4.02 Lesson Check Arithmetic Sequences (6)

167.7 feet is the length of the zipline.

The angle of inclination is the angle formed between a horizontal line and a line or surface that is sloping or inclined. It is a measure of the steepness or slope of the line or surface and is typically expressed in degrees or as a trigonometric ratio.

We have a zipline that drops 30 feet from one treetop to a second treetop.

If the angle of inclination from the shorter tree to the taller tree is 10 degrees.

Let AB be the distance between two trees and BC be the drop in height from A to C. Then,

We have BC/AB = tan(θ)

Where θ = 10 degrees

We know BC = 30 feet.

So,

AB = BC/tan(θ) = 30/tan(10°) = 167.7 feet (rounded to one decimal place)

Therefore, the length of the zipline is 167.7 feet.

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On the opening day of the exhibition, 30 adult tickets were sold.

Let's use the following variables to represent the number of adult and child tickets sold:

a: the number of adult tickets sold

c: the number of child tickets sold

From the problem, we will use linear equation system. we know that the total number of tickets sold is 80, so we have:

a + c = 80 (Equation 1)

We also know that the total revenue from ticket sales is $180, so we have:

3a + 2c = 180 (Equation 2)

We can use Equation 1 to solve for one of the variables in terms of the other:

c = 80 - a

Substituting this into Equation 2, we get:

3a + 2(80 - a) = 180

Simplifying this equation, we get:

a + 160 = 90

a = 30

Therefore, by using linear equation system, 30 adult tickets were sold on the opening day of the exhibition.

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Charlie can make 6 hamburger form 1.56 pounds of meat if each uses 0.26 pounds.

The number of hamburger made by 0.26 pounds meat = 1

So, the number of hamburger possible from 1.56 pounds of meat = total amount of meat/amount of meat in one hamburger

Now, keep the values in formula to find the required answer

Number of hamburger = 1.56/0.26

Performing division on Right Hand Side of the equation to find the possible number of hamburger

Number of hamburger = 6

The 6 hamburger can be made from the meat.

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Simplified form of the algebraic expression (x^2 - x - 12) / (x^2 - 4) = (x + 3) / (x - 2)

To simplify the given algebraic expression (x^2 - x - 12) / (x^2 - 4), we first need to factor both the numerator and denominator as much as possible.

We can factor the numerator using the product-sum method or the quadratic formula, which yields:

x^2 - x - 12 = (x - 4)(x + 3)

Similarly, we can factor the denominator as a difference of squares, which gives:

x^2 - 4 = (x - 2)(x + 2)

Now, we can substitute these factorizations into the original expression:

(x^2 - x - 12) / (x^2 - 4) = [(x - 4)(x + 3)] / [(x - 2)(x + 2)]

At this point, we can simplify the expression by canceling out the factors that appear in both the numerator and denominator. Specifically, we can see that (x - 4) and (x + 2) appear in both the numerator and denominator, so they cancel out:

[(x - 4)(x + 3)] / [(x - 2)(x + 2)] = (x + 3) / (x - 2)

So the simplified expression is (x + 3) / (x - 2).

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The mean when the time required to play a certain board game is uniformly distributed between 15 and 60 minute is 35.6.

In statistics, the mean is a measure of central tendency that is calculated by summing up a set of numerical values and dividing by the number of values in the set. The mean is also known as the arithmetic mean or the average.

For example, suppose we have the following set of numbers: 3, 5, 7, 10, and 12. To find the mean, we add up these numbers (3 + 5 + 7 + 10 + 12 = 37) and divide by the number of values in the set (5). The mean of this set of numbers is 7.4, which represents the typical or average value of the set.

The formula for the mean is:

mean = (sum of values) / (number of values)

By using the Excel formula= AVERAGE (data), sample mean will be 35.6.

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The answer is no, you do not have enough time to climb all 3 walls within 7 1/2 minutes.

What is the conversion of the unit?

A conversion factor is a fraction equal to ' 1 '.  It has the same quantity in the numerator and denominator, but they're in different units.  You use it to convert a number from one unit to another unit.

There are different ways to approach this problem, but one possible method is to convert everything to a common unit, such as seconds.

First, convert 7 1/2 minutes to seconds by multiplying by 60:

7.5 minutes x 60 seconds/minute = 450 seconds

Next, multiply the time it takes to climb each wall by 3 to find the total time needed:

3 walls x 155 seconds/wall = 465 seconds

Comparing the total time needed (465 seconds) to the available time (450 seconds), we see that there is not enough time to climb all three walls.

Therefore, the answer is no, you do not have enough time to climb all 3 walls within 7 1/2 minutes.

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Answer:

u multiply 3 with 8 then u get ur answer the u do the same method which is multiplication with 6 with 4 to get ur answer

Rotation: Rotate the larger circle by the same angle as the smaller circle around the origin. Rotate the smaller circle by any angle. Although changing direction, this metamorphosis keeps the shape and size intact.

Any point in the plane that is a certain distance from another point forms a circle (center). Thus, it is a curve formed up of points that are separated from one another by a predetermined distance in the plane. Moreover, at every angle, it is rotationally symmetric about the centre. The closed, two-dimensional plane of a circle has every pair of points equally separated from the "centre." By drawing a line through the circle, one can create a line of circular symmetry. Moreover, at every angle, it is rotationally symmetric about the centre.

If two circles have the same shape but different sizes, they are comparable. The circles are centred at the origin in this case, allowing us to compare their radii to see if they are equal. The ratio of the larger and smaller circles' radii is 8/2, or 4.

Translation: Move the smaller circle to the origin and the larger circle in the same direction to a place four times away from the origin. While changing location, this transformation keeps the object's shape and size.

Rotation: Rotate the larger circle by the same angle as the smaller circle around the origin. Rotate the smaller circle by any angle. Although changing direction, this metamorphosis keeps the shape and size intact.

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Answer:

4

Step-by-step explanation:

Answer:

13m

Step-by-step explanation:

pls mrk me brainliest

The rule is to minus 4 from the x-coordinate and add 8 to the other. The coordinates of A after the reflection are (-x,y). Thus, it is present to the left of the Y-axis. Yes, the final figure is congruent to the original figure.

To translate a point 4 units left and 8 units up, we subtract 4 from the x-coordinate and add 8 to the y-coordinate.

Now, let’s apply this rule to point A. If A has coordinates (x,y), then after translation it will have coordinates (x-4,y+8).

For the second question, we can find the new location of A by using the coordinates we just found. So if A was originally located at (x,y), it will now be located at (x-4,y+8).

To reflect a point over the y-axis, we negate its x-coordinate. So if A has coordinates (x,y), then after reflection it will have coordinates (-x,y).

Using this rule, we can find that after reflection over y-axis, point A will have coordinates (-x,y).

Finally, since translation and reflection are both rigid transformations, they preserve distance and angles between points. Therefore, the final figure is congruent to the original figure.

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Correct question is:

ABC is translated 4 units to the left and 8 units up, then reflected across the y-axis.  Answer the questions to find the coordinates of A after the translation.

1. Give the rule for translating a point 4 units left and 8 units up.

2. After the translation, where is A located?

3. Give the rule for reflecting a point over the y-axis.

4. What are the coordinates of A after the reflection?

5. Is the final figure congruent to the original figure? How do you know?

Answer: The asnwer is 8

Step-by-step explanation:

Answer:

d = negative 5 cosine (StartFraction pi Over 2 EndFraction t)  [y=-5*cos(π/2)]

Step-by-step explanation:

See the attached graph for the explanation.  Desmos graphing software was used to plot the 4 equation options (using x in place of t and y in place of d).

The given points were added to see which of the graphed lines they best match.  We can see that the third option, y=-5*cos(π/2), intersects all four points.

Two of the options (1st and 3rd) lie too close to y=0 to see their difference on the scale of the graph, so we can eliminate them.  (Options 1 and 3)

Option 2 has an amplitude higher than the given points, so it can also be eliminated.

y=-5*cos(π/2) best represents the given points.

Probability that the thread length of a randomly selected bolt is within 1.5 SDs of its mean value is 0.8664, is farther than 2.5 SDs from its mean value is 0.0124 and between 1 and 2 SDs from its mean value is 0.2728.

Probability that the thread length of a randomly selected bolt is within 1.5 SDs of its mean value P (μ - 1.5σ < X < μ + 1.5σ)= P(Z < 1.5) - P(Z < -1.5)Here, Z is the standard normal variable P(Z < 1.5) = 0.9332 (from standard normal table)P(Z < -1.5) = 0.0668 (from standard normal table) So, P (μ - 1.5σ < X < μ + 1.5σ) = 0.9332 - 0.0668= 0.8664

Thus, probability that the thread length of a randomly selected bolt is within 1.5 SDs of its mean value is 0.8664. Probability that the thread length of a randomly selected bolt is farther than 2.5 SDs from its mean value P (X < μ - 2.5σ) + P (X > μ + 2.5σ) = P (Z < -2.5) + P (Z > 2.5)P (Z < -2.5) = 0.0062 (from standard normal table)P (Z > 2.5) = 0.0062 (from standard normal table)

So, P (X < μ - 2.5σ) + P (X > μ + 2.5σ) = 0.0062 + 0.0062 = 0.0124  Probability that the thread length of a randomly selected bolt is between 1 and 2 SDs from its mean value P (μ - 2σ < X < μ - 1σ) = P (Z < -1) - P (Z < -2) + P (Z < 1) - P (Z < 2)P (Z < -1) = 0.1587 (from standard normal table)

P (Z < -2) = 0.0228 (from standard normal table)P (Z < 1) = 0.8413 (from standard normal table)P (Z < 2) = 0.9772 (from standard normal table) So, P (μ - 2σ < X < μ - 1σ) = 0.1587 - 0.0228 + 0.9772 - 0.8413= 0.2728

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Answer:

its bar graph

Step-by-step explanation:

thanks for the question

please mark me brainless

The respοnses fοr favοurite vacatiοn spοt can be described best by a pie chart.

One sοrt οf graph that illustrates the infοrmatiοn in the circular graph is a pie chart. It is a sοrt οf graphical representatiοn οf data where the slices οf pie depict the relative sizes οf the data. A list οf numerical and categοrical variables is necessary fοr a pie chart. Pie in this cοntext refers tο the entire thing, and slices tο its cοmpοnent pοrtiοns.

If yοu asked "What is yοur favοrite vacatiοn spοt?" tο a grοup οf peοple, the mοst apprοpriate type οf graph tο represent the respοnses wοuld be a pie chart.

A pie chart is a circular chart that is divided intο slices tο represent the prοpοrtiοn οf each categοry in a dataset.

In this case, each slice οf the pie chart wοuld represent a different vacatiοn spοt, and the size οf each slice wοuld cοrrespοnd tο the prοpοrtiοn οf respοndents whο selected that vacatiοn spοt as their favοrite.

Pie charts are useful fοr displaying categοrical data, where the categοries are mutually exclusive and add up tο 100%.

They are easy tο read and understand, and can quickly shοw the distributiοn οf respοnses amοng the different categοries.

On the οther hand, a bar graph οr a line graph wοuld nοt be apprοpriate fοr this type οf data since the respοnses are nοt numerical οr cοntinuοus.

A line plοt wοuld alsο nοt be apprοpriate since it is used tο display a series οf data pοints, and in this case, there is οnly οne data pοint per categοry.

Therefοre, a pie chart is the best chοice.

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Answer:

Step-by-step explanation:

Given equation,

→ 0.48 = ?/25

Let's change the symbol into x,

→ 0.48 = x/25

Now we have to,

→ Find the required value of x.

Then the value of x will be,

→ 0.48 = x/25

→ x/25 = 0.48

→ x = 0.48 × 25

→ [ x = 12 ]

Hence, the value of x is 12.

The domain can be written as 3 <x < 81.75, which includes all x values that are feasible and fit within the constraints of the issue.

The most appropriate domain for this situation is (c) 3 < x < 81.75.

The reason for this is that the taxi charges $3 for the first mile, so x must be greater than 1. After that, the taxi charges $2.25 for every mile after the first, so the domain must exclude x = 0. Additionally, the problem states that the farthest the taxi will travel is 35 miles, so the domain must also include x < 35.

Therefore, the domain can be expressed as 3 < x < 81.75, which allows for all possible values of x that fall within the given parameters of the problem.

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The dimensions of the ramp are approximately 1.73 feet in height, 5.19 feet in width, and 22.96 feet in length.

First we can use the formula for the volume of a rectangular prism:

volume = length × width × height

Substituting the expressions we found for the length, width, and height in terms of h, we get:

150 cubic feet = (10h + 5 feet) × (3h feet) × (h feet)

Multiplying out the terms on the right-hand side, we get:

150 cubic feet = 30h^3 + 15h^2 cubic feet

Subtracting 150 cubic feet from both sides, we get:

0 = 30h^3 + 15h^2 - 150 cubic feet

Dividing both sides by 15 cubic feet, we get:

0 = 2h^3 + h^2 - 10

This is a cubic equation that we can solve using various methods as factoring. One solution is:

h ≈ 1.73 feet

Substituting this value back into the expressions we found for the width and length, we get:

The width is 3h ≈ 5.19 feet.

The length is 10h + 5 ≈ 22.96 feet.

Therefore, the dimensions of the ramp are approximately 1.73 feet in height, 5.19 feet in width, and 22.96 feet in length.

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After addressing the issue at hand, we can state that As a result, the equation value of x is roughly 10.57 units (rounded to two decimal places).

An equation is a mathematical proclamation that proves the equality of two expressions capable of connecting through an equal sign '='. For instance, 2x - 5 = 13. Explanations include 2x-5 and 13. The '=' symbol links up the two expressions. A mathematical formula containing two formulas on either side of a =) (=) is known as an equation. It depicts the equivalence relationship between left and right methodologies. L.H.S. = R.H.S. (left edge = top half) in any formula.

Using the information provided, we can construct the following equation based on the concept of similar triangles:

x/(9+18) = 10/(BC) (BC)

9 + 18 = 27 = AB = AP + PB

Because triangle ABC is a right triangle (angle B is 90 degrees), we can apply the Pythagorean theorem to calculate the length of segment BC:

BC2 = AB2 - AC2 BC2 = 272 - 102 BC2 = 649 BC = sqrt (649)

When we plug this value into our original equation, we get:

x/(9+18) = 10/sqrt (649)

When we simplify, we get:

x/27 = 10/sqrt (649)

When we multiply both sides by 27, we get:

x = 270/sqrt (649)

As a result, the value of x is roughly 10.57 units (rounded to two decimal places).

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if () is not defined for non-integer values of d, then f (3.5) would not make sense.

In mathematics, an inequality is a statement that compares two values or expressions using a relational operator, such as less than (<), greater than (>), less than or equal to (≤), greater than or equal to (≥), or not equal to (≠). The values being compared can be numbers, variables, or expressions.

by the question.

a. At the beginning of the epidemic, the number of days since the epidemic began is 0. Therefore, substituting d = 0 in the equation f(d) = 50- () gives f (0) = 50 - 0 = 50. So, there were 50 people with the flu at the beginning of the epidemic.

b. The rate at which the flu is spreading can be determined by examining the coefficient of d in the equation f(d) = 50- (). Specifically, if the coefficient is positive, then the flu is spreading at an increasing rate, and if the coefficient is negative, then the flu is spreading at a decreasing rate. Additionally, the magnitude of the coefficient gives an indication of how quickly the flu is spreading. However, since the expression in the parentheses is not given in the question, it is not possible to determine the rate at which the flu is spreading.

c. f(1) represents the number of people with the flu after one day since the epidemic began. Substituting d = 1 in the equation f(d) = 50- (), we get f(1) = 50 - (). Therefore, f (1) depends on the value of ().

d. It is not possible to determine whether f(3.5) makes sense in this situation without knowing the value of (). If () is defined for non-integer values of d, then f(3.5) would make sense and represent the number of people with the flu after 3.5 days since the epidemic began.

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For the second order differential equation, we find that Height = 1333.33 meters, Velocity = 240 meters/second.

The acceleration of a rocket fired vertically upwards t seconds after launch is given by a = 20 + 4t m/s². The second order differential equation for the height of the rocket is given by ℎ′′ = a.

The initial conditions for the rocket are:

ℎ(0) = 0 (the rocket starts from the ground) and ℎ′(0) = 0 (the rocket is not moving initially). For the differential equation, we integrate the acceleration once to obtain the velocity, and then integrate the velocity to obtain the height.

Integrating a = 20 + 4t gives v = 20t + 2t² + C1, where C1 is a constant of integration. Using the initial condition v(0) = 0, we get C1 = 0. Integrating v = 20t + 2t² gives ℎ = 10t² + 2/3 t³ + C2, where C2 is another constant of integration.  Using the initial condition ℎ(0) = 0, we getC2 = 0.

Therefore, the general solution for the height of the rocket is ℎ = 10t² + 2/3 t³.The velocity of the rocket is given by v = ℎ′.

At t = 10 s, the height of the rocket is ℎ(10) = 10 × 100 + 2/3 × 1000 = 1333.33 m. The velocity of the rocket at t = 10 s is v(10) = ℎ′(10) = 20 × 10 + 2 × 10² = 240 m/s.

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Sin(pi - theta) has a value of 4/9. sin(pi - theta) is equal to sin for any value of theta (theta). sin(pi - theta) has a value of 4/9.

We may calculate the value of sin(pi - theta) using the trigonometric identity sin(pi - theta) = sin(pi)cos(theta) - cos(pi)sin(theta):

Pi minus theta equals sin (pi)

cos(pi)sin - cos(theta) (theta)

We may simplify the expression to: since sin(pi) = 0 and cos(pi) = -1

0*cos(theta) - (-1)*sin = sin(pi - theta) (theta)

Pi minus theta equals sin (theta)

The value of sin(theta) can now be substituted to obtain:

Theta = 4/9 sin(pi - theta)

Hence, sin(pi - theta) has a value of 4/9.

The value of theta determines the value of sin(pi - theta). In terms of the trigonometric functions of theta, there is a generic formula to get sin(pi - theta): Pi minus theta equals sin (pi)

cos(pi)sin - cos(theta) (theta)

We may simplify the expression to: since sin(pi) = 0 and cos(pi) = -1

0*cos(theta) - (-1)*sin = sin(pi - theta) (theta)

Pi minus theta equals sin (theta)

Hence, sin(pi - theta) is equal to sin for any value of theta (theta).

Hence, sin(pi - theta) has a value of 4/9.

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The required expression can express h in terms of A and b as [tex]$ h = \frac{2A - a}{b} $$[/tex]

Mathematical expressions consist of at least two numbers or variables, at least one math procedure, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical procedure. An expression's form is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

First, we can start by isolating the term that contains h on one side of the equation. To do this, we will first distribute the 0.5 term to get:

A = 0.5a + 0.5bh

Then, we can subtract 0.5a from both sides to get:

A - 0.5a = 0.5bh

Next, we can divide both sides by 0.5b to isolate h:

[tex]$ \frac{A - 0.5a}{0.5b} = h $$[/tex]

Simplifying the expression further, we can see that:

[tex]$$ \boxed{h = \frac{2A - a}{b}} $$[/tex]

Therefore, we can express h in terms of A and b as:

[tex]$ h = \frac{2A - a}{b} $$[/tex]

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Aproximate speed of the Earth's rotation around the Sun is 18.5 miles per second (30 km per second). 110,000 kilometers per hour is equal to 30 kilometers per second.

"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."

We always count the unit or amount value first and then calculate the more or less amount value.

For this reason, this procedure is called a unified procedure.

Many set values ​​are found by multiplying the set value by the number of sets.

A set value is obtained by dividing many set values ​​by the number of sets.

Hence, Aproximate speed of the Earth's rotation around the Sun is 18.5 miles per second (30 km per second). 110,000 kilometers per hour is equal to 30 kilometers per second.

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If the club has a payment plan in which a member can pay $50 down and the rest in 12 equal payments, the monthly payment is $42.50

To calculate the monthly payment for a health club membership with a payment plan, we first need to subtract the down payment of $50 from the total cost of $560. This leaves us with $510 to be paid in 12 equal monthly installments.

To find out how much each monthly payment would be, we divide the remaining balance ($510) by the number of months (12). Therefore, the monthly payment would be:

$510 ÷ 12 = $42.50

Therefore, A member would need to pay $50 down and $42.50 per month for the next 12 months to cover the cost of a $560 annual membership.

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The radius is half that distance.r = 1/2(d) where d = distance between the endpoints of the diameter.

1. Writing the equation of the circle in standard formWe know that the endpoints of a diameter are (2,4) and (-14,-8) respectively, and that the midpoint of the diameter is the center of the circle. Therefore, let's begin by calculating the midpoint of the diameter using the midpoint formula:x = (x1 + x2)/2y = (y1 + y2)/2x = (2 + (-14))/2 = -6y = (4 + (-8))/2 = -2So, the midpoint is (-6,-2) which is the center of the circle. Now, we can use the distance formula to calculate the radius. Recall that the diameter is the distance between the two endpoints of the diameter, so the radius is half that distance.r = 1/2(d) where d = distance between the endpoints of the diameter.So, d = sqrt[(x2 - x1)^2 + (y2 - y1)^2]d = sqrt[(-14 - 2)^2 + (-8 - 4)^2]d = sqrt[(-16)^2 + (-12)^2]d = sqrt[256 + 144]d = sqrt[400] = 20So, r = 20/2 = 10. Now that we have the center and radius, we can use the standard form equation of a circle which is:(x - h)^2 + (y - k)^2 = r^2where (h,k) is the center and r is the radius.Substituting our values into the equation, we have:(x + 6)^2 + (y + 2)^2 = 100Expanding and simplifying, we can write the equation of the circle in standard form as:x^2 + 12x + y^2 + 4y + 20 = 0This is the equation in standard form.2. Graphing the circleTo graph the circle, we need to plot the center which is (-6,-2) and then draw the circle with radius 10 units. The circle will be a curve that is equidistant from all points on it to the center. Here's a sketch of the circle.
3. An equation of the circle in standard form is x² + 12x + y² + 4y + 20 = 0.

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Answer:

(1)100

(2)120

(3)80

(4)200

(5)42.85

Step-by-step explanation:

The answers explanation is:

P=RB, p=percentage

r=rate

b=base,so

P=RB

P/R=RB/R

B=P/R

For example, (1)B=P/R

B=5/5/100

B=5*100/5

B=500/5

B=100 and so on - - -

GOOD LUCK!

a) The probability is equal to the proportion of the range that lies below 17 minutes.P(X< 17) = (17 - 16) / (23 - 16) = 1/7

b) The probability is equal to the proportion of the range that lies above 22 minutes.P(X > 22) = (23 - 22) / (23 - 16) = 1/7

c)  The probability is equal to the proportion of the range that lies between 18 and 20 minutes.P(18 ≤ X ≤ 20) = (20 - 18) / (23 - 16) = 2/7

d) The mean and standard deviation of the download times are 19.5 and 1.4 minutes, respectively.

The probability that the download time will be less than 17 minutes.The probability is equal to the proportion of the range that lies below 17 minutes.P(X< 17) = (17 - 16) / (23 - 16) = 1/7

The probability that the download time will be more than 22 minutes.The probability is equal to the proportion of the range that lies above 22 minutes.P(X > 22) = (23 - 22) / (23 - 16) = 1/7

The probability that the download time will be between 18 and 20 minutes.The probability is equal to the proportion of the range that lies between 18 and 20 minutes.P(18 ≤ X ≤ 20) = (20 - 18) / (23 - 16) = 2/7

The mean and standard deviation of the download times.Using the formula for the mean and standard deviation for a uniform distribution with a range of [a, b],μ = (a + b) / 2 = (16 + 23) / 2 = 19.5σ = (b - a) / sqrt(12) = (23 - 16) / sqrt(12) ≈ 1.4 Therefore, the mean and standard deviation of the download times are 19.5 and 1.4 minutes, respectively.

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Answer:

To work out the pressure that the car exerts on the road, we need to divide the force by the area of contact between the car and the road.

Since each of the car's 4 tyres has an area of 0.03 m² in contact with the road, the total area of contact is:

Total area of contact = 4 × 0.03 m² = 0.12 m²

So, the pressure that the car exerts on the road can be calculated as:

Pressure = Force / Area of contact

Pressure = 15,600 N / 0.12 m²

Pressure = 130,000 N/m²

Therefore, the pressure that the car exerts on the road is 130,000 N/m².