A man left on a trip of 450 kilometres at 10 am. He stopped for a rest for
40 minutes and had another break of an hour for lunch. What time did he
finish the trip, if he was travelling at an average speed of 50 kilometres per
hour?

The 75 entries in a costume contest, 31 entrants were dressed as heroes and 31 entrants were wearing a mask. 8: No masks or costumes were worn by contestants .

The possibility of an event occurring is described by the concept of probability. In real life, we frequently have to make predictions about the future. We might know about the result of an occasion.

We declare that there is a possibility that the event will take place when this occurs.

In conclusion, probability can be used in a lot of great ways in business, entertainment, and this new area of artificial intelligence.

By simply dividing the total number of possible outcomes by the favorable number, the probability of an event can be calculated using the probability formula.

n(A)=31 and n(B) = 20 and n(AB) =9

50-42 = 8

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Answer:

Step-by-step explanation:

51.1

Answer:

Step-by-step explanation:

answer: 51.1

The equation of the function in vertex form is given by f(x)=-2(x-2)²-7/2.

It is the point at which the maximum or minimum value of a function is achieved. It is also known as the turning point of the graph of the function.

The equation of the function in vertex form is given by f(x)=a(x-h)²+k.

Using the given table, we can calculate the values of a, h and k.

Substituting the values of x and f(x) from the table, we get:-

-3/2=a(-1/2-h)²+k

-9/4=a(0-h)²+k

-5/2=a(1/2-h)²+k

-3/2=a(3/2-h)²+k

3/2=a(5/2-h)²+k

15/4=a(3-h)²+k

Solving these equations simultaneously, we get

a=-2, h=2 and k=-7/2

Therefore, the equation of the function in vertex form is given by

f(x)=-2(x-2)²-7/2.

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Answer:

Step-by-step explanation:

[tex]x^2=17^2-15^2[/tex]     (Pythagoras Theorem)

[tex]x^2=64[/tex]

[tex]x=8[/tex]

If the altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the triangle is increasing at a rate of 1 square centimeter/minute. then the Base of the triangle is changing at a rate of 28.2 cm/min when the altitude is 10 cm and the area is 94 sq cm.

The given data is the altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the triangle is increasing at a rate of 1 square centimeter/minute. then the rate of the base of the triangle changing when the altitude is 10 centimeters and the area is 94 square centimeters is calculated as,

  Area of a triangle = 1/2 * base * height

    The given area of the triangle is 94 square centimeters.

 Area of the triangle = 1/2 * base * altitude

 94 = 1/2 * b * 10b

      = 18.8 centimeters

Differentiate w.r.t t 94 = 1/2 * b * hdb/dt

                                     = -94 / 5 dA/dt

                                     = 1 square centimeter/minute

                                     = dh/dt * b / 2dh/dt

                                      = (2 / b) * dA/dt

             Substitute the values in the above equation,

                         3 = (2 / 18.8) * dA/dtdA/dt

                           = (3 * 18.8) / 2

                           = 28.2

        square centimeters/minute Base of the triangle is changing at a rate of 28.2 cm/min when the altitude is 10 cm and the area is 94 sq cm.

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Finally, if the line has a slope of zero, it is a horizontal line. In this case, changing x will have no effect on y.

A graph is a data structure used to represent relationships or connections between objects. It consists of a set of vertices (also known as nodes) and a set of edges that connect pairs of vertices. The edges can be directed (pointing from one vertex to another) or undirected (not having a direction).

Graphs are used to model a wide range of real-world problems, such as social networks, transportation networks, computer networks, and many others. They are also used in computer science algorithms and data structures, such as shortest path algorithms, network flow algorithms, and data compression algorithms.

by the question.

The relationship between the change in x and the corresponding change in y on a graph depends on the slope of the line. The slope of a line is the ratio of the change in y to the change in x, and it represents how steep the line is.

If the line has a positive slope, that means it is slanting upwards from left to right. In this case, an increase in x will result in an increase in y, and a decrease in x will result in a decrease in y. The larger the slope, the more dramatic this effect will be.

On the other hand, if the line has a negative slope, it is slanting downwards from left to right. In this case, an increase in x will result in a decrease in y, and a decrease in x will result in an increase in y. Again, the larger the slope, the more pronounced this effect will be.

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Answer:

We can use trigonometry to solve this problem. Let's call the distance from point A to the boat "x" and the distance from point B to the boat "y". Then we have:

In triangle AOC, tan(12) = OC / x

In triangle BOC, tan(64) = OC / y

We want to find the distance from point A to point B, which is the difference between x and y:

Distance AB = y - x

To solve for x and y, we need to eliminate OC. We can do this by setting the two expressions for OC equal to each other and solving for OC:

tan(12) = OC / x

OC = x tan(12)

tan(64) = OC / y

OC = y tan(64)

x tan(12) = y tan(64)

y = x tan(12) / tan(64)

Now we can substitute this expression for y into the equation for Distance AB:

Distance AB = y - x

Distance AB = x tan(12) / tan(64) - x

We can simplify this expression by factoring out an x:

Distance AB = x (tan(12) / tan(64) - 1)

Now we just need to plug in the values and calculate:

Distance AB = x (0.2174 - 1)

Distance AB = -0.7826 x

Since distance cannot be negative, we know that x > 0. Therefore, the boat is between point A and point B, and the distance from point A to point B is:

Distance AB = x (0.2174 - 1)

Distance AB = -0.7826 x

Distance AB ≈ 1.28 x

We don't know the actual value of x, but we can see that the distance from point A to point B is approximately 1.28 times the distance from point A to the boat when Jaxson measured the angle of depression to be 12 degrees.

Step-by-step explanation:

Answer:434

Step-by-step explanation:It’s correct

Answer: x=6

Step-by-step explanation:

Step 1: Add all the 4's together (20) and then you get 20+(5*x)=50

5x6=30+20=50.

After calculation, we know that the time taken by the lorry is 3 hours and 20 minutes.

Time is the ongoing progression of existence and things that happen in what seems to be an irrevocable order from the past, present, and forward into the future.

Military time starts with 0000, also known as "zero hundred hours" or just "zero hundred," at the stroke of midnight.

Then, multiply each hour by one hundred, such that 1 a.m. is equal to 0100 (zero one hundred) hours, 2 a.m. is equal to 0200 (zero two hundred) hours, and so on.

So, we need to calculate the time as follows:

Leaving time = 14:55

Arriving time = 18:15

Then,

14:55 to 15:15 = 20 minutes

Then, 15:15 to 18:15 = 3 hours

Then, the total time taken would be:

3 hours and 20 minutes

Therefore, after calculation, we know that the time taken by the lorry is 3 hours and 20 minutes.

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Complete question:

On the return journey, the lorry leaves at 14 55 and arrives at the factory at 18 15. Calculate the time taken.

Rοunding tο the nearest whοle number, the area οf the actual game rοοm in square feet is 56 square feet.

Geοmetry is a branch οf mathematics that deals with the study οf shapes, sizes, relative pοsitiοns οf figures, and the prοperties οf space.

Tο find the area οf the actual game rοοm in square feet, we first need tο cοnvert the given dimensiοns frοm inches tο feet. Since there are 12 inches in a fοοt, we have:

Length οf rectangle = 2 inches ÷ 12 inches/fοοt = 0.1667 feet

Width οf rectangle = 4.5 inches ÷ 12 inches/fοοt = 0.375 feet

Next, we need tο find the area οf the rectangle in square feet using the scale οf 1 tο 30. This means that 1 inch οn the drawing represents 30 inches in real life. Tο cοnvert this tο feet, we divide by 12, sο 1 inch οn the drawing represents 2.5 feet in real life. Therefοre, we have:

Length οf rectangle = 2 inches × 2.5 feet/inch = 5 feet

Width οf rectangle = 4.5 inches × 2.5 feet/inch = 11.25 feet

The area οf the rectangle is:

Area = length × width = 5 feet × 11.25 feet = 56.25 square feet

Hence, Rοunding tο the nearest whοle number, the area οf the actual game rοοm in square feet is 56 square feet.

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To make 70 cups of fruit soda with a juice-to-sparkling water ratio of 4:3, Milo will need 40 cups of juice and 30 cups of sparkling water.

If the juice-to-sparkling water ratio is 4:3, then we can write it as 4x:3x, where x is a common factor.

Let's say Milo wants to make a total of 7x cups of fruit soda (since 4x + 3x = 7x). We know that 7x = 70 cups, so x = 10.

Therefore, Milo needs 4x = 40 cups of juice and 3x = 30 cups of sparkling water.

You will therefore need 40 cups of juice and 30 cups of sparkling water to generate 70 cups of fruit soda with a 4:3 juice-to-sparkling water ratio.

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Answer: 99 cm^2

Step-by-step explanation:

The easiest way to solve the surface area of these shapes is to draw a net of the shape and calculate the area of all the different shapes in the net.

Area for triangle: 1/2 * b*h - or for this shape just base times height because you have 2 triangles.

Area for rectangle: length times width.

The measurements I came up with are 15 for BOTH the triangles, 30 for one of the rectangles, 18 for the other, and 36 for the last rectangle which put together all equal to 99 cm^2.

Tell me if it works

Answer:

663

Step-by-step explanation:

SA= 2b+Ph= 2(1/2*6*2.5)+(6*3*6)(6)

Answer:

x=5, y=20

Step-by-step explanation:

3y+5+5y+15=180

8y=160

y=20

17x-70=2x+5

15x=75

x=5

Yes, there are enough evidence to show mean CO2 emission is lower in 2010 than in 2004.

The random variable is mean CO2 emission per capita , population parameter is CO2 emission per capita in population and null hypothesis is rejected as p-value is smaller than significant value.

The random variable is represented as the mean CO2 emission per capita.

The population parameter represented as the interest is the true mean CO2 emission per capita in the population in 2010.

Let μ_0 be the population mean CO2 emission per capita in 2004

And μ_1 be the population mean CO2 emission per capita in 2010.

The null hypothesis is,

There is no difference in the mean CO2 emissions per capita between 2004 and 2010,

H0: μ_0 = μ_1

The alternative hypothesis is,

The mean CO2 emissions per capita in 2010 are lower than the mean CO2 emissions per capita in 2004,

Ha: μ_0 > μ_1

To determine whether there is enough evidence to reject the null hypothesis,

Collect data on CO2 emissions per capita in 2010 and perform a hypothesis test .

Using a suitable statistical test such as a one-sample t-test.

If the test results in a p-value that is smaller than the chosen significance level (typically 0.05).

Reject the null hypothesis .

And conclude that there is enough evidence to show that the mean CO2 emissions per capita are lower in 2010 than in 2004.

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Therefore, the area of triangle XYZ is 2 square units.

Area is a measure of the size of a two-dimensional shape or surface. It is defined as the amount of space inside the boundary of a flat or planar figure, such as a triangle, square, rectangle, or circle. The unit of area is typically square units, such as square meters (m²), square feet (ft²), or square centimeters (cm²).

Here,

To determine the area of triangle XYZ with coordinates (6,1), (2,5), and (10,9), we can use the formula for the area of a triangle:

Area = (1/2) * base * height

where the base is any side of the triangle and the height is the perpendicular distance from the base to the opposite vertex.

Distance between (6,1) and (2,5):

= √((6 - 2)² + (1 - 5)²)

= √(20)

So, the base of the triangle is √(20).

We can use the formula for the distance between a point and a line to do this:

Distance from (10,9) to line passing through (6,1) and (2,5):

= |(10 - 6)(5 - 1) - (2 - 6)(9 - 1)| / √((5 - 1)² + (6 - 2)²)

= 4 / √(20)

So, the height of the triangle is 4 / √(20).

Now, we can plug in the values for the base and height into the formula for the area of a triangle:

Area = (1/2) * base * height

= (1/2) * √(20) * (4 / √(20))

= 2

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The probability of you, Leonard, and Sheldon being chosen together is 1/1140.

Probability is calculated by the total number of ways an event can occur divided by the total number of possible outcomes.

In this case, the total number of ways three students can be drawn out of 20 is 20C3 or 1140.

The probability of selecting you, Leonard, and Sheldon out of the three spots is 1/1140, or approximately 0.000877 or 0.0877%.

Total number of students in physics department = 20.Number of student spots for a conference trip to Cancun = 3.The probability that you, Leonard, and Sheldon are chosen is equal to the total number of ways you, Leonard, and Sheldon can be chosen divided by the total number of ways 3 students can be chosen from 20 students.

The number of ways that you, Leonard, and Sheldon can be chosen is 1 since you all need to be chosen together.

The total number of ways that 3 students can be chosen from 20 students is given by 20C3 (the combination of 20 objects taken 3 at a time).20C3 = (20*19*18)/(3*2*1) = 1/140

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Therefore , the solution of the given problem of unitary method comes out to be least quantity of paint (40 fl oz) and the purple jar has the most (80 fl oz). (36 fl oz).

To accomplish the task, one may use this generally accepted ease, preexisting variables, as well as any significant components from the original Diocesan customizable query. If so, there might be an opportunity to interact with the item once more. Otherwise, every significant factor that affects how algorithmic evidence behaves will be gone.

Here,

We must convert all the measurements to the same units in order to evaluate the amounts of paint in each jar. All quantities should now be expressed in fluid ounces (fl oz):

=> 2 gallons 4 liquid ounces = 36 liquid ounces.

=> 80 fluid ounces = 5 glasses

=> equivalent to 39 fluid ounces

The quantities of paint in the jars are as follows:

=> 36 fl oz. blue container

=> 80 fl oz. purple container

=> 39 fl oz. green container

As a result, the blue jar has the least quantity of paint (40 fl oz) and the purple jar has the most (80 fl oz). (36 fl oz).

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Answer:

Step-by-step explanation:

A grain οf salt is abοut 5 times as wide as a human cheek cell.

A standard fοrm οf a number in Maths is basically mentiοned fοr the representatiοn οf large numbers οr small numbers. We use expοnents tο represent such numbers in standard fοrm.

The cοrrect definitiοn οf standard fοrm cοuld be explained better in terms οf decimal numbers and fοllοwing certain rules. As we knοw, decimal numbers are the simplified fοrm οf fractiοns.

Sοme fractiοns give decimal numbers which have numbers after decimal at thοusandths, hundredths οr tenths place. But there are sοme fractiοns, which give a big decimal number. Tο represent such big numbers, we use simpler fοrms, which are alsο stated as Scientific nοtatiοn

Tο cοmpare the sizes οf the grain οf salt and the human cheek cell, we need tο divide the diameter οf the grain οf salt by the diameter οf the cheek cell:

[tex]\frac{(3*10^{-4} meters)}{(6*10^{-5 }meters)} \\\\=5[/tex]

Therefοre, a grain οf salt is abοut 5 times as wide as a human cheek cell.

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The probability of selecting green, blue, red, and yellow marbles from the bag is 1/35.

To find the probability of choosing specific marbles from the bag, we first need to find out the total number of ways in which four marbles can be selected from seven marbles.

The total number of ways in order to select 4 marbles from 7 marbles is given by the combination formula:

C(7,4) = 7!/(4!3!) = 35

There are 35 ways in which four marbles which will be selected from the bag. We need to find out the number of ways in which we can select green, blue, red, and yellow marbles.

We have only one way to select these specific four marbles from the bag. Number of ways to select green, blue, red, and yellow marbles is 1.

Probability of selecting green, blue, red, and yellow marbles:

P = (Number of ways to select green, blue, red, and yellow marbles) / (Total number of ways to select 4 marbles)

P = 1/35

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Answer:

The answer to your problem is, y = 1

Step-by-step explanation:

2(4y - 1) = 6, use distributive property: a(b - c) = ab - ac

8y - 2 = 6, add 2 to both sides

8y = 8, divide both sides by 8

Y = 1

Thus the answer to your problem is, y = 1

Answer:

1 is the answer

I took the test

Using transformations, we can find that the graph J represents the correct graph of f(x) and h(x).

A transformation is a change to the graph of a parent function. Translations, reflections, and dilations are the three different forms of transformations. A function can be altered either vertically (affecting the y-values) or horizontally (affecting the x-values) (affects the x-values).

[tex]h(x) = (x + 1) (x − 3)[/tex]

[tex]= x^2 --3x + x-3[/tex]

[tex]= x^2- 2x - 3[/tex]

The graph of f(x) = x² is transformed to create the graph of h(x) = 2f(x) = 2x

Now, for  [tex]x = 0, f(x) = 0[/tex] and  [tex]h(x) = 0[/tex]

Therefore, both the graphs h(x) = 0trough the origin.

Now, for   [tex]x = 1, f(x) = 1[/tex]  and [tex]h(x) = 2[/tex]

Therefore, [tex]f(1) < h(1)[/tex]

Hence, the graph J represents the correct graph of f(x) and h(x).

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According to the given situation in the question the cost of one pen is £1.02 and the cost of one pencil is £0.12 .

Let the cost of one pen be x.

Let the cost of one pencil be y.

So, from the given condition given in question the equations are :-

The cost of 3 pens and 2 pencils is £3. 30 can be written in the equation, 3x + 2y = 3. 30 —-- (1)

The cost of 3 pencils and 2 pens is £2. can be written in the equation, 2x + 3y = 2 —--- (2)

So by solving equation (1) and (2),

3×equation (2) - 2×equation(1)

Now subtract 6x+4y=6.6 from 6x + 9y=6

5y = 0.6

y = 0.12

Put y = 0.12 in equation(1) then x = 1.02

Hence the cost of one pen is £1.02 and the cost of one pencil is £0.12.

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—-------- Correct question format is given below —--------

(Q). The cost of 3 pens and 2 pencils is £3. 30. The cost of 3 pencils and 2 pens is £2. 95.What is the cost of one pencil and one pen?

With the help of given angle elevation we can conclude that, the saguaro cactus is approximately 2.19 meters tall.

What is trigonometry?

Trigonometry is a branch of mathematics that focuses on the relationships between the sides and angles of triangles.

What is angle elevation?

Angle elevation, also known as angle of elevation, is the angle between a horizontal line and a line of sight (or direction) to an object above the horizontal line.

We can use trigonometry to solve this problem. Let's call the height of the cactus "h". Then we can set up the following equation:

tan(26.1) = h / 4.5

To solve for "h", we can first multiply both sides by 4.5:

4.5 * tan(26.1) = h

Using a calculator, we can evaluate tan(26.1) to be approximately 0.4877. Multiplying this by 4.5 gives:

h = 2.19465

Rounding to the nearest hundredth, we get:

h ≈ 2.19 meters

Therefore, the saguaro cactus is approximately 2.19 meters tall.

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(1)/(x)=(1)/(y)-(1)/(z) is an example of an equation that can be used to express z in terms of x and y. z can be expressed in terms of x and y as z= xy+1/y-x.

It is typically written using an equals sign “=” to show that the two expressions on either side of the equals sign are the same.

To solve the equation, it must first be rearranged so that z is on its own side of the equation.

This can be done by multiplying both sides of the equation by x and then subtracting (1)/(y) from both sides.

(1)/(x)=(1)/(y)-(1)/(z)

1-1/y= (x/y-x/z)-1/y

This yields the equation

y-1/y=(x/y-1/y)-(x/z+1/y)

y-1/y= (x-1/y)-(xy+1/zy)

(y-1/y)-(x-1/y)= (-xy)+1/zy

y-x/y= xy+1/zy

y-x=(xy+1)y/zy

Once the equation has been rearranged, the next step is to solve for z.

z= xy+1/y-x

z= xy+1/y-x

Therefore, z can be expressed in terms of x and y as z= xy+1/y-x.

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3 x 10-2 is 30,000 times less powerful than 9 x 10-2. If 3 x 10 towards the negative 2 power equals times as much as 9 x 10 to a second power, then

Another way to put it is 2 + 3 = 6. As we've seen, is equivalent to 2 3. The multiplier is the quantity that multiplies the number of these equal groups by the multiplicand, the quantity of items in each group.

Given that 10-2 is 1/100 and 10-2 is 100, we may rephrase the formulas as follows:

9 x 100 = 900

3 x 1/100 = 0.03

At this point the values are comparable:

How many times more than 0.03 is 900?

We may calculate it by dividing 900 by 0.03: 900 0.03 = 30,000

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The image of point A after being reflected over the y-axis would have coordinates (2, 4).

When a point is reflected over the y-axis, it is essentially being flipped to the opposite side of the y-axis while remaining at the same distance from it.

In this case, point A has coordinates (-2, 4), which means it is located 2 units to the left of the y-axis and 4 units above the x-axis. When we reflect this point over the y-axis, its x-coordinate will change sign, meaning it will move 2 units to the right of the y-axis, while its y-coordinate will remain the same, meaning it will stay 4 units above the x-axis.

The point A has coordinates (-2, 4).

When a point is reflected over the y-axis, its x-coordinate changes sign while the y-coordinate remains the same.

Therefore, the image of point A after this transformation would have coordinates (2, 4).

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Answer:

Step-by-step explanation:

B and C

The measure of the angle for the first circle is π/4 and the measure of the angle for the second circle is π. Since π is larger than π/4, we can conclude that the angle measure for the second circle is greater than the angle measure for the first circle.

The central angle of a circle is defined as the angle subtended at the center of the circle by an arc on the circumference. The measure of a central angle is proportional to the length of the arc it subtends, and the constant of proportionality is given by the formula:

angle measure = arc length / radius

Using this formula, we can find the measures of the central angles of the two circles:

For the first circle with radius 16 units and arc length 4π, the angle measure is:

angle measure = arc length / radius = (4π) / 16 = π/4

For the second circle with radius 5 units and arc length 5π, the angle measure is:

angle measure = arc length / radius = (5π) / 5 = π

Therefore, the measure of the angle for the first circle is π/4 and the measure of the angle for the second circle is π. Since π is larger than π/4, we can conclude that the angle measure for the second circle is greater than the angle measure for the first circle.

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Answer:

HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

Step-by-step explanation:

You have to construct a probability tree diagram.