The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 12 seconds.

What is the probability that the arrival time between vehicles is 12 seconds or less?

On solving the inequalities a ≥ 10, y ≥ 55, 7a + 10y ≥ 690, the solution is obtained as (20,55).

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

Use the variables a and y to represent the number of student and adult tickets sold, respectively.

Then write the following system of inequalities -

a ≥ 10 (they must sell a minimum of 10 student tickets)

y ≥ 55 (they must sell at least 55 adult tickets)

7a + 10y ≥ 690 (they must make no less than $690 from ticket sales)

The first two inequalities are constraints on the number of tickets sold, and the third inequality represents the revenue constraint.

To find a possible solution, graph these inequalities on a coordinate plane and look for the feasible region that satisfies all three inequalities.

Alternatively, solve the system of inequalities using algebra.

First, simplify the third inequality by subtracting 7a from both sides -

10y ≥ 690 - 7a

Then, divide both sides by 10 -

y ≥ (690 - 7a)/10

This inequality represents the revenue constraint in terms of the number of student tickets sold.

Now combine the revenue constraint with the other two constraints -

a ≥ 10

y ≥ 55

y ≥ (690 - 7a)/10

Use substitution to solve for a in terms of y -

y ≥ (690 - 7a)/10

10y ≥ 690 - 7a

7a ≥ 690 - 10y

a ≥ (690 - 10y)/7

To find a possible solution, substitute a = (690 - 10y)/7 into the other two constraints -

(690 - 10y)/7 ≥ 10

y ≥ 55

These inequalities can be simplified -

690 - 10y ≥ 70

y ≥ 55

The first inequality can be solved for y -

-10y ≥ -620

y ≤ 62

Since it is known y ≥ 55, the feasible values for y are between 55 and 62, inclusive -

55 ≤ y ≤ 62

Now use the expression for a in terms of y to find the corresponding values of a -

a = (690 - 10y)/7

For each value of y between 55 and 62, inclusive, we can calculate a and check whether it satisfies the constraints -

a ≥ 10

y ≥ 55

7a + 10y ≥ 690

For example, when y = 55 -

a = (690 - 10(55))/7 = 20

7a + 10y = 7(20) + 10(55) = 690

Therefore, these values satisfy all three constraints, so one possible solution is a = 20 and y = 55.

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Answer:

Below

Step-by-step explanation:

1/81    *    27^5   =

1/(3^4)   *   (3^3)^5 =

3^-4    *    3^(3 *5)

3^-4    *   3^15

3^(-4 + 15)

3^11

The expression  1/81 * 27⁵ can be written as a power of 3 as 3¹¹.

Exponents are the method of writing numbers, especially large numbers, in terms of a base and an exponent, which is written as the power of base.

Given expression is,

1/81 × 27⁵

We have to write the expression as a power of 3.

Write each term as a power of 3.

81 can be written as 3⁴.

27 can be written as 3³.

1/81 × 27⁵ = (1 / 3⁴) × (3³)⁵

We can use two rules here, 1/aᵇ = a⁻ᵇ and (xᵃ)ᵇ = xᵃᵇ.

1/81 × 27⁵ = 3⁻⁴ × 3¹⁵

Multiplication rule of exponent states that xᵃ × xᵇ = xᵃ⁺ᵇ.

1/81 × 27⁵ = 3⁻⁴⁺¹⁵

                = 3¹¹

Hence the expression can be written as 3¹¹.

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The correct linear inequality would be y > 2x + 1.

Option (A) is correct.

What is linear inequality?

A linear inequality is an inequality that can be written in the form of a linear equation with an inequality symbol, such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

We can see that the line passes through the points (-1, -1) and (0, 1), and has a positive slope. The equation of the line can be found using the point-slope form:

y - y1 = m(x - x1), where m is the slope and (x1, y1) is one of the points on the line.

Using the point (-1, -1) and the slope 2, we get:

y - (-1) = 2(x - (-1))

y + 1 = 2x + 2

y = 2x + 1

Since the line is dashed, the inequality is not inclusive of the points on the line. Therefore, we use the inequality symbol > rather than ≥.

so the linear inequality would be  y > 2x + 1.

Therefore, the correct linear inequality would be y > 2x + 1.

Option (A) is correct.

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Answer:

volume of a sphere = [tex]\frac{4}{3} \pi r^{3}[/tex]

Radius = 18.8/2 = 9.4 cm

volume of the required sphere = [tex]\frac{4}{3} \pi (9.4)^{3}[/tex]

                                                   = [tex]\frac{4}{3}(3.14)(9.4)^{3}[/tex]

                                                   =3477.4 cm^3 (cor to nearest tenth)

Therefore, the following exponential probability density function P(4 ≤ x ≤ 6) is 0.1406 (rounded to four decimal places).

Probability is a measure of the likelihood or chance of an event occurring. It is a mathematical concept that quantifies the degree of uncertainty of an outcome in a given situation or experiment. Probability is usually expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Here,

(a) The formula for P(x ≤ x0) is the cumulative distribution function (CDF), which gives the probability that the random variable x is less than or equal to a certain value x0. For the exponential probability density function given, the CDF is:

F(x) = P(x ≤ x0) = ∫[0,x0] f(x) dx = ∫[0,x0] (1/5)e*(-x/5) dx

(b) To find P(x ≤ 4), we substitute x0 = 4 into the CDF formula and evaluate the integral:

P(x ≤ 4) = F(4) = ∫[0,4] (1/5)e*(-x/5) dx

= [-e*(-x/5)] from x = 0 to 4

= -e*(-4/5) + 1

≈ 0.3297 (rounded to four decimal places)

(c) To find P(x ≥ 5), we note that P(x ≥ 5) = 1 - P(x < 5), where P(x < 5) is the probability that x is less than 5. Using the CDF formula, we have:

P(x < 5) = F(5) = ∫[0,5] (1/5)e*(-x/5) dx

= [-e*(-x/5)] from x = 0 to 5

= -e*(-1) + 1

≈ 0.6321

Therefore, P(x ≥ 5) = 1 - P(x < 5) = 1 - 0.6321 = 0.3679 (rounded to four decimal places).

(d) To find P(x ≤ 6), we use the CDF formula with x0 = 6:

P(x ≤ 6) = F(6) = ∫[0,6] (1/5)e*(-x/5) dx

= [-e*(-x/5)] from x = 0 to 6

= -e*(-6/5) + 1

≈ 0.4703

(e) To find P(4 ≤ x ≤ 6), we note that P(4 ≤ x ≤ 6) = P(x ≤ 6) - P(x < 4), where P(x < 4) is the probability that x is less than 4. Using the CDF formula, we have:

P(x < 4) = F(4) = ∫[0,4] (1/5)e*(-x/5) dx

= [-e*(-x/5)] from x = 0 to 4

= -e*(-4/5) + 1

≈ 0.3297

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Complete question:

Consider the following exponential probability density function. f(x) = 1 5 e−x/5 for x ≥ 0 (a) Write the formula for P(x ≤ x0). (b) Find P(x ≤ 4). (Round your answer to four decimal places.) (c) Find P(x ≥ 5). (Round your answer to four decimal places.) (d) Find P(x ≤ 6). (Round your answer to four decimal places.) (e) Find P(4 ≤ x ≤ 6). (Round your answer to four decimal places.)

Answer:

See Screenshot

Step-by-step explanation:

Answer:

Step-by-step explanation:

x inter for line a = 1

x inter for line B = -4

Line A is greater then Line B

The area of the parallelogram with base 50 ft and height 37 ft is 1850 sq. ft.

The region or space a parallelogram occupies in a two-dimensional plane is known as the area of a parallelogram. A particular kind of quadrilateral is a parallelogram. A quadrilateral is referred to as a parallelogram if it has two sets of parallel opposite sides. A parallelogram can be anything from a rectangle to a square to a rhombus. Shapes—2D or 3D—are the foundation of geometry. Each of these forms has a unique set of features and uses a separate area formula.

The area of the parallelogram is given by the formula:

A = (b)(h)

Given that,

b = 50 ft

h = 37 ft

Substitute the values in the equation of area:

A = (50)(37)

A = 1850 sq. ft

Hence, the area of the parallelogram is 1850 sq. ft.

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The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle.

Since the diameter of the garden is 42m, the radius is half of that, which is:

r = 42m / 2 = 21m

The circumference of the circular garden is therefore:

C = 2πr = 2π(21m) = 42πm

If the gardener makes 4 rounds of the fence, he will need to purchase 4 times the circumference of the garden in barbed wire. Therefore, the length of barbed wire he needs to purchase is:

4 x 42πm = 168πm

This is approximately equal to 527.79m, if we use the value of π to two decimal places.

Answer:

528 M

Step-by-step explanation:

CIRCUMFERENCE OF GARDEN= 2 pi r

r=42/2 =21

circumference = 2x (22/7) x21

=132 m

To make 4 rounds= 4 x 132 = 528m

Therefore , the solution of the given problem of plotting data comes out to be  their line plot is given below table.

The most typical technique to present data using a chart is to graph the connection between two extra variables. Diagrams created manually or digitally are also acceptable. Starting at the origin, move three pieces up and two types to the right. It is essential to show the numbers of rows 2, 3, & 4 just on standard system. Be sure to expression yourself clearly. The letter P is represented by the pinkish squiggle next to the number 2.3.

Here,

In the given problem, Jessica and her friend measured the lengths of the fish they caught one day.

The measurements in inches are given in the table:

Jessica's Fish (inches) Friend's Fish(inches)

13.2                       12.5

14.3                      15.6

15.1                   13.7

12.4                          14.1

13.9                          13.0

Thus , their line plot is given above.

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The domain of the function is (-∝, -3) ∪ (-3, +∝)

The range is (-∝, 3) ∪ (3, +∝) and the asymptotes are x = -3 and y = 3

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

f(x) = 2/(x + 3) + 3

Set the denominator to not equal to 0

So, we have

x + 3 ≠ 0

So, we have

x ≠ -3

As an interval notation, we have

(-∝, -3) ∪ (-3, +∝)

Here, we have

f(x) = 2/(x + 3) + 3

When x = -3, we have

f(-3) = undefined + 3

This means that

f(x) ≠ -3

As an interval notation, we have

(-∝, 3) ∪ (3, +∝)

In (a), we have

x ≠ -3

This means that

Vertical asymptote: x = -3

In (b), we have

f(x) ≠ -3

This means that

Horizontal asymptote: y = 3

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The price of one square meter of the coffee and plantain farm is $0.05.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

1 hectare of the farm = $500

Now,

To determine the price per square meter of a coffee and plantain farm.

We would need to divide the cost of 1 hectare = $500 by the number of square meters in a hectare.

So,

One hectare is 10,000 square meters.

This means,

= $500 ÷ 10,000 sq m

= $0.05 per square meter

Therefore,

The price of one square meter of the coffee and plantain farm is $0.05.

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The complete question.

What is the price of a square meter of coffee and plantain farms?

If 1 hectare of the farm is $500.

Answer:

11, 7, 3, -1, -5, -9

Step-by-step explanation:

To find the next two terms in the sequence 11, 7, 3, -1, we need to determine the pattern or rule that generates the sequence.

In this case, we can see that each term is decreasing by 4, so the next two terms should be -5 and -9.

Therefore, the complete sequence is:

11, 7, 3, -1, -5, -9

Let's start by finding the amount that Alex earns per hour before overtime. We know that he works 40 hours, so if we let his hourly pay be x, then his total pay before overtime can be expressed as 40x.

Since Alex gets 50% more than his usual pay for overtime, his overtime pay per hour would be 1.5x, or his usual pay plus 50% of his usual pay. This means that for the 6 hours of overtime he worked, he would earn a total of 6 * 1.5x = 9x.

Now we can write an expression for Alex's total pay, including overtime:

Total pay = 40x + 9x

Simplifying this expression, we get:

Total pay = 49x

So Alex's total pay, including overtime, is 49 times his hourly pay.

Answer:

Step-by-step explanation:

To express 799 cm² as a fraction of 0.13 m², we need to convert the units of one of the areas so that they are both in the same units.

1 cm = 0.01 m (since there are 100 cm in 1 meter)

So, we can convert 799 cm² to m² by dividing by (100 cm/m)²:

799 cm² = (799/10000) m²

Now, we can express 799 cm² as a fraction of 0.13 m²:

(799/10000) m² ÷ 0.13 m² = (799/10000) ÷ 0.13

Simplifying this fraction, we get:

(799/10000) ÷ 0.13 = 0.0799 ÷ 0.13

= 0.6138461538

Therefore, 799 cm² is equal to approximately 0.6138 of 0.13 m², or we can say:

799 cm² = (0.6138/1) × 0.13 m²

So, we can express 799 cm² as a fraction of 0.13 m² as:

799 cm² = 0.6138 × 0.13 m² (approximately)

or

799 cm² = 6138/10000 × 0.13 m²

or

799 cm² = 6138/100000 × m².

Substitute the value of y in the first equation with the second equation.

6x + 3(1-x) = 15

Simplify and solve for x:

6x + 3 - 3x = 15

3x + 3 = 15

3x = 12

x = 4

Now, substitute the value of x in the second equation to solve for y:

y = 1 - x

y = 1 - 4

y = -3

Therefore, the solution to the system of equations is (4, -3).

This graph shows how far Han is from his house as he drives. (0, 10) is the Y Vertical intercept. Han is therefore originally located 10 miles from his house.Horizontal intercept of X (10,0) It indicates that it takes 10 minutes to reach.

The point where the graphs of a function and relation meets the y-axis of the coordinate system is known as a y-intercept, also referred to as a vertical intercept. Analytic geometry is used for this, with the widely accepted standard that the variable y is represented by the vertical axis and the variable x by the horizontal axis.

Anything straight to the horizon is said to as horizontal. Since the vertical is the polar opposite of the horizontal, everything that intersects it at a right angle of 90 degrees is known as vertical. Hence, the line that runs form left to center is seen as being horizontal.

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Answer:

The economy car weighs 800 pounds.

Answer:

a) You will reach 9 meters above the pool.

b) The length of time you are in the air is 2 seconds.

c) The height of the diving board is 7 meters.

Step-by-step explanation:

Given quadratic equation:

[tex]m(d)=-4d^2 + 5.5d + 7[/tex]

To determine how far above the pool you reach on your dive, find the y-value of the vertex of the given quadratic equation.

The formula for the x-value of the vertex is -b/2a for a quadratic equation in the form y=ax²+bx+c.  Therefore, the x-value of the vertex for the given equation is:

[tex]\implies -\dfrac{5.5}{2(-4)}=0.6875[/tex]

To find the y-value of the vertex, substitute d = 0.6875 into the given equation:

[tex]\begin{aligned}m(0.6875)&=-4(0.6875)^2+5.5(0.6875)+7\\&=-1.890625+3.78125+7\\&=1.890625+7\\&=8.890625\\&=9\; \sf m\;(nearest\;meter)\end{aligned}[/tex]

Therefore, you will reach 9 meters above the pool (rounded to the nearest meter).

You will hit the water when your height is zero. Therefore, to find the length of time you are in the air, set the given quadratic equation to zero and solve for d using the quadratic formula.

[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}[/tex]

[tex]\implies d=\dfrac{-5.5 \pm \sqrt{5.5^2-4(-4)(7)}}{2(-4)}[/tex]

[tex]\implies d=\dfrac{-5.5 \pm \sqrt{142.25}}{-8}[/tex]

[tex]\implies d=\dfrac{-5.5 \pm \sqrt{142.25}}{-8}[/tex]

[tex]\implies d=-0.803357..., \;2.178357...[/tex]

As time is positive we can discount the negative solution. Therefore, the length of time you are in the air is 2 seconds (rounded to the nearest second).

The height of the diving board is the y-intercept of the graph of the equation. The y-intercept is the value of y when x = 0. Therefore, to find the height of the diving board, substitute d = 0 into the equation.

[tex]\begin{aligned}\implies d(0)&=-4(0)^2+5.5(0)+7\\&=0+0+7\\&=7\end{aligned}[/tex]

Therefore, the height of the diving board is 7 meters.

For a game, Bob has a total of 60 adventure cards. The distribution of cards, c, to players, p, is shown in the table. c = 60 ÷ p

Probability defines the possibility of occurrence of an event. Probability is the unit of measurement for an event's likelihood. It represents the proportion of positive results to all results. For instance: Receiving the numbers 3 and 5 while rolling the dice, as well as getting both an even and an odd number.

The equation would read: c = 60 / 2, which implies c = 30 if p=2. The equation would read 12 = 60 / p, p = 5, 20 = 60 / 3, etc. If c = 12, the equation would read... 12 = 60 / p, and p = 5, and so on, 20 = 60 / 3, and 15 = 60 / 4.

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The perimeter of the figure is 43 units.

The perimeter of a figure is the sum of the whole sides of the figure. Therefore, the figure above is a composite figure, let's find the perimeter of the shape as follows:

Hence,

Perimeter of the figure = 8 + 3 + 5 + 7 + 10 + 2 + 8

Therefore,

Perimeter of the figure = 11 + 12 + 12 + 8

Perimeter of the figure = 23 + 20

Perimeter of the figure = 43 units

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Answer:  a

Step-by-step explanation:

karabee kailash

Rounding to the nearest whole number, we can conclude that 24 people did not agree with the proposal.

If the idea was rejected by 56% of the group, then 44% of the group, or 100%, agreed with the plan.

Let x be the proportion of the group who rejected the proposition. The percentage of the group that approved of the idea was then 44%, or 0.44 times the total number of group members.

The problem states that there are 43 individuals in the group as a whole. As a result, we may construct the equation shown below:

x + 0.44(43) = 43

When we find x and simplify, we get:

x = 43 - 0.44(43) (43)

x = 23.96

We can estimate that 24, or the nearest whole number, did not support the proposition.

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Answer:

Step-by-step explanation:

(a) To find the number of students who did not like either sport, we can use the formula:

Total students = Students who like basketball + Students who like hockey - Students who like both sports + Students who like neither sport

We know that the total number of students surveyed is 30, and we also know the number of students who like basketball, hockey, and both sports. We can use this information to solve for the number of students who like neither sport:

30 = 13 + 18 - 4 + Students who like neither sport

Simplifying this equation, we get:

3 = Students who like neither sport

Therefore, there were 3 students who did not like either sport.

(b) To find the number of students who liked exactly one of the sports, we can subtract the number of students who liked both sports from the total number of students who liked at least one of the sports. We know that 13 students liked basketball, 18 students liked hockey, and 4 students liked both sports. To find the number of students who liked at least one sport, we can add the number of students who liked basketball and the number of students who liked hockey, but we need to make sure we don't count the 4 students who liked both sports twice:

Number of students who liked at least one sport = Students who like basketball + Students who like hockey - Students who like both sports

Number of students who liked at least one sport = 13 + 18 - 4 = 27

Therefore, the number of students who liked exactly one sport is:

Number of students who liked exactly one sport = Number of students who liked at least one sport - Number of students who liked both sports

Number of students who liked exactly one sport = 27 - 4 = 23

So there were 23 students who liked exactly one of the sports.

Answer:

a) {0,1,3,5,8}

b) -

Step-by-step explanation:

the composition cannot be performed cos 3 is mapped to 2 by g, but 2 is not in the domain of f

The trignometric ratios are given by1. B = 180 - (90 + 58) (sum of triangles)

B = 32°

Let's find a and b using trigonometric ratios:

Reference angle = 58°

Opposite = a = ?

Hypotenuse = c = 27

Adjacent = b = ?

✔️To find a, apply SOH:

Sin 58 = Opp/Hyp

Sin 58 = a/27

a = 27*Sin 58

a = 22.8972986 ≈ 22.9 (nearest tenth)

✔️To find b, apply CAH:

Cos 58 = Adj/Hyp

Cos 58 = b/27

b = 27*Cos58

b = 14.3 (nearest tenth)

2. B = 180 - (90 + 63) (sum of triangles)

B = 27°

Let's find a and b using trigonometric ratios:

Reference angle = 63°

Opposite = a = 11

Hypotenuse = c = ?

Adjacent = b = ?

✔️To find b, apply TOA:

Tan 63 = Opp/Adj

Tan 63 = 11/b

b = 11/Tan 63

b = 5.6 (nearest tenth)

✔️To find c, apply SOH:

Sin 63 = Opp/Hyp

Sin 63 = 11/c

c = 11/Sin 63

c = 12.3 (nearest tenth)

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Therefore, the equation for the line tangent to the curve when x = 4 is y = (7/4) x + 7.

An equation is a mathematical statement that shows the equality between two expressions. Equations are used to solve problems and find solutions to mathematical or real-world problems. They typically involve variables, which are symbols that represent unknown values, and constants, which are known values that are used in the equation. Equations can take many forms, but they generally follow the pattern: expression = expression. Equations are an important tool in mathematics, science, and engineering, and they can be used to model and analyze many different types of systems and processes.

Here,

a. To find the equation for the secant line through the points where x has the given values, we need to find the slope of the line passing through the two points. The two points we need to consider are (4, 14) and (9, 21):

slope = (change in y) / (change in x)

= (21 - 14) / (9 - 4)

= 7 / 5

Now we can use the point-slope form of a line to find the equation of the secant line passing through these two points:

y - 14 = (7/5) (x - 4)

Simplifying this equation, we get:

y = (7/5) x + 6.6

Therefore, the equation for the secant line passing through the points where x has the given values is y = (7/5) x + 6.6.

b. To find the equation for the line tangent to the curve when x has the first value, we need to find the derivative of the function y = 7sqrt(x) with respect to x:

y' = (7/2) x*(-1/2)

Evaluating this derivative at x = 4, we get:

y'(4) = (7/2) (4*(-1/2)) = 7/4

This is the slope of the tangent line at x = 4. We can use the point-slope form of a line to find the equation of the tangent line at this point:

y - 14 = (7/4) (x - 4)

Simplifying this equation, we get:

y = (7/4) x + 7

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