Please help urgent thank you I am so confused

The equation is y = 7.75x, where x is the number of hours Steven babysits and y is the amount he charges.

To represent the relationship between the number of hours Steven babysits (x) and the amount he charges (y), we can use a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept.

From the given information, we can identify two data points:

(4, 31.00) and (8, 62.00)

Using these points, we can calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

m = (62.00 - 31.00) / (8 - 4)

m = 31.00 / 4

m = 7.75

Now, we can substitute one of the points and the slope into the equation to find the y-intercept (b).

Using the point (4, 31.00):

31.00 = 7.75(4) + b

31.00 = 31.00 + b

b = 0

Therefore, the equation that represents the relationship between the number of hours Steven babysits (x) and the amount he charges (y) is:

y = 7.75x

The equation is y = 7.75x, where x is the number of hours Steven babysits and y is the amount he charges.

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The equations of the asymptotes of the hyperbola are y = (5/9)x - 79/9 and y = -(5/9)x + 79/9.

To find the equations of the asymptotes of the hyperbola defined by the equation:

[tex]-25x^2 + 81y^2 + 100x + 1134y + 1844 = 0[/tex]

We can rewrite the equation in the standard form by isolating the x and y terms:

[tex]-25x^2 + 100x + 81y^2 + 1134y + 1844 = 0[/tex]

Rearranging the terms:

[tex]-25x^2 + 100x + 81y^2 + 1134y = -1844[/tex]

Next, let's complete the square for both the x and y terms:

[tex]-25(x^2 - 4x) + 81(y^2 + 14y) = -1844\\-25(x^2 - 4x + 4 - 4) + 81(y^2 + 14y + 49 - 49) = -1844\\-25((x - 2)^2 - 4) + 81((y + 7)^2 - 49) = -1844[/tex]

Expanding and simplify

[tex]-25(x - 2)^2 + 100 - 81(y + 7)^2 + 3969 = -1844\\-25(x - 2)^2 - 81(y + 7)^2 = -1844 - 100 - 3969\\-25(x - 2)^2 - 81(y + 7)^2 = -4913[/tex]

Dividing both sides by -4913:

[tex](x - 2)^2/(-4913/25) - (y + 7)^2/(-4913/81) = 1[/tex]

Comparing this equation to the standard form of a hyperbola:

[tex](x - h)^2/a^2 - (y - k)^2/b^2 = 1[/tex]

We can determine that the center of the hyperbola is (h, k) = (2, -7). The value of [tex]a^2[/tex] is (-4913/25), and the value of [tex]b^2[/tex] is (-4913/81).

The equations of the asymptotes can be found using the formula:

y - k = ±(b/a)(x - h)

Substituting the values we found:

y + 7 = ±(√(-4913/81) / √(-4913/25))(x - 2)

Simplifying:

y + 7 = ±(√(4913) / √(81)) × √(25/4913) × (x - 2)

y + 7 = ±(√(4913) / 9) × √(25/4913) × (x - 2)

Rationalizing the denominators and simplifying:

y + 7 = ±(5/9) ×(x - 2)

Finally, rearranging the equation to isolate y:

y = ±(5/9)x - 10/9 - 7

Simplifying further:

y = ±(5/9)x - 79/9

In light of this, the equations for the hyperbola's asymptotes are y = (5/9)x - 79/9 and y = -(5/9)x + 79/9.

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Answer:

[tex]\boxed{y=\dfrac{5}{9}x-\dfrac{73}{9}}\;\; \textsf{and} \;\;\boxed{ y=-\dfrac{5}{9}x-\dfrac{53}{9}}[/tex]

Step-by-step explanation:

First, rewrite the given equation in the standard form of a hyperbola by completing the square.

Given equation:

[tex]-25x^2+81y^2+100x+1134y+1844=0[/tex]

Arrange the equation so all the terms with variables are on the left side and the constant is on the right side:

[tex]-25x^2+100x+81y^2+1134y=-1844[/tex]

Factor out the coefficient of the x² term and the coefficient of the y² term:

[tex]-25(x^2-4x)+81(y^2+14y)=-1844[/tex]

Add the square of half the coefficient of x and y inside the parentheses of the left side, and add the distributed values to the right side:

[tex]-25(x^2-4x+4)+81(y^2+14y+49)=-1844-25(4)+81(49)[/tex]

Factor the two perfect trinomials on the left side and simplify the right side:

[tex]-25(x-2)^2+81(y+7)^2=2025[/tex]

Divide both sides by the number of the right side so the right side equals 1:

[tex]\dfrac{-25(x-2)^2}{2025}+\dfrac{81(y+7)^2}{2025}=\dfrac{2025}{2025}[/tex]

      [tex]\dfrac{-(x-2)^2}{81}+\dfrac{(y+7)^2}{25}=1[/tex]

        [tex]\dfrac{(y+7)^2}{25}-\dfrac{(x-2)^2}{81}=1[/tex]

As the y²-term is positive, the hyperbola is vertical (opening up and down).

The standard equation of a vertical hyperbola is:

[tex]\boxed{\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1}[/tex]

Therefore, comparing this with the rewritten equation:

The formula for the equations of the asymptotes of a vertical hyperbola is:

[tex]\boxed{y=\pm \dfrac{a}{b}(x-h)+k}[/tex]

Substitute the values of h, k, a and b into the formula:

[tex]y=\pm \dfrac{5}{9}(x-2)-7[/tex]

Therefore, the equations for the asymptotes are:

[tex]\boxed{y=\dfrac{5}{9}x-\dfrac{73}{9}}\;\; \textsf{and} \;\;\boxed{ y=-\dfrac{5}{9}x-\dfrac{53}{9}}[/tex]

The cost per trainee for the 5-week training course is $7,000.

To find the cost per trainee, we divide the total cost of the training course by the number of trainees.

Total cost of the training course = $140,000

Number of trainees = 20

Cost per trainee = Total cost of the training course / Number of trainees

Cost per trainee = $140,000 / 20

Cost per trainee = $7,000

Therefore, the cost per trainee for the 5-week training course is $7,000.

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Answer:

(r q)(-3) = -3

(q r)(-3) = -3

Step-by-step explanation:

let x = 1

q(1) = -1 +2 = 1

r(1) = 1² = 1

(r q)(-3) = ?

(1×1)(-3) = -3

(q r)(-3) = ?

(1×1)(-3) = -3

The correct option that would be sufficient to prove the right triangles ∆WXZ and ∆WYX is (A) WZ/WX = XW/YW

The perpendicular height of the right triangle divides the triangle in two triangles with the same proportions as the original triangle.

Considering the smaller right triangle ∆WXZ and the bigger triangle ∆WYX;

the side WZ of ∆WXZ will correspond to the side WX of ∆WYX and similarly, side XW of ∆WXZ will correspond to the side of ∆WYX

so we can we the proportion as;

WZ/WX = XW/YW

Therefore, the proportion WZ/WX = XW/YW would be sufficient to prove the right triangles ∆WXZ and ∆WYX

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Answer:

f(x) = 4x² - 2x + 11

f'(x) = 8x - 2

m = f'(3) = 8(3) - 2 = 24 - 2 = 22

41 = 22(3) + b

41 = 66 + b

b = -25

y = 22x - 25

Answer:

Step-by-step explanation:

a) Let's denote the number of coffees sold as 'x' and the number of cappuccinos sold as 'y'.

The equation that represents the given information is:

2.50x + 3.75y = 222.50

b) To solve the equation, we need to find the values of 'x' and 'y' that satisfy the equation.

Since we have two variables and only one equation, we cannot determine the exact values of 'x' and 'y' independently. However, we can find possible combinations that satisfy the equation.

Let's proceed by assuming values for one of the variables and solving for the other. For example, let's assume 'x' is 40 (number of coffees):

2.50(40) + 3.75y = 222.50

100 + 3.75y = 222.50

3.75y = 222.50 - 100

3.75y = 122.50

y = 122.50 / 3.75

y ≈ 32.67

In this case, assuming 40 coffees were sold, we get approximately 32.67 cappuccinos.

We can also assume different values for 'x' and solve for 'y' to find other possible combinations. However, keep in mind that the number of drinks sold should be a whole number since it cannot be fractional.

Therefore, one possible combination could be around 40 coffees and 33 cappuccinos sold.

The two options that would prove that ΔABC ~ ΔXYZ include the following:

A. BA/YX = BC/YZ = AC/XZ

C. AC/XZ = BA/YX, ∠A≅∠X

In Mathematics and Geometry, two triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Based on the side, side, side (SSS) similarity theorem, we can logically deduce the following congruent angles and similar triangles:

BA/YX = BC/YZ = AC/XZ (ΔABC ≅ ΔXYZ)

Based on the side, angle, side (SAS) similarity theorem, we can logically deduce the following congruent angles and similar sides:

AC/XZ = BA/YX, ∠A≅∠X

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Answer:

A''(-1, 1), B''(-4, 2), C''(-2, 4)

Step-by-step explanation:

When rotated 180°, the symbol of the coordinames change

i.e., if x = 2 it becomes x = -2 and if y = -4, it becomes y = 4

so the coordinates A(1, -1), B(4, -2), C(2, -4)

change to A''(-1, 1), B''(-4, 2), C''(-2, 4)

The number of wheelbarrow loads of soil required for this project is 71.

The landscaper uses a wheelbarrow to transport soil to a particular region of the garden. A wheelbarrow can accommodate roughly 6 cubic feet of soil. Once the pile has a diameter of 13 feet and a height of 3 feet, the landscaper determines that there will be enough soil for the project.

Area of a cone =1/3πr²hwhere r = 13/2 feet and h = 3 feet.

Substituting the given values to find the area of the cone.1/3 x 3.14 x (6.5)² x 3 = 422.55 cubic feet.Then, divide the total amount of soil required by the volume of soil that a wheelbarrow can hold to determine the number of wheelbarrow loads required.

Number of wheelbarrow loads = (Volume of soil needed) / (Volume of one wheelbarrow)Volume of one wheelbarrow = 6 cubic feet.The total volume of soil required is 422.55 cubic feet.

Therefore, the number of wheelbarrow loads required is:Number of wheelbarrow loads = (422.55) / (6) = 70.42 ≈ 71 wheelbarrow loads, which is the final answer.

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Answer:

2921

Step-by-step explanation:

[tex]2540 + 2540 * \frac{15}{100} \\\\= 2540 + 381\\\\= 2921[/tex]

Answer:

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

the numbers on the right of the arrow are half the value of the corresponding numbers on the left, then

32 → [tex]\frac{1}{2}[/tex] (32)

32 → 16

The correct time(s) when you are at the same height as the top of the tower are approximately -1.57 hours, 1.57 hours, 4.71 hours, 7.85 hours, 11.00 hours, and so on.

To find the time or times during the ride on the London Eye when you are at the same height as the top of the Elizabeth Tower, we can solve the given equation for t.

320 = -197cos(π/15(t)) + 246

First, let's isolate the cosine term:

-197cos(π/15(t)) = 320 - 246

-197cos(π/15(t)) = 74

Next, divide both sides by -197:

cos(π/15(t)) = 74 / -197

Now, we can take the inverse cosine (arccos) of both sides to solve for t:

π/15(t) = arccos(74 / -197)

To isolate t, multiply both sides by 15/π:

t = (15/π) * arccos(74 / -197)

Using a calculator to evaluate the arccosine term and performing the calculation, we find the value(s) of t:

t ≈ -1.57, 1.57, 4.71, 7.85, 11.00, ...

These values represent the time(s) during the ride on the London Eye when you are at the same height as the top of the Elizabeth Tower. Note that time is typically measured in hours, so these values can be converted accordingly.

In light of this, the appropriate time(s) when you are at the same altitude as the tower's peak are roughly -1.57 hours, 1.57 hours, 4.71 hours, 7.85 hours, 11.00 hours, and so forth.

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The expression that is always equivalent to sin x when 0° < x < 90° is (1) cos (90° - x). Option 1

To understand why, let's analyze the trigonometric functions involved. In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Since we are considering angles between 0° and 90°, we can guarantee that the side opposite the angle will always be the shortest side of the triangle, and the hypotenuse will be the longest side.

Now let's examine the expression cos (90° - x). The cosine of an angle is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. In a right triangle, when we subtract an angle x from 90°, we are left with the complementary angle to x. This means that the remaining angle in the triangle is 90° - x.

Since the side adjacent to the angle 90° - x is the same as the side opposite the angle x, and the hypotenuse is the same, the ratio of the adjacent side to the hypotenuse remains the same. Therefore, cos (90° - x) is equivalent to sin x for angles between 0° and 90°.

On the other hand, options (2) cos (45° - x) and (3) cos (2x) do not always yield the same value as sin x for all angles between 0° and 90°. The expression cos x (option 4) is equivalent to sin (90° - x), not sin x.

Option 1 is correct.

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The interval for the graphed function that has a local minimum of 0 is [-2, 0].

To determine the interval for the graphed function that has a local minimum of 0, we need to examine the behavior of the graph around the x-values where it crosses the x-axis.

We know that the graph crosses the x-axis at -2.5, 0, and 3. Since the local minimum occurs at 0, we need to find the interval where the graph is decreasing to the left of 0 and increasing to the right of 0.

From the given information, we can determine the following:

The graph is decreasing between -2.5 and 0 because it crosses the x-axis at -2.5 and 0, and the minimum value is at (-1.56, -6).

The graph is increasing between 0 and 3 because it crosses the x-axis at 3, and the maximum value is at (1.2, 2.9).

The correct option is [–2, 0].

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Question

On a coordinate plane, a curved line with minimum values of (negative 1.56, negative 6) and (3, 0), and a maximum value of (1.2, 2.9), crosses the x-axis at (negative 2.5, 0), (0, 0), and (3, 0), and crosses the y-axis at (0, 0). Which interval for the graphed function has a local minimum of 0? [–3, –2] [–2, 0] [1, 2] [2, 4]

Answer: 140

Step-by-step explanation: 120-(-20) to 120 + 20 goes to 140.

Answer:

The system of linear inequalities represented by the graph is:

y > x - 2 and y < x + 1

This system of inequalities indicates that y is greater than x - 2, which represents the upper boundary of the shaded region in the graph. Additionally, y is less than x + 1, which represents the lower boundary of the shaded region. The intersection of these two conditions is the region between the lines, satisfying both inequalities.

The calculated value of m in the triangular prism is 13

From the question, we have the following parameters that can be used in our computation:

The triangular prism

Where, we have

Volume = 1170

The volume of the triangular prism is calculated as

Volume = Base area * Height

So, we have

1/2 * m * 18 * 10 = 1170

Evaluate the products

This gives

90m = 1170

So, we have

m = 13

Hence, the value of m is 13

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Answer:

40, 50, 30 Yes

13, 5, 12 Yes

10, 10, 15 Yes

41, 9, 40 Yes

Step-by-step explanation:

16, 10, 6

10 + 6 = 16

No

40, 50, 30

30 + 40 > 50

Yes

13, 5, 12

5 + 12 > 13

Yes

70, 20, 25

20 + 25 < 70

No

10, 10, 15

10 + 10 >15

Yes

41, 9, 40

9 + 40 > 41

Yes

Answer:

[tex]y=\boxed{2}\:\cos \left(\boxed{1}\;x\right)+\boxed{3}[/tex]

Step-by-step explanation:

The graph of the solid black line is the cosine parent function, y = cos(x).

The standard form of a cosine function is:

[tex]\boxed{y = A \cos(B(x + C)) + D}[/tex]

where:

From inspection of the graph, the x-values of the turning points (peaks and troughs) of the parent function and the new function are the same. Therefore, the period of both functions is the same, and there has been no horizontal shift. So, B = 1 and C = 0.

The mid-line of the new function is y = 3. Therefore, D = 3.

The y-value of the peaks is y = 5. The amplitude is the distance from the mid-line to the peak. Therefore, A = 2.

Substituting these values into the standard formula we get:

[tex]y = 2 \cos(1(x + 0)) + 3[/tex]

[tex]y=2 \cos (1(x))+3[/tex]

[tex]y= 2 \cos(x) + 3[/tex]

Therefore, the equation of the trigonometric graph is:

[tex]y=\boxed{2}\:\cos \left(\boxed{1}\;x\right)+\boxed{3}[/tex]

Answer:

I can't understand the language but try people who can

Answer:

Step-by-step explanation:

To find the values of the given expressions using the function g(x) = 2x^2 - 2x + 9, we substitute the given values into the function and simplify the expression. Let's calculate each of the following:

a) g(0)

To find g(0), substitute x = 0 into the function:

g(0) = 2(0)^2 - 2(0) + 9

g(0) = 0 - 0 + 9

g(0) = 9

b) g(-1)

To find g(-1), substitute x = -1 into the function:

g(-1) = 2(-1)^2 - 2(-1) + 9

g(-1) = 2(1) + 2 + 9

g(-1) = 2 + 2 + 9

g(-1) = 13

c) g(2)

To find g(2), substitute x = 2 into the function:

g(2) = 2(2)^2 - 2(2) + 9

g(2) = 2(4) - 4 + 9

g(2) = 8 - 4 + 9

g(2) = 13

d) g(-x)

To find g(-x), substitute x = -x into the function:

g(-x) = 2(-x)^2 - 2(-x) + 9

g(-x) = 2x^2 + 2x + 9

e) g(1 - t)

To find g(1 - t), substitute x = 1 - t into the function:

g(1 - t) = 2(1 - t)^2 - 2(1 - t) + 9

g(1 - t) = 2(1 - 2t + t^2) - 2 + 2t + 9

g(1 - t) = 2 - 4t + 2t^2 - 2 + 2t + 9

g(1 - t) = 2t^2 - 2t + 9

Therefore:

a) g(0) = 9

b) g(-1) = 13

c) g(2) = 13

d) g(-x) = 2x^2 + 2x + 9

e) g(1 - t) = 2t^2 - 2t + 9

The probability that a flight has 100 or more passengers and arrives on time is approximately 0.12 or 12%.

Let A be the event that a flight has 100 or more passengers, and B be the event that the flight arrives on time. We want to find the probability of the intersection of these two events, P(A ∩ B).

We are given:

- P(B) = 0.80, the probability that any given flight arrives on time

- P(A) = 0.30, the probability that any given flight has 100 or more passengers

- P(B | A) = 0.40, the conditional probability that a flight arrives on time given that it has 100 or more passengers (since 60% of such flights are late)

We can use the formula for conditional probability to find P(A ∩ B):

P(A ∩ B) = P(B | A) * P(A)

         = 0.40 * 0.30

         = 0.12

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Step-by-step explanation:

When we simplify the expression, we get:

0.0048 * 0.81 / 0.027 * 0.04 = (0.0048 / 0.027) * (0.81 / 0.04)

Using a calculator to evaluate the two fractions separately, we get:

0.0048 / 0.027 ≈ 0.1778

0.81 / 0.04 = 20.25

Substituting these values back into the original expression, we get:

(0.0048 / 0.027) * (0.81 / 0.04) ≈ 0.1778 * 20.25

Multiplying these two values together, we get:

0.1778 * 20.25 ≈ 3.59715

To express the answer in standard form, we need to write it as a number between 1 and 10 multiplied by a power of 10. We can do this by moving the decimal point three places to the left, since there are three digits to the right of the decimal point:

3.59715 ≈ 3.59715 × 10^(-3)

Therefore, the final answer in standard form is approximately 3.59715 × 10^(-3).

In a trial of 10 versus 500, the experimental probability is expected to be closer to the theoretical probability when there are more trials (500 in this case).

The experimental probability and theoretical probability can be compared in a trial of 10 versus 500 by understanding the concepts behind each type of probability.

Theoretical probability is based on mathematical calculations and is determined by analyzing the possible outcomes of an event. It relies on the assumption that the event is equally likely to occur, and it can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Theoretical probability is often considered the expected or ideal probability.

On the other hand, experimental probability is determined through actual observations or experiments. It involves conducting the event multiple times and recording the outcomes to determine the relative frequency of a specific outcome. The experimental probability is an estimation based on the observed data.

In the given trial of 10 versus 500, we can expect the experimental probability to be closer to the theoretical probability when the number of trials (or repetitions) is larger. In this case, with 500 trials, the experimental probability is likely to be a more accurate representation of the true probability.

When the number of trials is small, such as only 10, the experimental probability may deviate significantly from the theoretical probability. With a smaller sample size, the observed outcomes may not accurately reflect the expected probabilities calculated theoretically.

In summary, in a trial of 10 versus 500, the experimental probability is expected to be closer to the theoretical probability when there are more trials (500 in this case). As the number of trials increases, the observed frequencies are likely to converge towards the expected probabilities calculated theoretically.

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Answer:

Step-by-step explanation:

To find the time it takes for the turtle to reach the pond, we can use the formula:

Time = Distance / Speed

Given that the turtle travels at a speed of 1/12 mile per hour and the distance to the pond is 5/6 mile, we can substitute these values into the formula:

Time = (5/6) / (1/12)

To simplify this, we can multiply the numerator by the reciprocal of the denominator:

Time = (5/6) * (12/1) = (5 * 12) / 6 = 60 / 6 = 10

Therefore, it will take the turtle 10 hours to reach the pond.

Answer:

(- 4, - 4 )

Step-by-step explanation:

x - 5y = 16 → (1)

4x - 2y = - 8 → (2)

multiplying (1) by - 4 and adding to (2) will eliminate x

- 4x + 20y = - 64 → (3)

add (2) and (3) term by term to eliminate x

(4x - 4x) + (- 2y + 20y) = - 8 - 64

0 + 18y = - 72

18y = - 72 ( divide both sides by 18 )

y = - 4

substitute y = - 4 into either of the 2 equations and solve for x

substituting into (1)

x - 5(- 4) = 16

x + 20 = 16 ( subtract 20 from both sides )

x = - 4

solution is (- 4, - 4 )