A motorist is pumping gas into a car at a rate of 5/12 of a gallon every 1/24 of a minute. At this rate, how many gallons of gas will he have pumped into his car on 1/2 of a minute?

The solution involves sorting the points by their x-coordinate, and then checking for collinearity by comparing the slopes of all pairs of points.

To determine in O(n² log n) time whether any three points in a set of n points are collinear, we first sort the points by their x-coordinate. This can be done in O(n log n) time using a standard sorting algorithm such as QuickSort.

Then, for each pair of points, we calculate the slope between the points and store it in a hash table. If two points have the same slope, then we know that the three points are collinear.

By checking all pairs of points, we can determine in O(n²) time whether any three points are collinear. The overall time complexity of the solution is O(n² log n), since sorting the points takes O(n log n) time, and checking for collinearity takes O(n²) time.

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26 cards must be selected from a standard deck of 52 cards to guarantee that at least four hearts, four diamonds and five clubs are selected.

We have given that standard deck of 52 cards.

And we have to find the number of cards must be selected from a deck to get at least four hearts, four diamonds and five clubs.

So four hearts + four diamonds + five clubs = 13 cards

The worst case, we may select all the spade i.e 13 cards before any heart, diamond and club.

So the guarantee that at least four hearts, four diamonds and five clubs are selected, 13 + 13 = 26

Therefore 26 cards must be selected from standard deck of 52 cards to guarantee that at least four hearts, four diamonds and five clubs are selected.

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Answer:

Step-by-step explanation:

model car 1 : regular car 16

model 6.25 inches : actual car 6.25*16 = 100 inches

1foot = 12 inches

100/12 = 8 feet and 4 inches

model car 2 : regular car 35

model 6.25 inches : actual car 6.25*35/2 = 109. 375 inches

Equation::

If words be x

Equation in slope intercept form

So

#1

More words=25-15=10

Cost:-

#2

Extra words=50-15=35

Cost:-

Answer:

a. $17.50

b. $31.25

Step-by-step explanation:

a.

For $12 you get 15 words.

For a 25-word ad, you need 10 more words than the 15 you get for $12, so you must add 10 words at $0.55 per word.

cost = $12 + 10 × $0.55

cost = $12 + $5.5

cost = $17.50

b.

50 words is 25 words more than 25 words, so you must pay for 25 words more than the cost of the 25-word ad in part a.

cost = $17.50 + 25 × $0.55

cost = $17.50 + $13.75

cost = $31.25

The dimensions (in m) maximize its volume  is  mathematically given as

\(x=\frac{4\sqrt{3}}{3}\) m   for Lenght and Width

\(h=\frac{2\sqrt{3}}{3}\) m  for height

Generally, the equation for is  mathematically given as

The equation for the area is given as

\(A=x^2+4xh\\\\A=16=4xh\\\\ A=16-x^2\)

\(h=\frac{16-x^2}{4x^2}\)

Volume of box

\(V=x^2 *h\\\\V=x^2*(\frac{16-x^2}{4x^2})\\\\V=4x-x^3\)

Therefore, by differentiating V and making x the subject of the formula we have

\(V'=4-\frac{3x^2}{4}\)

Therefore, with V' =0

\(x^2=16/3\)

\(x^2=\sqrt{16/3}\\\\x=\frac{4}{\sqrt{3}}\\\\\)

\(x=\frac{4\sqrt{3}}{3}\)

Now we will sub the value of x to the h equation

\(\begin{aligned}&h=\frac{16-(\frac{4}{\sqrt{3}})^2}{4 (\frac{4}{\sqrt{3}})} \\\\&h=\frac{16-\frac{16}{3}}{\frac{16}{\sqrt{2}}} \\\\&h=\frac{2 \sqrt{3}}{3} \mathrm{~m}\end{aligned}\)

Now we differntite the derivate of V (V')

\(V''=\frac{-3x}{2}\\V''=\frac{3(\frac{4\sqrt{3}}{3})}{2} \\V''=-2\sqrt{3} < 0 \\\\\) at maximium

In conclusion, the dimensions (in m) maximize its volume.

\(x=\frac{4\sqrt{3}}{3}\)    for Lenght and Width

\(h=\frac{2\sqrt{3}}{3}\)   for height

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The fraction as a mixed number can be written as 4 and 7/10.

If there is a fraction, containing numerator(upper value) and denominator(lower value).

When the numerator is less than the denominator, the fraction is called proper fraction, otherwise it is an improper fraction.

A proper fraction is also called a fraction which is less than 1 And an improper fraction is ≥ 1

Since mixed fraction contains a sum of whole number and a proper fraction.

We have given the 47/10

Now,

it can be written as;

4 7/10

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The complete question is;

Write 47/10 as a mixed number.

Answer: wee wee woo woo peep pop doo doo

Step-by-step explanation:You have to be a cool kid to know answer

Answer: Ax+By=c

2x+6y=14

4x+1y=8

x=1.54

y=1.82

Step-by-step explanation:

For a particle in an elliptical orbit with time period T, the expression 1/ε^2 = 4/3 holds, where ε is the eccentricity of the ellipse.



To derive the expression for the time period of a particle moving in an elliptical orbit, we can start by considering Kepler's Second Law, which states that the area swept out by the radius vector of the particle in equal intervals of time is constant.

Using this law, we can equate the area swept out by the particle in one complete orbit to half the area of the ellipse. This gives us:

π * a * b = (1/2) * π * a * b * (1 - e^2),

where a is the semi-major axis, b is the semi-minor axis, and e is the eccentricity of the ellipse.

By simplifying this equation, we get:

1 - e^2 = (1/2)^2,

which yields:

e^2 = 1 - (1/2)^2 = 3/4.

Finally, taking the square root of both sides, we obtain:

e = √(3/4) = √3/2.

Therefore, 1/ε^2 = 1/(√3/2)^2 = 4/3.

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(a) Number of 18-bit strings with exactly eight 1's: C(18, 8).

(b) Number of 18-bit strings with at least fifteen 1's: \(2^18 - (C(18, 0) + C(18, 1) + C(18, 2) + ... + C(18, 14)).\)

(c) Number of 18-bit strings with at least one 1: \(2^18 - 1.\)

(d) Number of 18-bit strings with at most one 1: C(18, 0) + C(18, 1) = 1 + 18 = 19.

In mathematics, the binomial coefficient, often denoted as "n choose k" or "C(n, k)", is a value that represents the number of ways to choose k objects from a set of n distinct objects without regard to their order. The binomial coefficient is calculated using combinatorial formulas and plays a fundamental role in combinatorics and probability theory.

(a) To determine the number of 18-bit strings that contain exactly eight 1's, we need to choose the positions for the 1's in the string. The total number of ways to choose the positions is given by the binomial coefficient. In this case, we have 18 positions to choose from, and we want to choose 8 positions for the 1's. Therefore, the number of 18-bit strings with exactly eight 1's is given by:

C(18, 8)

(b) To determine the number of 18-bit strings that contain at least fifteen 1's, we can consider the complement. The total number of 18-bit strings is 2¹⁸ since each bit has 2 possible values (0 or 1). To find the number of strings with at least fifteen 1's, we subtract the number of strings with fewer than fifteen 1's from the total number of strings:

\(2^18 - (C(18, 0) + C(18, 1) + C(18, 2) + ... + C(18, 14))\)

(c) To determine the number of 18-bit strings that contain at least one 1, we can again use the complement. The total number of 18-bit strings is \(2^18\), and the number of strings with no 1's is 1 (the all-0 string). So, the number of strings with at least one 1 is:

\(2^{18} - 1\)

(d) To determine the number of 18-bit strings that contain at most one 1, we can count the number of strings with no 1's (1 string) and the number of strings with exactly one 1 (C(18, 1)). So, the total number of strings with at most one 1 is:

C(18, 0) + C(18, 1) = 1 + 18 = 19

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The graph is given in the image below:

To plot a full cycle of y = 7sin(6x), begin by dividing the period (2π) by six to obtain π/3, which is then used to mark every increment of π/6 along the x-axis.

Additionally, since y ranges from -7 to 7, label the y-axis in increments of either 1 or 2.

Plot the key points at (0,0), (π/12,7), (π/6,0), (π/4,-7), and (π/3,0), and finally connect them smoothly with a curve to complete the plot of one full cycle.

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Answer:

Yes I agree

Step-by-step explanation:

The value of z can be easily determined using the property of linear pair and alternate angles

Given that:

A figure with two parallel lines and the values of x, y, and z are undetermined.

She might be thinking in the following ways:

If she gets the value of x, she can find the value of the exterior angle using linear pair.

The angle formed by the linear pair of x is alternate to z.

The alternate angles are equal to each other.

So, the value of z is determined.

Thus, the value of z can be easily determined using the property of linear pair and alternate angles.

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Answer:

x=2

Step-by-step explanation:

20 - 7x = 6x - 6

      +7x   +7x

----------------------------

20 =  13x - 6

+6              +6

----------------------------

26 = 13x

----    -----

13x      13x

Answer:

First, we will divide 130/2 = 65. This is how much miles he travels in 1 hour. Then, we divide 65/ 2 = 32.5 or 32. Mr. Peters travel 32.5 milies or you can say it as 32.

I hope this helps!

Step-by-step explanation:

The given system of linear equations has infinitely many solutions with one arbitrary parameter.

To solve the system of linear equations, let's simplify the equations and group the variables:

Equation 1: 3x + 5y + 5z = 0

Equation 2: -3x + 8y + 7z = 0

Equation 3: -2x + 4y - 10z = 0

If we subtract Equation 1 from Equation 2, we get:

11y + 2z = 0 ---> y = -2z/11

If we subtract Equation 1 from Equation 3, we get:

5x - 9y - 15z = 0 ---> x = 9y/5 + 3z

Now, we can express the solutions in terms of an arbitrary parameter. Let's choose z as the arbitrary parameter. Then we have:

y = -2z/11

x = 9(-2z/11)/5 + 3z ---> x = -18z/55 + 3z ---> x = (-18z + 165z)/55 ---> x = 147z/55

Thus, the solution to the system of linear equations can be written as:

x = 147z/55, y = -2z/11, z = z

Since z is the arbitrary parameter, we can set it equal to itself. Therefore, the system has infinitely many solutions with one arbitrary parameter.

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Answer:

if my math is correct

Step-by-step explanation:

2501.50

2504.65

Answer:

0.25 or 25%

Step-by-step explanation:

65*2x=_________

32x+1=_________

x=65*2x=32x+1

`this is the solution `

The Scientific notation of given numbers are  \(3400=3.4 \times 10^{-3}\), \(0.000023=2.3 \times 10^{5}\), 4.50, \(1,000,000=1 \times 10^{6}\) and \(0.00671=6.71 \times 10^{-3}\).

The given numbers are 3400, 0.000023, 4.50, 1,000,000 and 0.00671.

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.

Now, \(3400=3.4 \times 10^{-3}\), \(0.000023=2.3 \times 10^{5}\), 4.50, \(1,000,000=1 \times 10^{6}\) and \(0.00671=6.71 \times 10^{-3}\).

Therefore, the Scientific notation of given numbers are  \(3400=3.4 \times 10^{-3}\), \(0.000023=2.3 \times 10^{5}\), 4.50, \(1,000,000=1 \times 10^{6}\) and \(0.00671=6.71 \times 10^{-3}\).

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Answer:

16 weeks

Step-by-step explanation:

just took test today hope this help mark me as brailist and add me

Answer:

16 weeks

Step-by-step explanation:

\(y = -27x + 577\)

Since y represents the amount of money left in her account, we can replace it with $145 to solve for x (number of weeks)

\(145=-27x+577\)

Switch sides:

\(-27x+577=145\)

Subtract 577 from both sides:

\(-27x+577-577=145-577\\\)

\(-27x=-432\)

Divide both sides by -27:

\(\frac{-27x}{-27}=\frac{-432}{-27}\)

\(x=16\)

After 16 weeks, Alma will have $145 left in her account.

Answer:

answer is ABCD

Step-by-step explanation:

I took the quiz

Answer:

4 digit

The answer is 2255

Step-by-step explanation:

√5085025 = 2255

Thus, The answer is 2255

-TheUnknownScientist 72

Answer:

Step-by-step explanation:

36/6x9/3=18x

Answer: 18

Step-by-step explanation: 36/6×9/3

36/6=6

6×9/3

54/3

18

​  

Answer:

Step-by-step explanation:

to ez its =12

Answer:

a b c and 6

Step-by-step explanation:

Answer:

it's B,C and E

Step-by-step explanation

do you people go to flvs?

Partial initialization allows us to initialize only some elements of an array, leaving the rest with default values.

The statement you provided, `int num]= (88, 92, 75, 95, 82)`, contains syntax errors and is not a valid example of partial initialization of an array in C or C++.

To understand partial initialization of an array, let's consider a correct example. Suppose we have an integer array named `num` with a size of 10. We want to initialize the first five elements of the array with specific values, and the remaining elements should be set to 0. Here's how partial initialization would look like:

int num[10] = {88, 92, 75, 95, 82};

In this example, we declare an integer array `num` with a size of 10. We provide an initializer list inside curly braces `{}` to initialize the elements of the array. The first five elements are explicitly initialized with values `88`, `92`, `75`, `95`, and `82`. The remaining elements are automatically set to 0 because we haven't provided explicit values for them.

Partial initialization allows us to initialize only some elements of an array, leaving the rest with default values. It's particularly useful when we want to set certain values while keeping others as defaults, such as zero in the case of integers.

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Answer:

102

Step-by-step explanation:

24+12+5+17+6+19+4+15=102

Answer:

5

Step-by-step explanation:

9×5/9=45/9

=5

just multiply the stuff in parantheses and then add and then divide.

Answer:

5

Step-by-step explanation:

3^2*(2+3); 9*5=45

(2+1)*3; (3)*3=9

So 45/9 =5

Answer:

See Explanation

Step-by-step explanation:

The graphs are not given; however, I'll answer with the graph equation and also attach the graph...

Represent the boxes with x and the cash received with y.

When x = 5

y = 13.50

When x = 10

y = 27

First, we need to get the slope of the graph.

m = (y2 - y1)/(x2 - x1).

m = (27 - 13.5)/(10 - 5)

m = 13.5/5

m = 2.7

Next, is to determine the graph equation using

y - y1 = m(x - x1)

y - 13.5 = 2.7(x - 5)

y - 13.5 = 2.7x - 13.5

y = 2.7x - 13.5 + 13.5

y = 2.7x..

See Attachment for graph

Answer:

x = 60°

Step-by-step explanation:

Given that it is a right triangle, then it means that one of its angles has a measure of 90°. And since we have another angle with a measure of 30°, then we can add these two measures and subtract from 180° (because the sum of the measures of all the angles within a triangle is 180°).

Therefore:

x = 180° - 90° - 30°

x = 60°