 2) + ($0.25 x m)

$50 + $0.25m

The equation that can be used to determine the total cost of renting from Company B is: ($35 x 2) + ($0.15 x m)

$70 + $0.15m

The equation that can be used to determine the number of miles where it would be cheaper to rent for two days from Company B is:

$70 + $0.15m  < $50 + $0.25m

$70 - $50 < $0.25m - $0.15m

$20 < $0.10m

m < $20 / 0.10

m < 200

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The solution to Log x+y = logbx − logby Given log630 ≈ 1.898 and log62 ≈ 0.387, log615 ≈ 2.086.

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 1000 = 10³, its logarithm in base 10 is 1000 is 3, or log₁₀ = 3.

log 630 = log (6 * 62 * 10)

log 630= log 6 + log 62 + log 10 =

log 630= 1 + 0.387 + 1

log 630= 2.387

And

log 615 = log (6 * 62 * 5)

log 615 = log 6 + log 62 + log 5

log 615 = 1 + 0.387 + 0.699

log 615 = 2.086

In the current case, log 630 ≈ 1.898 and log 62 ≈ 0.387. It was discovered that the logarithm of 615 is approximately 2.086 and that these logarithmic values are utilized to simplify other logarithmic calculations.

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Answer:

The fourth option, \(y=2x-3\)

Step-by-step explanation:

It is given that the table represents a linear function. We are asked to write an equation for the function.

\(\boxed{\begin{minipage}{8 cm}\underline{Finding the Equation of a Line:}\\\\$y-y_1=m(x-x_1)$ \ \text{(Point-slope form)}\\\\where:\\\phantom{ww}$\bullet$ $m$ is the slope of the line.\\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\ \\ \underline{Finding the Slope:} \\ \\ $m=\dfrac{y_2-y_1}{x_2-x_1} $\end{minipage}}\)

(1) - Calculate the slope of line

Defining two points on the table:

\((x_1,y_1)\rightarrow (1,-1) \\\\(x_2,y_2)\rightarrow (3,3)\)

Now using the slope equation:

\(m=\dfrac{y_2-y_1}{x_2-x_1} \\\\\\\Longrightarrow m=\dfrac{3-(-1)}{3-1}\\\\\\\Longrightarrow m=\dfrac{4}{2}\\\\\\\therefore \boxed{m=2}\)

(2) - Find the equation of the line using point-slope form

\((x_1,y_1)\rightarrow (1,-1)\\\\m=2\\\\\\y-y_1=m(x-x_1)\\\\\\\Longrightarrow y-(-1)=2(x-1)\\\\\\\Longrightarrow y+1=2x-2\\\\\\\therefore \boxed{\boxed{y=2x-3}}\)

Thus, the fourth option is correct.

Answer:

It is a metaphor.

Step-by-step explanation:

Hope it helps

Answer: y = -3/5x - 6

Step-by-step explanation:

There are a few equations that can be used for this, but the simplest one would be y = mx + b

We are given:

y = -3

m = -3/5 (slope)

x = -5

b = ?

Our equation is this, we are solving for b

==> -3 = -3/5 ( -5) + b

==> -3 = -3/5 ( -5) + b ( multiply the brackets)

==> -3 = 3 + b ( subtract 3 to both sides)

==> -6 = b

Now we can make the desired equation in slope intercept form;

y = -3/5x - 6

Hope this helped! Have a great day :D

Answer:-13/3

Step-by-step explanation:

Jyotsana must sell the eggs at a price of 80.5 rs per hundred eggs to earn a profit of 15%.

Jyotsana bought 4000 eggs at a rate of 8.40 rs per dozen. We can calculate the cost of one egg as follows:

Cost of 1 egg = (Cost of 1 dozen) / 12

Cost of 1 egg = 8.40 / 12

Cost of 1 egg = 0.70 rs

To earn a profit of 15%, Jyotsana needs to sell the eggs at a price that is 15% more than her cost price. Let's call this selling price "x". To calculate "x", we need to first calculate the cost of 100 eggs, which is:

Cost of 100 eggs = 100 × Cost of 1 egg

Cost of 100 eggs = 100 × 0.70

Cost of 100 eggs = 70 rs

Now, Jyotsana wants to earn a profit of 15% on her cost price, which means her selling price should be:

x = Cost price per hundred eggs + 15% of Cost price per hundred eggs

x = 70 + (15/100) × 70

x = 70 + 10.5

x = 80.5 rs

Therefore, Jyotsana must sell the eggs at a price of 80.5 rs per hundred eggs to earn a profit of 15%.

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Answer:

385$

Step-by-step explanation:

30% off of 600 is 180. 600-180=420. Then, 35$ off would be 385.

Answer:

pretty sure it's 65

Step-by-step explanation:

They're usually congruent for these type of angles. Also, y would be 50

Answer:

x = 50°

Step-by-step explanation:

y = 65° because the base angles of an isosceles triangle are equal

x = 50° because angles in a triangle add up 180°

Answer:

H

Step-by-step explanation:

The answer is graph H

Answer:

it`s H

Step-by-step explanation:

literaly it`s H

Answer:

4      HAH AHQ HQH!!!

Step-by-step explanation:

1 1 1 1

Answer:

4

Step-by-step explanation:

2+2 is 4

E[d] = ∫∫ √(R²+ r² - 2Rr cos(Θ - θ)) * (1/(9π)) dr dθ

Evaluating this integral will give us the expected travel distance of the helicopter.

The constant c can be computed by considering the total area of the disc and setting it equal to 1. The expected travel distance of the helicopter can be calculated by integrating the distance traveled from the accident location to the hospital over the joint density function.

To compute c, we need to find the total area of the disc. The area of a disc with radius R is given by A = πR². In this case, the radius is 3 km, so the total area is A = π(3²) = 9π km². Since the accident happens uniformly at random, the joint density function gR,Θ(r,θ) is constant over the disc, meaning it has the same value for all points within the disc. Therefore, we can set the total probability equal to 1 and solve for c:

1 = ∫∫ gR,Θ(r,θ) dA = ∫∫ cr dA = c ∫∫ dA = cA

Since A = 9π km², we have cA = c(9π) = 1. Solving for c, we get c = 1/(9π).

To compute the expected travel distance of the helicopter, we integrate the distance traveled from the accident location to the hospital over the joint density function. The distance between two points in polar coordinates can be calculated using the formula d = √(R² + r²- 2Rr cos(Θ - θ)), where R and r are the radii, and Θ and θ are the angles.

The expected travel distance can be computed as:

E[d] = ∫∫ d * gR,Θ(r,θ) dr dθ

Substituting the expression for d and the value of gR,Θ(r,θ) = 1/(9π), we have:

E[d] = ∫∫ √(R²+ r² - 2Rr cos(Θ - θ)) * (1/(9π)) dr dθ

Evaluating this integral will give us the expected travel distance of the helicopter.

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Answer:

h = 8 inches

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = \(\frac{1}{2}\) bh ( b is the base and h the height )

given A = 24 and b = 6 , then

\(\frac{1}{2}\) × 6 × h = 24 , that is

3h = 24 ( divide both sides by 3 )

h = 8 inches

Answer:

Step-by-step explanation:

The dimension of the basis is {[1 0 0 2], [-1 1 0 0]}.

To find a basis for the subspace S = span {[1 -1 0 2], [3 -5 4 8], [0 1 -2 -1]}, we can use the same method as in the example. First, we put the vectors in a matrix and row-reduce it:

[1 -1 0 2]
[3 -5 4 8]
[0 1 -2 -1]

R2 - 3R1 -> R2
R3 -> R3 + 2R1

[1 -1 0 2]
[0 -2 4 2]
[0 1 -2 -1]

-1/2R2 -> R2

[1 -1 0 2]
[0 1 -2 -1]
[0 1 -2 -1]

R3 - R2 -> R3

[1 -1 0 2]
[0 1 -2 -1]
[0 0 0 0]

We can see that the last row is all zeros, so we have only two pivots and one free variable. This means that the dimension of the subspace S is 2. To find a basis, we can write the pivots as linear combinations of the original vectors:

[1 -1 0 2] = [1 0 0 2] + [-1 1 0 0]
[0 1 -2 -1] = [0 1 -2 -1]

Therefore, a basis for S is {[1 0 0 2], [-1 1 0 0]}.

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The presence of multiplication in an equation shows a context of repeated addition of values of that equation.

Multiplication is defined as one of the major arithmetic operation that shows the repeated addition of values of which a final figure is gotten. The other arithmetic operations include the following:

When there is multiplication sign in a mathematical expression it shows the context that repeated addition is needed to arrive at the desired value.

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Yes, the two cones are congruent because they have the same radius, height, and volume, indicating that they share the same shape and size. Their identical properties provide clear evidence of their congruence.

Congruence means that two objects have the same shape and size. In this case, the cones have the same radius, height, and volume, which are all key properties that determine their shape and size.

To demonstrate their congruence, we can examine the relationships between these properties. Since the cones have the same radius, their circular bases are identical in size. The height of the cones is also the same, meaning their slant heights and lateral surfaces are equal.

Additionally, the volume of a cone is calculated using the formula V = (1/3)πr^2h, where r is the radius and h is the height. Given that the volumes of the two cones are equal, it implies that their radii and heights are proportional.

Considering all these factors, we can confidently conclude that the two cones are congruent. Their identical radii, heights, and volumes provide substantial evidence that they share the same shape and size, satisfying the criteria for congruence.

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Nevertheless, it appears that the question is not fully formed; the appropriate request should be:

Answer:

55

Step-by-step explanation:

the value of the expression 5y² + 4x when x = 2.5 and y = 3 will be 55.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression 5y² + 4x

To calculate the value of expression at x = 2.5 and y = 3

Substitute the value of x and y in the expression:

=> 5y² + 4x

=> 5* 9 + 4 * 2.5

=> 45 + 10

=> 55

therefore, 55 is the value of the expression 5y² + 4x when x = 2.5 and y = 3.

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The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.

In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.

Given:

The following steps can be used in order to determine the measure of angle a:

Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.

Step 2 - Apply the sum of interior angle property on triangle PQR.

\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)

\(\angle\text{Q}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-60\)

\(\angle\text{R}=60^\circ\)

Step 3 - Now, apply the sum of interior angle property on triangle PSR.

\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)

\(\angle\text{S}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-90\)

\(\angle\text{R}=45^\circ\)

Step 4 - Now, the measure of angle a is calculated as:

\(\angle\text{a}=60-45\)

\(\angle\text{a}=15\)

The measure of angle a is 15 degrees.

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The total surface area of the three figures are 702 square feet.

According to this problem, we are required to determine the amount of metal needed to build three pieces with the dimensions presented in the figure.

In this case, we need to estimate the total surface area (\(A_{T}\)), in square feet, required for the production of the three pieces, that is, the product of the number of pieces (n), no unit, and the surface area of each piece (A).

Now we proceed to calculate the total surface area:

\(A_{T} = n\cdot A\)

\(A_{T} = 3\cdot \left[(5\,ft)\cdot (8\,ft) + (2\,ft)\cdot (8\,ft)+(8\,ft)\cdot (7\,ft)+(3\,ft)\cdot (8\,ft) \\\)

\(+(5\,ft)\cdot (8\,ft)+2\cdot (3\,ft)\cdot (5\,ft) + 2\cdot (4\,ft)\cdot (2\,ft) + (3\,ft)\cdot (4\,ft) ]\)

\(A_{T} = 702\,ft^{2}\)

The total surface area of the three figures are 702 square feet. \(\blacksquare\)

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Answer: 12 ft

Step-by-step explanation:

Our equation is y = 15.2 - .537x where "y" is the temperature and "x" is the depth. We want to find the depth when the temperature is 9 degrees. Therefore, we need to plug in y = 9 and find x:

9 = 15.2 - .537x

We subtract 15.2 from both sides and divide by -1 on both sides so that we are working with positive numbers only:

6.2 = .537x

We then divide both sides by .537 to isolate x:

11.55 = x

This rounds to 12, meaning that at 9 degrees, the depth is 12ft.

Answer:

D- g(x) is shifted 2 units right and 5 units up

The two processes that caused the puddle to form and then disappear were evaporation and infiltration.

Evaporation is the process in which liquid water turns into vapor and rises into the atmosphere. It occurs when the air around the puddle is warmer than the liquid, causing the water molecules to move faster and spread out. This allows the water to evaporate into a gas. The rate of evaporation is proportional to the water surface area and the difference in temperature between the air and the water.

Infiltration is the process in which water is absorbed into the ground. It occurs when the water in the puddle is drawn into the soil due to gravity and capillary action. This process is influenced by the soil type, the amount of water, and the soil's porosity. The rate of infiltration is proportional to the soil's permeability, which is a measure of how quickly water can move through the soil.

The combination of evaporation and infiltration caused the puddle to form and then disappear. As the water evaporated, the puddle shrank until it was gone. Simultaneously, the water that remained was absorbed into the ground until all of the puddle was gone.

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The validity of the given argument by utilizing the rules of implication and replacement rules.

To perform a proof of validity for the given argument, we'll use the rules of implication and replacement rules.

Here is the step-by-step proof:

1. P v (D v G) (Premise)

2. G -> O (Premise)

3. ~P & ~O (Premise)

4. /D (Assumption for conditional proof)

5. D v G (Disjunction Elimination from premise 1, using disjunction elimination rule)

6. G (Disjunctive Syllogism from step 4 and 5)

7. O (Modus Ponens using premise 2 and step 6)

8. ~P (Conjunction Elimination from premise 3)

9. P (Disjunctive Syllogism from premise 1 and step 8)

10. P & ~P (Conjunction Introduction from step 9 and step 8)

11. ~(Q v T) (Modus Tollens using premise 3 and step 10)

12. ~B (Premise)

13. (~B v A) (Disjunction Introduction from step 12)

14. (Q v T) v ~(~B & A) (Disjunction Introduction from step 13)

15. (~B & A) -> (R & S) (Premise)

16. (Q v T) v (R & S) (Hypothetical Syllogism using step 14 and step 15)

17. ~(~B & ~A) & B (Premise)

18. ~(~B & ~A) (Conjunction Elimination from step 17)

19. B (Conjunction Elimination from step 17)

20. (~B & A) (Conjunction Introduction from step 18 and step 19)

21. R & S (Modus Ponens using step 16 and step 20)

22. Valid (Conclusion)

The above proof shows the validity of the given argument by utilizing the rules of implication and replacement rules.

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Answer:

11:27 am.

Step-by-step explanation:

The time which has passed when Tom overtakes Hazel is after Hazel has walked 1 hr 15 minutes and in that time Hazel has walked

1.25 * 4.8

= 6 km.

So, Tom runs 6 km in 10:15 - 9.39 = 36 minutes

= 0.6 hrs.

So, Tom's speed is 6/0.6 = 10 km/hr.

,

and Tom will take 18/10 = 1.8 hours to finish the route,

= 1 hr 48 minutes

So he finishes the route at

9:39 + 1:48

= 11:27 am.

Answer:

The Lower Left Option

Step-by-step explanation:

The upper-left graph is neither increasing or decreasing, it's slope is infinite

The upper-right graph decreases, then increases slightly, and increases again

The last graph increases then decreases

Answer: rate of change = 2

Step-by-step explanation:

Answer:

Dividing

x=3.03

Step-by-step explanation:

Dividing gets us smaller numbers and makes it easier to work with

2,000(x - 0.03)/2,000 = 6,000/2,000

x-0.03=3

x=3+0.03

x=3.03

The sketch of graph of f(x) is downward-facing parabola. The value of K is 1/6. The probability that the actual tracking weight is greater than the prescribed weight is 2/9. The probability that the actual weight is within of the .25g prescribed weight is 1/2.  The probability that the actual weight differs from the prescribed weight by more than 0.5 g is approximately 0.3334.

To sketch the graph of f(x), we first note that the function is defined only on the interval [2, 4], and it is zero everywhere else. On this interval, the function is a downward-facing parabola centered at x = 3. We can plot the graph.

To find the value of k, we need to use the fact that the total area under the curve of f(x) must be equal to 1, since f(x) is a probability density function. Therefore, we can integrate f(x) over the interval [2, 4] and set the result equal to 1:

1 = ∫[2,4] k(1 - (x-3)^2) dx

 = k[x - (x-3)^3/3] evaluated from 2 to 4

 = k[(4 - (4-3)^3/3) - (2 - (2-3)^3/3)]

 = k(4 - 8/3 + 2 + 8/3)

 = k(6)

Thus, k = 1/6.

To find the probability that the actual tracking weight is greater than the prescribed weight of 3g, we need to integrate f(x) over the interval [3, 4]:

P(X > 3) = ∫[3,4] f(x) dx

         = ∫[3,4] 1/6(1 - (x-3)^2) dx

         = 1/6[x - (x-3)^3/3] evaluated from 3 to 4

         = 1/6[(4 - (4-3)^3/3) - (3 - (3-3)^3/3)]

         = 1/6(4 - 8/3)

         = 2/9

Therefore, the probability that the actual tracking weight is greater than the prescribed weight.

The given pdf is:

f(x) = k(1 - (x-3)^2)    2 <= x <= 4

      0                 otherwise

To find the value of k, we need to integrate the pdf over its support, which is from 2 to 4, and set the result equal to 1:

1 = ∫₂⁴ k(1 - (x-3)^2) dx

 = k ∫₂⁴ (1 - (x-3)^2) dx

 = k [x - (x-3)^3/3] ₂⁴

 = k [4 - (4-3)^3/3 - 2 + (2-3)^3/3]

 = k [8/3 - 2/3]

 = 2k

Therefore, k = 1/2.

To find the probability that the actual weight differs from the prescribed weight by more than 0.5 g, we need to calculate the probability of the event { |X - 3| > 0.5 }. This event represents the set of all values of X that are more than 0.5 g away from the prescribed weight of 3 g.

We can calculate this probability as follows:

P(|X - 3| > 0.5) = P(X < 2.5 or X > 3.5)

= P(X < 2.5) + P(X > 3.5) (by the addition rule of probability)

Now, using the given pdf of X, we can find these probabilities as:

P(X < 2.5) = 0 (since f(x) = 0 for x < 2.0)

P(X > 3.5) = ∫(3.5 to 4) f(x) dx

= ∫(3.5 to 4) k(1-(x-3)^2) dx (using the given pdf)

= k ∫(0.5 to 1) (1-t^2) dt (where t = x-3)

= k [t - (1/3)t^3] (evaluating the integral)

= k [(4-3.5) - (1/3)((1-0.5^3)]

= k [0.1667]

Therefore, the required probability is:

P(|X - 3| > 0.5) = P(X < 2.5 or X > 3.5) = P(X > 3.5) = k [0.1667]

We need to find the value of k to calculate the probability. The pdf of X must integrate to 1 over its entire domain, so we have:

1 = ∫(2 to 4) f(x) dx

= k ∫(2 to 4) (1-(x-3)^2) dx

= k ∫(-1 to 1) u (1-u^2) du (where u = x-3)

= k [u^2/2 - u^4/4] (evaluating the integral)

= k [(1/2) - (1/4)]

= k [0.5]

Thus, k = 2.

Substituting this value of k in the expression we derived earlier, we get:

P(|X - 3| > 0.5) = P(X < 2.5 or X > 3.5) = P(X > 3.5) = k [0.1667]

= 2 [0.1667]

= 0.3334

Therefore, the probability is more than 0.5 g is approximately 0.3334.

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_____The given question is incomplete, the complete question is given below:

The actual tracking weight of a stereo cartridge that is set to track at 3g

on a particular changer can be regarded as a continuous rv X

with pdf f(x) = k(1-(x-3)^2)   2less than equal to x less than equal to 4, f(x) = 0  otherwise

a. Sketch the graph of f(x)

.

b. Find the value of k.

.

c. What is the probability that the actual tracking weight is greater than the prescribed weight?

d. What is the probability that the actual weight is within

of the .25g prescribed weight?

e. What is the probability that the actual weight differs from the prescribed weight by more than .5g

?

Answer:

i have no idea

Step-by-step explanation:

i actually dont know but thnks for the points BTW