This distance-time graph shows the journey of a lorry.
What was the fastest speed that the lorry reached
during the journey?
Give your answer in kilometres per hour (km/h) and
give any decimal answers to 2 d.p.
Distance travelled (km)
280-
240-
200-
160
120-
80-
40
0
2
4
Time (hours)
2,4,6,8

Answer: 1/12

Step-by-step explanation:

From the question, we are informed that Cameryn mixes 1 1/4 gallons of water with 5/6 gallons of food coloring to create a solution for her science project. The gallons for the solution will then be:

= 1 1/4 + 5/6

= 1 3/12 + 10/12

= 1 13/12

= 1 + 1 1/12

= 2 1/12

If Cameryn only uses 2 gallons of the solution for her experiment, the number of gallons of solution that will be leftover will be:

= 2 1/12 - 2

= 1/12 gallons

Both the graphs have same slope and are parallel and g(x) is translated 3 units down the y - axis.

The general equation of a straight line is -

y = mx + c

Where -

[m] is the slope of the line.

[c] is the y - intercept

We have the following functions -

f(x) = -4x

g(x) = -4x - 3

Refer to the graph attached. The graph of g(x) is the graph of f(x) shifted 3 units downwards. Both the graphs have same slope and are parallel.

Therefore, both the graphs have same slope and are parallel and g(x) is translated 3 units down the y - axis.

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There are 0.621371 miles in 1 kilometer.

Step 1: Convert 1 kilometer to centimeters
1 kilometer = 100,000 centimeters (since 1 km = 1000 m and 1 m = 100 cm)

Step 2: Convert centimeters to inches
100,000 centimeters × (1 inch / 2.54 cm) = 39,370.0787 inches

Step 3: Convert inches to miles
There are 63,360 inches in 1 mile (1 mile = 5280 feet and 1 foot = 12 inches). So, we'll divide the inches by 63,360 to get miles.

39,370.0787 inches ÷ 63,360 inches/mile = 0.621371192 miles

Therefore, 1 kilometer is approximately 0.621371192 miles.

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Answer:

b is about 25.5, c is about 18.7

Step-by-step explanation:

Using the law of sines, you can find the measure of side b with the following equation:

\(\dfrac{\sin 48}{19}=\dfrac{\sin 85}{b}\)

\(b\approx 25.5\)

Similarly, for c, you can do the following:

\(\dfrac{\sin 48}{19}=\dfrac{\sin 47}{c}\)

\(c\approx 18.7\)

Hope this helps!

If the probability that Mary will win a game is 0.03, and loosing game is 0.97 then the excepted value of game is equals to -$1.11.

Expected Value of the game is the mean of the probability distribution of the payout values, denoted by E(X). It is equal to the sum of the products of each possible payout value and its corresponding probability, that is\(E( x) = \sum_{i } x_i p( x_i) \\\)

where, xᵢ --> payouts

p(xᵢ) --> probability for corresponding to payouts. Let's consider X be a variable denotes the payouts ( the amount the player wins for a particular outcome of the game). Here possible value of x are $60 and -$3. Now, determine probabilities corresponding to payouts.

Probability that Mary will win a game= 0.03

Probability that marry will not win a game

= 1 - 0.03 = 0.97

So, Probability distribution table is

x $60 -$3

P(x) 0.03 0.97

Now, using formula of excepted value,

E(X) = - (prize for winning game × (Probability of winning) + (Prize for loosing game)×(Probability of loosing the game or \(E( x)= \sum_{i } x_i p( x_i)\\ \) Substitute all known values

= $60× 0.03 - $3× 0.97

= $1.80 - $2.91

= -$1.11

Hence required value is -$1.11.

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Answer:

x = 80°

y = 10°

Step-by-step explanation:

Angles B and D are 100°

Because segments AB and DC are parallel, and BC and AD are, too, the angles formed when they intersect must equal 180° for each line they intersect. That means that angle A must be 80°, and angle C must be, too. Since C is the same angle as x, x measures 80°.

The angles of Triangle ABE measure 90°, 80°, and y. The triangle - angle theorem says that the 3 interior angles of a triangle all add up to 180°. For triangle ABE, 90° + 80° + y = 170° + y. Since 170° + y must equal 180°, y = 10°.

Answer:

22

Step-by-step explanation:

Answer:

22 yd

Step-by-step explanation:

Answer:

In 1911, he went on a no salt diet, (which he eased up after some time and convincing from doctors) which is bad for you since you need salt to survive. He also gave up meat and became a vegetarian, though he did attempt veganism, but faced many health problems, so he discontinued it. The last reason was because he fasted. A lot. And for long periods of time.

(a) The range of c₁ (the objective coefficient of x₁) for which this BFS remains optimal is c₁ ≤ 2.

(b) The range of b₂ (the right-hand side of the second constraint) for which this BFS remains optimal is 3 ≤ b₂ < 4.

(c) The dual price of the second constraint is 0.

(a) The optimality condition for a linear programming problem requires that the objective coefficient of a non-basic variable (here, x₁) should not increase beyond the dual price of the corresponding constraint. In this case, the dual price of the second constraint is 0, indicating that increasing the coefficient of x₁ will not affect the optimality of the basic feasible solution. Therefore, the range of c₁ for which the BFS remains optimal is c₁ ≤ 2.

(b) The range of b₂ for which the BFS remains optimal is determined by the allowable range of the corresponding dual variable. In this case, the dual price of the second constraint is 0, implying that the dual variable associated with that constraint can vary within any range. As long as 3 ≤ b₂ < 4, the dual variable remains within its allowable range, and thus, the BFS remains optimal.

(c) The dual price of a constraint represents the rate of change in the objective function value per unit change in the right-hand side of the constraint, while keeping all other variables fixed. In this case, the dual price of the second constraint is 0, indicating that the objective function value does not change with variations in the right-hand side of that constraint.

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Answer:

See Explanation

Step-by-step explanation:

Given

\(Price = 29.50 + 13.50(p - 2)\)

The question has missing details. However, I will solve on a general term.

A possible question could be to find the cost of purchasing (say 10 bottles).

To do this, we simply substitute 10 for p.

So:

\(Price = 29.50 + 13.50(p - 2)\)

\(Price = 29.50 + 13.50(10 - 2)\)

\(Price = 29.50 + 13.50 * 8\)

\(Price = 29.50 + 108\)

\(Price = 137.50\)

i.e. $137.50 for 10 pint bottles

Another possible question is to calculate the number of pint bottles that amount to (say $70).

To do this, we simply substitute 70 for Price.

So:

\(Price = 29.50 + 13.50(p - 2)\)

\(70 = 29.50 + 13.50(p - 2)\)

Collect like terms

\(70 - 29.50 = 13.50(p - 2)\)

\(40.5= 13.50(p - 2)\)

Divide both sides by 13.50

\(3= p - 2\)

Add 2 to both sides

\(3 + 2 = p - 2 + 2\)

\(5 = p\)

\(p = 5\)

i.e. $70 will buy 5 pint bottles

Use this explanation to find solution to your question

Answer:

\(5110, 5111, 5112\)

Step-by-step explanation:

Let \(x=\) first consecutive number

\(x + (x+1)+(x+2) = 15333\) (\(x\) is the first number, \(x+1\) would be the second consecutive number of the sequence, and \(x+2\) would be the third)

\(3x + 3 = 15333\)

\(3x = 15330\)

\(x = 5110\)

\(x+1 = 5110+1\)

\(= 5111\)

\(x+2 = 5110 + 2\)

\(= 5112\)

\(\therefore\) the consecutive numbers that sum up to \(15333\) are \(5110, 5111,\) and \(5112\)

Hope this helps :)

13 weeks.

Our equation is \(y=-24x + 379\).
x is the amount of weeks that has passed. x is being multiplied by -24. The +379 is our y-intercept. This means that per week, the account loses $24. The y-intercept also means that the account started with having $379 in it.

Finally, y is the output of the equation. This means that when you plug in the number of weeks, we see how much money is in the bank account with the y-value.

For example, if we solve for 2 weeks;

\(y=-24(2)+379=-48+379=331\). So after 2 weeks, the account will have $331 left.

Now to find the answer. We can plug in the final amount that we are given ($67) and then solve from there.

\(67=-24x+379\)

Next we isolate x and its coefficient:

\(67-379=-24x+379-379\)

\(-312=-24x\)

Multiply both by -1 to get positive numbers:

\(-312*-1=-24x*-1\)

\(312=24x\)

Now divide both sides by 24 to completely isolate x.

\(\frac{312}{24}=\frac{24x}{24}\)

\(13=x\)

OR

\(x=13\).

This means that when x = 13, y = 67. When 13 weeks pass, the amount of money in the account is equal to $67.

Therefore, the amount of time it takes for the account to be depleted to $67 is 13 weeks.

Answer:

So the probability of this happening is exactly 1 - it must be true

Step-by-step explanation:

If we calculate modulo(5) for each of the six numbers (the integer remainder after dividing by 5), we will get six values from 0 to 4.

By the pigeonhole principle, since there are 6 numbers and only 5 possible values, at least two must share the same value modulo 5. Pick two of those, say x and y, in which case x mod 5 = y mod 5, therefore (x - y) mod 5 = 0. In other words, their difference is a multiple of 5.

So the probability of this happening is exactly 1 - it must be true

Answer:

First use the distributive property.

2(4x) 2(-2) = 8(x) 8(-7)

You will get 8x - 4 = 8x - 56

This answer has no solutions since -4 does not equal -56.

Answer: no solution

Step-by-step explanation: So i'm guessing we're solving for x? no sweat

First Distribute the constants on the outside of the expression so 2(4x-2)=8(x-7) becomes 8x-4=8x-56 right now we have a problem. X is on both sides and we don't want that cause it complicates things so we want our variable x in this case on one side. if you subtract 8x from either side your left with no variable so there is no solution.

Answer:

the answer is B

x = 1

Step-by-step explanation:

the symmetry is in the middle of the curve like a mirror and the equation of the mirror or symmetry line is x=1

Answer:

A. 6 ∙ (30 - 1)

Step-by-step explanation:

How can we re-write the expression below into “friendlier” terms? 6 ∙ 29

options:

A. 6 ∙ (30 - 1)

B. 6 ∙ (16 + 13)

C. 6 ∙ (19 + 10)

D. 6 ∙ (21 + 8)

Re-writing an expression in friendlier term means expressing the term using numbers that are closest to the expression.

Checking all options,

A. 6 ∙ (30 - 1)

Option A seems closer to 6 ∙ 29 because, 30 - 1 which is very easy to evaluate gives 29

Moreover, 29 is very close to 30

Compared to other options, which have values that requires more thinking in evaluation

Transportation has become an essential part of our daily lives. It has transformed over time and has improved access to transportation services, increased connectivity, and intermodal options.

To meet the various transportation needs, different modes of transportation have evolved, including water, air, rail, 3PL, cross-docking, truck, intermodal, and pipeline. Each mode of transportation has unique characteristics and advantages. In this regard, matching the following transportation characteristics with the appropriate mode of transportation is necessary.

The most capable mode of transportation is the water mode of transportation. It has the highest capacity and can transport a vast amount of goods over long distances. It can transport large, heavy, and bulky goods that are difficult to transport by other modes of transportation. The mode of transportation that provides the most accessibility is the truck mode of transportation. It can reach almost any location as it can travel on roads and highways. It offers door-to-door service, which means that it can pick up the goods from the sender and deliver them to the receiver. The most reliable mode of transportation is the rail mode of transportation. It is not affected by traffic or weather conditions, which means that it can transport goods on time. It also has a low risk of accidents or delays, which makes it a reliable mode of transportation.

The fastest mode of transportation over a long distance is the air mode of transportation. It is the quickest mode of transportation as it can travel at high speeds and can cover long distances in a short time. This makes it ideal for transporting goods that need to be delivered urgently. The mode of transportation that has the lowest per-unit cost is the water mode of transportation. It is the most cost-effective mode of transportation as it can transport a large number of goods at once, which reduces the cost per unit.

Match the following descriptions with the appropriate transportation intermediary. The transportation intermediary that consolidates LTL shipments into FTL shipments is cross-docking. It takes small shipments from multiple companies and consolidates them into larger shipments. The transportation intermediary that is a nonprofit cooperative that arranges for members' shipments is 3PL.The transportation intermediary that brings shippers and carriers together is the intermodal mode of transportation. It provides an intermodal network to connect different modes of transportation to transport goods efficiently.

The transportation intermediary that purchases blocks of rail capacity and sells it to shippers is rail transportation. It makes it easier for shippers to transport goods using the rail mode of transportation.

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Solving an equation in algebra - mathematics will BOMDAS rule. Multiplication, division, addition, and subtraction are performed before.

However, in order to simplify things, if there are any exponential or logarithmic components, solve them first before applying BOMDAS to reduce them to a single solvable term. This is required by the rules.

So the list goes as

1. Exponents

2. Roots

3. Multiplication

4. Division

5. additional

6. Subtraction

However. Using a regular or scientific calculator will generate a lot of debate. A scientific calculator will adhere to the principles, while a typical calculator will evaluate from left to right or precisely the operator used first.

Using a scientific calculator, 5+2x3=11 instead of the normal one's 5+2x3=21.

Furthermore, the preferred behavior norm for division and multiplication is different.

Thus, people's difficulty with mathematics is not unjustified. The choice of how you want to approach it is ultimately up to you.

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The equation representing the total cost of getting the computer fixed is T = 0.10V + 20H.

Let's define the variables in this situation:

V = Value of the computer (in dollars)

C = Initial charge (in dollars)

S = Service fee (in dollars)

H = Hours of service

According to the given information, there is an initial charge of 10% of the value of the computer, which can be represented as:

C = 0.10V

Additionally, there is a service fee of $20 per hour, so the total service fee can be calculated as:

S = 20H

The value of the computer is given as $525, so we substitute V with 525 in the equation for the initial charge:

C = 0.10 × 525

Now we can summarize the equation to represent the total cost (T) to get the computer fixed:

T = C + S

Substituting the equations for C and S, we have:

T = 0.10V + 20H

Therefore, the equation representing the total cost of getting the computer fixed is:

T = 0.10V + 20H, where V represents the value of the computer in dollars, and H represents the hours of service.

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Answer:

5

Step-by-step explanation:

-15/(-3)

When dividing a negative by a negative, the negatives cancel out, so you're left with 15/3.

15/3 is 5.

Answer:

Ratio should be equal so ratio is 3:3

The ratio of the triangles to circles in the diagram below would be; 1: 1

Suppose that we've got two quantities with measurements as 'a' and 'b'

Then, their ratio(ratio of a to b) a:b We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained.

Thus, there are three circles and three triangles shown in the figure.

Therefore, the ratio will be;

three circles: three triangle

3 : 3

1: 1

Hence, the ratio of the triangles to circles in the diagram below would be; 1: 1

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There are several reasons that explain why one can expect a negative correlation between class size and test score and these are as follows:

1. Large class sizes might inhibit the ability of teachers to give personalized attention to each of the students and this can cause most of the students to have a low score.

2. Large class sizes will also inhibit student engagement and resource allocation, thus causing most of the students to have low test scores.

There are many reasons why class sizes can have a negative effect on resource allocation. For one thing, when the classroom is large, the students will be unable to have a close relationship with their teachers and this will cause them to have a poor understanding of certain subjects.

One can expect a negative correlation in this case. Also, large class sizes will also limit student engagement.

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Answer: Below

Step-by-step explanation:

The domain is all real numbers. The range is also all real numbers.

Hope this helped!

Answer:

It's C/ Option 3

Step-by-step explanation:

trust me

Answer:

True

Step-by-step explanation:

If one partition is x feet long, the other partition will be 36 - x feet long.

Given that there are 36 feet of dividers, we can use them to create two partitions. Let's assume that one of the partitions is x feet long. Since the total length of the dividers is 36 feet, the length of the other partition can be found by subtracting x from 36. Therefore, the length of the other partition will be 36 - x feet.

This arrangement ensures that the lengths of the two partitions add up to the total length of the dividers. By assigning the variable x to one partition, we can express the length of the other partition in terms of x. Thus, the length of the other partition is given by the expression 36 - x.

In summary, if one partition is x feet long, the other partition will be 36 - x feet long.

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5x+4=-11

so subtract 4 from both sides

your left with

5x=-15

Divide 5 from both sides

x=-3

Answer:

5475.41N

Step-by-step explanation:

Work done = Force × distance

Given

Work done = 16700Joules

Distance = 3.05m

Required

Force

Substitute the given values into the formula as shown

16700 = Force × 3.05

Force = 16700/3.05

Force = 5475.41N

Hence the applied force is 5475.41N

The force required to apply to the person to fire them out of the cannon is required.

The force applied to the person to fire them out the cannon is 5475.41 N.

W = Work done to shoot the person out of the cannon ball = 16700 J

s = Displacement of the person in the cannon = 3.05 m

F = Force applied to the person

Work done is given by

\(W=Fs\\\Rightarrow F=\dfrac{W}{s}\\\Rightarrow F=\dfrac{16700}{3.05}\\\Rightarrow F=5475.409\approx 5475.41\ \text{N}\)

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