please help!!!!!!!!!!!!!!!!!!!!!!

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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The cost of a single unit is given as follows:

$1.05.

El costo de un plátano es el seguiente:

$1.05.

The cost of a single unit is obtained applying the proportions in the context of the problem.

The cost of 22 units is of $23.10, hence the cost of a single unit is obtained dividing the total cost by the number of units, as follows:

23.1/22 = $1.05.

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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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It is best to draw a table of outcomes and list all the possible outcomes when you roll a pair of numbered cubes. As follows:

                          1             2           3            4          5          6

                   1    ( 1 , 1 )   ( 1 , 2 )   ( 1 , 3 )   ( 1 , 4 )   ( 1 , 5 )   ( 1 , 6 )

                   2   ( 2 , 1 )  ( 2, 2 )   ( 2 , 3 )  ( 2 , 4 )  ( 2 , 5 )  ( 2 , 6 )

                   3   ( 3 , 1 )  ( 3 , 2 )  ( 3 , 3 )   ( 3 , 4 )  ( 3 , 5 )  ( 3 , 6 )

                   4   ( 4 , 1 )  ( 4 , 2 )  ( 4 , 3 )   ( 4 , 4 )  ( 4 , 5 )  ( 4 , 6 )

                   5   ( 5 , 1 )  ( 5 , 2 )  ( 5 , 3 )  ( 5 , 4 )  ( 5 , 5 )  ( 5 , 6 )

                   6   ( 6 , 1 )  ( 6 , 2 )  ( 6 , 3 )  ( 6 , 4 )  ( 6 , 5 )  ( 6 , 6 )

- Each cube has 6 faces, Hence, 6 numbers for each are expressed as row and column for first and second cube respectively.

- Now locate and highlight all the even pairs shown in bold.

- The total number of even pairs outcomes are = 9.

- The total possibilities are = 36.

- The probability of getting even pairs as favorable outcome can be expressed as:

                 P ( Even pairs ) = Favorable outcomes / Total outcomes

                 P ( Even pairs ) = 9 / 36

                 P ( Even pairs ) = 1 / 4.

- So the probability of getting an even pair when a pair of number cubes are rolled is 1/4

Answer:

a)

[tex] \frac{1}{( - 7)^{4} } [/tex]

Answer:

[tex](-7)^-^4=\frac{1}{(-7)^4}[/tex]

Step-by-step explanation:

The user aswati already wrote the correct answer, but I wanted to help explain why their answer is correct so that you'll understand.

According to the negative exponent rule, when a base (let's call it m) is raised to a negative exponent (let's call it n), we rewrite it as a fraction where the numerator is 1 and the denominator is the base raised to the same exponent turned positive.

Thus, the negative exponent rule is given as:

[tex]b^-^n=\frac{1}{b^n}[/tex]

Thus, [tex](-7)^-^4[/tex] becomes [tex]\frac{1}{(-7)^4}[/tex]

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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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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The tangent line at that point is:

y = (-3/25)*x + 6/5

so m = -3/25, and b = 6/5

To find the slope at that point, we need to evaluate the derivative at that point.

y = 3/x

The derivative is:

y' = -3/x²

When x = 5, we have:

y' = -3/5² = -3/25

So that is the slope, m.

Now let's find the line.

The line must pass trhough the point (5, 3/5), then:

3/5 = (-3/25)*5 + b

3/5 = -3/5 + b

3/5 + 3/5 = b

6/5 = b

The equation of the line is:

y = (-3/25)*x + 6/5

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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

Answer:

2, 4, 10, 20, 50, and 100.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the maximum width of an aircraft seat that will accommodate 98% of all adult women, we need to determine the corresponding z-score for the 98th percentile of the normal distribution.

First, we find the z-score corresponding to the 98th percentile using a standard normal distribution table or calculator. The z-score for the 98th percentile is approximately 2.05.

Next, we use the z-score formula to find the corresponding value in the original distribution:

z = (x - μ) / σ

Solving for x (the maximum width of the aircraft seat):

x = z * σ + μ

Substituting the values given:

x = 2.05 * 4.36 + 37.6

x ≈ 45.98

Therefore, the maximum width of an aircraft seat that will accommodate 98% of all adult women is approximately 46 cm (rounded to one decimal place).

In a sample of 5000 students, the mean GPA is 2.80 and their standard deviation is 0.35 and 1428 students score below 2.60.

To find the number of students scoring below 2.60, we need to calculate the area under the normal distribution curve to the left of this value.

First, we need to standardize the value of 2.60 using the z-score formula: z = (x - μ) / σ, where x is the value (2.60), μ is the mean (2.80), and σ is the standard deviation (0.35). Plugging in the values, we get z = (2.60 - 2.80) / 0.35 = -0.57.

Now, we can use a standard normal distribution table or a statistical calculator to find the area to the left of -0.57. Consulting a standard normal distribution table, we find that the area to the left of -0.57 is approximately 0.2857.

To calculate the number of students scoring below 2.60, we multiply this area by the total number of students in the sample: 0.2857 * 5000 ≈ 1428.5.

Since the number of students must be a whole number, we round down to 1428 students.

Therefore, approximately 1428 students score below 2.60 in the sample of 5000 students, assuming a normal distribution with a mean of 2.80 and a standard deviation of 0.35.

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Answer:

2921

Step-by-step explanation:

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

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 opposite of -5 can be represented by situations such as a temperature increase of 5 degrees and a financial gain of $5. Additionally, it can also represent a distance traveled of 5 miles and a weight gain of 5 pounds.

The opposite of -5 is 5. The opposite of a number represents the number with the opposite sign. Here are three situations that can be represented by the opposite of -5:

Situation 1: Temperature Change

If the temperature is currently -5 degrees Celsius and it undergoes a change in the opposite direction, it means it increases by 5 degrees. Therefore, the opposite of -5 represents a temperature increase of 5 degrees.

Situation 2: Financial Gain

Suppose you owe someone $5, and you receive the opposite of that amount. The opposite of owing $5 would be gaining $5. So, the opposite of -5 represents a financial gain of $5.

Additional situations that can be represented by the opposite of -5:

Situation 3: Distance Traveled

If a car has traveled -5 miles, indicating it has moved in the opposite direction, the opposite of that distance would be 5 miles. So, the opposite of -5 represents a distance traveled of 5 miles.

Situation 4: Weight Gain

Imagine someone loses 5 pounds (which can be represented as -5). The opposite of losing 5 pounds would be gaining 5 pounds. Thus, the opposite of -5 represents a weight gain of 5 pounds.

In each of these situations, the opposite of -5 denotes a change in the opposite direction or the reverse of the initial value.

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Step-by-step explanation:

If we wanted to extend the discussion beyond what has been shared so far, an additional question we could ask is:

"What is the ratio of adult tickets to children's tickets sold in a day?"

This question would provide insight into the distribution of ticket sales between adults and children and help us understand the demand for different movie genres or screenings among the audience.

Answer:

30

Step-by-step explanation:

22/33=20/x

cross multiply

22x=33x20

22x=660

x=660/22

x=30

Based on the quadratic function, an 18 year old would spend 3 hours watching television.

Using the quadratic function given :

The age is represented as the variable , 'z'

substitute z = 18 into the equation

y = (0.004*18²) - 0.314(18) + 7.5

y = 3.144

y = 3 hours approximately

Hence, an 18 year old spend approximately 18 hours watching television.

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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:

(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

Answer:

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

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 )

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.

Common ratio of the geometric sequence 9/8, 3/4, 1/2,...,8/81 is 2/3 and the number of all terms in this sequence is 7.

As we know that,

Common ratio of any G.P. is a constant number that is multiplied by the previous term to obtain the next term.

So, r= (n+1)th term / nth term

where r ⇒ common ratio

          (n+1)th term⇒ succeeding term

          nth term⇒ preceding term

According to the given question, r = (9/8) / (3/4)

                                                       r = (2/3)

We also know,

Any term of a G.P. [nth term] can be obtained by the formula:

Tₙ= a[tex]r^{n-1}[/tex]

where, Tₙ= nth term

            a= first term of G.P.

            r=common ratio

Since last term of the G.P. is given to be 8/81; putting this in the above formula will yield us the total number of terms.

   Tₙ= a[tex]r^{n-1}[/tex]

⇒ (8/81) = (9/8) x ([tex]2/3^{n-1}[/tex])

⇒ (64/729)= ([tex]2/3^{n-1}[/tex])

⇒[tex](2/3)^{6}[/tex] = ([tex]2/3^{n-1}[/tex])

⇒ n-1 = 6

⇒ n = 7

∴ The total number of terms in G.P. is 7.

Therefore, Common ratio of the sequence 9/8, 3/4, 1/2,...,8/81 is 2/3 and the number of all terms in this sequence is 7.

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The Common Ratio for this geometric sequence is 2/3 and the total number of terms in the sequence is 6.

The given mathematical sequence appears to be a geometric sequence, which is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the Common Ratio. In a geometric sequence, you can find the Common Ratio by dividing any term by the preceding term.  

So in this case, the second term (3/4) divided by the first term (9/8) equals 2/3. Therefore, the Common Ratio for this geometric sequence is 2/3.

To find the total number of terms in this sequence we use the formula for the nth term of a geometric sequence: a*n = a*r^(n-1), where a is the first term, r is the common ratio, and n is the number of terms. This gives us: 8/81 = (9/8)*(2/3)^(n-1). Solving this for n gives us n = 6. Therefore, the total number of terms in this sequence is 6.

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Answer:

Step-by-step explanation:

Step 1.   Determine the dollar amount of the markup

          175 - 79 = 96

Step 2:   Divide the markup Amount by the Cost

          96/79 = 1.215

Step 3:   Multiply by 100 and add the % sign

           1.215 x 100 = 121.5%

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 : Focus is (0,3)

To find the focus of the parabola defined by the equation (y - 3)² = -8(x - 2), we can compare it with the standard form of a parabolic equation: (y - k)² = 4a(x - h).

In the given equation, we have:

(y - 3)² = -8(x - 2)

Comparing it with the standard form, we can determine the values of h, k, and a:

h = 2

k = 3

4a = -8

Solving for a, we get:

4a = -8

a = -8/4

a = -2

Therefore, the vertex of the parabola is (h, k) = (2, 3), and the value of 'a' is -2.

The focus of the parabola can be found using the formula:

F = (h + a, k)

Substituting the values, we get:

F = (2 + (-2), 3)

F = (0, 3)

Therefore, the focus of the parabola defined by the equation (y - 3)² = -8(x - 2) is at the point (0, 3).

Answer:

Focus = (0, 3)

Step-by-step explanation:

The focus is a fixed point located inside the curve of the parabola.

To find the focus of the given parabola, we first need to find the vertex (h, k) and the focal length "p".

The standard equation for a sideways parabola is:

[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]

where:

If p > 0, the parabola opens to the right, and if p < 0, the parabola opens to the left.

Given equation:

[tex](y-3)^2=-8(x-2)[/tex]

Compare the given equation to the standard equation to determine the values of h, k and p:

The formula for the focus is (h+p, k).

Substituting the values of h, p and k into the formula, we get:

[tex]\begin{aligned}\textsf{Focus}&=(h+p,k)\\&=(2-2,3)\\&=(0,3)\end{aligned}[/tex]

Therefore, the focus of the parabola is (0, 3).