The distance between two towns, A and B, is 100 km. Mr Jones drove from A to B at an average speed of v km/h. (a) Write down an expression, in terms of v, for the time, in hours, that he took to complete the journey from A to B. [1]​

Answer: Check the numbers that are already there.

Step-by-step explanation:

Example, what times 6 equals 24? then divided 24 by that number. Do this for all the numbers

The value of the missing internal angle in the irregular polygon is equal to 125°.

The sum of internal angles (S), in degrees, in any convex polygon is determined by the following formula:

S = 180 · (n - 2)

Where n is the number of sides in the polygon.

According to the image seen beside, we find an irregular pentagon, that is, a polygon with five sides. First, determine the sum of internal angles:

S = 180 · (5 - 2)

S = 180 · 3

S = 540°

Second, find the value of the missing internal angles:

y = 540° - 86° - 142° - 72° - 115°

y = 125°

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Answer:

Step-by-step explanation:

4(4y+5)=3(y+7)

16y+20=3y+21

13y=1

y=1/13

Answer:

y = 1/13

Step-by-step explanation:

 (4y + 5) : 3 = (y+7) :4

Product of extremes = (4y + 5) * 4

                                  = 4y *4 + 5*4

                                  = 16y + 20

Product of mean = 3*(y +7)

                            = 3*y + 3*7

                            = 3y + 21

Product of extremes = product of mean

          16y + 20 = 3y + 21

Subtract 20 from both sides,

                  16y = 3y + 21 - 20

                  16y = 3y + 1

Subtract 3y from both sides,

               16y - 3y = 1

                     13y = 1

                        [tex]\boxed{\bf y =\dfrac{1}{13}}[/tex]          

Answer:

Step-by-step explanation:

m

The correct equation to show the cost of meat per pound at Sam's Grocery Store is x = 2y, where x is the cost of meat per pound at Sam's Grocery Store and y is the cost of meat per pound at Lane Grocery Store.

This equation represents the fact that the cost of meat per pound at Sam's Grocery Store is twice the cost of meat per pound at Lane Grocery Store.

For example, if the cost of meat per pound at Lane Grocery Store is $5, then the cost of meat per pound at Sam's Grocery Store would be 2 * $5 = $10.

So, the equation x = 2y accurately shows the relationship between the cost of meat per pound at Sam's Grocery Store and the cost of meat per pound at Lane Grocery Store.

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The  displacement x of the moving puck is; 0.43 meters

The displacement is defined as the change in position of an object. It is also called a vector quantity and has a direction and magnitude

The parameters given here are;

The polar coordinate initial velocity vector; U = 2.35 m/s, -22°

Final velocity vector; V = 6.42 m/s, +50°

This suggests to us that Cartesian x axis is parallel to angle 0° and y axis is parallel to +90°.

Change of velocity component parallel to +90° =  magnitude*sinθ,.

Thus, the change of that velocity

Δv = |V|sin(50) - |U|sin(-22)

Δv = 6.42sin(50) - 2.35sin(-22)

Δv = 4.9 - (-0.88)

Δv = +5.8 m/s

The equation for displacement is;

s = ut +1/2at^2

where acceleration time t = Δt = 0.215 s

initial velocity u = |U|sin(-22) = -0.88 m/s

acceleration parallel to u is a = Δv/Δt = +5.8/Δt

a = 5.8/t m/s^2

Thus;

s = -0.88t + ¹/₂* 5.8/t * t²

s = -0.88t +2.9t

s = 2.0t

s = 2.0 * 0.215

s = 0.43 m

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Based on the information from the sets, it can be inferred that the correct answer is: red, green (option C).

To identify the correct answer we must take into account the elements that are in each set. Once we identify this information, we must analyze the elements in common between the sets. In accordance with the above, we must take into account this:

Based on the above, the correct answer is red and green because these are the elements that have the sets A, B, and C.

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The fourth year increase in salary is 4.5 percent.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, Inka's starting annual salary was $55,600.

After her first year she received a 2% pay rise.

Now, 2% of 55,600

= 2/100 ×55,600

= 1112

So, salary of 2nd year is 55,600+1112=$56712

The next year she received a 3% pay rise.

Now, 3% of 56712

= 3/100 ×56712

= 1701.36

So, salary of 3rd year is 56712+1701.36=$58413.36

Last year she received an x% pay rise.

Now, x% of 58413.36+58413.36=61,042

x/100 ×58413.36=61,042-58413.36

584.1336x=2628.64

x=2628.64/584.1336

x=4.5%

Therefore, the fourth year increase in salary is 4.5%.

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The length of the rectangle is 8.2 feet.

Given area of the rectangle is 82 feet and width is 10 feet

let variable : length of rectangle

then the equation is 10x=82

x=82/10

x=8.2

x=length=8.2

Therefore the length of the rectangle is 8.2 feet.

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Answer:

i) 9

ii) 11

Step-by-step explanation:

First off, what is a "mode"?

The mode in a set of data is simply the most common answer/outcome;

Next, we need to understand the data;

In this case, families were asked about the number of cats they have;

The children answered 0, 1, 2 or 3;

8 families have 0 cats,

6 have 1,

10 have 2,

x have 3

So, the mode will be the most common answer to how many cats a family has;

As we can see from the data, the most common response was 2, i.e. 10 families have 2 cats, compared to only 8 with 0 cats and 6 with 1 cat;

If we know the mode is 2, the value of x has to be less than 10 as it is not the most common response;

The largest possible value will be 9.

If the mode is 3, then that means the x has to be the greatest number of responses;

Since the greatest number of responses to the other options is 10, then the number of responses to having 3 cats has to be at least 11;

The smallest possible value of x, if the mode is 3, will be 11.

The graph of f(x) = -0.1 |x| opens. The point (-100, -10) or (100, -10) is on the graph.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

We know that the graph of the function f(x) = a|x| opens upwards if the value of a > 0 and it opens downwards for a< 0.

For the given function the value of a = -0.1 < 0.

So, the graph of f(x) opens downwards.

The coordinates of the graph are determined by substituting the value of y in the given function:

f(x) = -0.1 |x|

-10 = -0.1 |x|

x = -100 or x = 100

So, the two points are (-100, -10) or (100, -10).

Hence, the graph of f(x) = -0.1 |x| opens. The point (-100, -10) or (100, -10) is on the graph.

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A geometric method is known as "stereographic projection" involves projecting a flat map of a sphere onto a three-dimensional surface with a point at its center.

This is one way to construct a sphere. The construction of geodesic domes, which gained popularity in the 1960s, is one example of an art and construction project that frequently makes use of this approach.

Using a solid material and carving it into the shape you want is another way to make a sphere. This can be accomplished using stone, clay, wood, and other materials. To produce a sphere with perfect symmetry, this method necessitates considerable skill and precision.

A third approach is to construct a sphere from numerous small, flat pieces. Paper or fabric can be used to accomplish this, with each piece being cut into a curved shape and glued together to form the sphere. Origami balls, for example, are a common decorative item made using this method.

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Answer:

  314 yd²

Step-by-step explanation:

You want the area of a circle that has a diameter of 20 yards.

The usual formula for the area of a circle is ...

  A = πr² . . . . . . where r is the radius

The radius of the circle is half the diameter, so is (1/2)(20 yd) = 10 yd.

Using this value in the formula, we find the area to be ...

  A = 3.14(10 yd)² = 314 yd²

Answer:

y ≤ 3/4x-2

The 3/4 is the slope, and -2 is y intercept

Answer:

Step-by-step explanation:

19?

Step-by-step explanation:

a row n adds the number n to the sum (= the first number from the right in row n-1), and therefore also n to the 3rd number from the right of row n-1.

in any case, the first number from the right is the result of

1 + 2 + 3 + 4 + 5 + ... + n-1 + n

that sum is

n(n+1)/2

for the row 20 that is

20×21/2 = 10×21 = 210

the 3rd number from the right in row 20 is then

210 - 2 = 208

Since ∠A and ∠B are vertical angles, they have equal measures, so m∠A = m∠B. We can set the two expressions equal to each other:

7x + 4 = 8x - 20

Solving for x:

-x = -24

x = 24

So, m∠A = 7x + 4 = 7 * 24 + 4 = 188, and m∠B = 8x - 20 = 8 * 24 - 20 = 188.

Therefore, the measure of ∠B is 188 degrees.

Event R: Drawing a Red Ballot, Event B: Drawing a Blue Ballot, Event Even: Drawing an Even Numbered Ballot, Event Odd: Drawing an Odd Numbered Ballot.

The general election is today, and volunteers are organizing the ballots. Depending on the part of the city in which a citizen lives, he or she receives a different ballot. The types of ballots consist of RED ballots numbered 1, 2, 3, 4 and BLUE ballots numbered 1, 2, 3, 4. First, the volunteers need to define the events of drawing a red ballot and drawing a blue ballot. This can be done by defining the events R and B, respectively. Next, the volunteers need to define the event of drawing an even numbered ballot and the event of drawing an odd numbered ballot. This can be done by defining events Even and Odd, respectively. The volunteers can then use these events to determine which ballots are being drawn by the citizens. For example, they can use the events R and Even to determine which citizens are drawing a red even numbered ballot.

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The length of line segment KJ is D. 3√5 units

A line segment in geometry is a section of a straight line that is enclosed by two clearly defined endpoints and contains all of the points on the line that lie inside those endpoints. The Euclidean distance between two ends of a line segment determines its length.

∠KMJ = 180° - 90° (adjacent angles on a straight line)

= 90°

Using Pythagorean Theorem,

KJ² = 6² + 3²

KJ² = 45

KJ = √45

= √9√5

= 3√5

The answer is D. The length of line segment KJ is 3√5 units.

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Answer:

Step-by-step explanation:

The two trains are moving apart from each other, so we can add their speeds to find their relative speed:

Relative speed = 75 + 95 = 170 miles per hour

We want to know how long it will take for the trains to be 204 miles apart. We can use the formula:

distance = rate × time

to solve for the time. Let t be the time in hours:

204 = 170t

Solving for t, we get:

t = 204/170

t ≈ 1.2 hours

Therefore, it will take approximately 1.2 hours for the two trains to be 204 miles apart.

The product of the given expression; 4x (x²) as required to be determined is; Choice 1; 4x³.

It follows from the task content that the product of 4x (x²) is to be determined as required.

Since the given expression is; 4x (x²); we have that;

4 • x • x²

It therefore follows from the product of powers law of indices that we have;

4•x³

= 4x³.

Ultimately, the product of the expression is; 4x³.

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The new credit card balance on her credit card is $219 if no interest is added on balance.

The total sum of money owing by a cardholder to their credit card company is known as their credit card balance. Balances fluctuate depending on when and how they are used; they rise when purchases are made and fall when payments are made by cardholders. Any sum that is left over at the end of the billing cycle is added to the bill for the following month and is subject to interest. The balances on a person's credit cards play a significant role in determining their credit score. Future lenders will evaluate them to assess the risk (and price) of extending further credit to their clients.

Given that Mabel owes $374 and make a repayment of $155.

Then the new credit card balance is, if no interest is added on balance

= $374 - $155

= $219

So, The new credit card balance on her credit card is $219

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3rd option is correct.

The probability that the committee will contain 2 accountants and 3 non-accountants is (6 × 56) / 792 = 6/66 = 3/33.

A corporate board refers to a governing body of a corporation, usually consisting of elected or appointed members, who are responsible for overseeing the management of the company and making important decisions related to its strategy, finances, operations, and other aspects. The board serves as a representative of the shareholders and is responsible for overseeing the actions of the CEO and other executives, ensuring that the company is run in a manner that benefits its stakeholders.

The probability that the committee will contain two accountants and three non-accountants can be calculated as follows:

The number of ways to choose 2 accountants out of 4 is 4 choose 2, or 4C2 = 6.

The number of ways to choose 3 non-accountants out of 8 (12-4) is 8C3 = 56.

The total number of ways to choose 5 people from 12 is 12C5 = 792.

Therefore, the probability that the committee will contain 2 accountants and 3 non-accountants is (6 × 56) / 792 = 6/66 = 3/33.

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Answer:

Below

Step-by-step explanation:

From mile 3 to mile 18 is 15 miles

   He needed   2 hrs - .75 hr  = 1.25 hr to run 15 miles

15 miles / 1.25 hr =  12 miles per hour    ( VERY fast !)

Answer:

[tex]3\left(x-\dfrac{5}{6}\right)^2-\dfrac{49}{12}[/tex]

Step-by-step explanation:

Given quadratic expression:

[tex]3x^2 - 5x - 2[/tex]

To complete the square, factor out the coefficient of the leading term:

[tex]\implies 3\left(x^2-\dfrac{5}{3}x-\dfrac{2}{3}\right)[/tex]

Add and subtract the square of half the coefficient of the term in x inside the parentheses:

[tex]\implies 3\left(x^2-\dfrac{5}{3}x+\left(\dfrac{\frac{-5}{3}}{2}\right)^2-\left(\dfrac{\frac{-5}{3}}{2}\right)^2-\dfrac{2}{3}\right)[/tex]

Simplify:

[tex]\implies 3\left(x^2-\dfrac{5}{3}x+\left(\dfrac{-5}{6}\right)^2-\left(\dfrac{-5}{6}\right)^2-\dfrac{2}{3}\right)[/tex]

[tex]\implies 3\left(x^2-\dfrac{5}{3}x+\dfrac{25}{36}-\dfrac{25}{36}-\dfrac{2}{3}\right)[/tex]

Factor the perfect square trinomial formed by the first three terms inside the parentheses:

[tex]\implies 3\left(\left(x-\dfrac{5}{6}\right)^2-\dfrac{25}{36}-\dfrac{2}{3}\right)[/tex]

Distribute:

[tex]\implies 3\left(x-\dfrac{5}{6}\right)^2-\dfrac{75}{36}-\dfrac{6}{3}[/tex]

[tex]\implies 3\left(x-\dfrac{5}{6}\right)^2-\dfrac{25}{12}-2[/tex]

Simplify:

[tex]\implies 3\left(x-\dfrac{5}{6}\right)^2-\dfrac{25}{12}-\dfrac{24}{12}[/tex]

[tex]\implies 3\left(x-\dfrac{5}{6}\right)^2-\dfrac{49}{12}[/tex]

In light of this, Liam's earnings after six years will be roughly $47,139.92.

Profits from Liam's company have reached $43,200, and they are growing at a 1.2% annual rate.

We can use the compound interest calculation to calculate the number of profits after six years.

The formula is P = P0 *[tex](1 + r/100)^t[/tex], If t is the number of years, which is 6, P0 is the initial sum of $43,200, r is the yearly interest rate of 1.2%, and t is the number of years.

By substituting these values into the formula,

we can calculate the final amount as P = 43,200 * [tex](1 + 1.2/100)^6[/tex] = 43,200 * [tex]1.012^6[/tex] = 43,200 * 1.07711 = $47,139.92.

In light of this, Liam's profits after six years will be roughly $47,139.92.

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Answer:

The solution to the system is (1.8, 7.6)

Step-by-step explanation:

To solve the system of linear equations by graphing, we need to plot the two lines on the same coordinate plane and find the point where they intersect, which will be the solution of the system.

Plot the lines:

y = 2/3x + 4 can be written as y = (2/3)x + 4, where the slope is 2/3 and the y-intercept is 4.

y = -x + 1 can be written as y = -x + 1, where the slope is -1 and the y-intercept is 1.

Find the intersection point:

To find the intersection point, we can substitute the x-value from one equation into the other equation. Let's use y = 2/3x + 4.

Substitute x from y = 2/3x + 4 into y = -x + 1:

-x + 1 = 2/3x + 4

Multiplying both sides by -3, we get:

3x - 3 = -2x - 12

Adding 2x to both sides, we get:

5x - 3 = -12

Adding 12 to both sides, we get:

5x = 9

Dividing both sides by 5, we get:

x = 1.8

Now that we have x, we can substitute it back into either equation to find the corresponding y-value. Let's use y = 2/3x + 4:

y = 2/3x + 4

y = 2/3 * 1.8 + 4

y = 3.6 + 4

y = 7.6

So the solution to the system is (1.8, 7.6), which is the point where the two lines intersect.

The area and volume based on the information will be area 144 √3 square meters and 240√3 cubic meters

To calculate the area of the hexagonal prism, you need to calculate the area of each face and add them up. To calculate the area of one face of the hexagon, you can use the following formula:

Area of a regular hexagon = (3 * √3) / 2 * side^2

Plug in the side length of 4m:

Area of a face = (3 * √3) / 2 * 4^2 = (3 * √3) / 2 * 16 = 24 * √3

So the area of one face is 24 * √3 square meters. There are a total of 6 faces, 3 of which are hexagons, so the total area of the hexagonal prism is:

Total area = 6 * (24 * √3) = 144 * √3 square meters

To calculate the volume of the hexagonal prism, multiply the area of one face by the height:

Volume = (24 * √3) * 10 = 240 * √3 cubic meters

So the volume of the hexagonal prism is 240 * √3 cubic meters

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Nelson is asked to move water to fill a container in the shape of a hexagonal prism with the following measurements: Side of the polygon= 4m and Height= 10m. Help him calculate the area of the figure and then the volume. And assuming that we have another prism three times the space, what would its volume be?