Ex 2: A car can get 10 miles on 1 ½ gallons of gas. How many gallons of gas are needed
if you need to go 150 miles?

The code sorts the skill array in ascending order.

It then creates a HashMap to store the number of occurrences of each skill level. The left and right pointers are initialized to point to the first and last elements of the skill array. The result variable is used to store the sum of the effectiveness of all teams that can be created. The code then iterates through the skill array using the left and right pointers. If both pointers point to skills that have more than one occurrence, then two of each skill are used to create the team, and effectiveness is added to the result.

If only one pointer points to a skill with more than one occurrence, then one instance of that skill is paired with one instance of the other skill to form a team. Otherwise, if both pointers point to skills that have only one occurrence, then one instance of each skill is used to create the team. In any case, when a team is created, the HashMap is updated accordingly.

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The value of solution of the expressions are,

⇒ 84.05

We have to given that;

The expression is,

⇒ (8 × 10) + (4 × 1) + (5 × 1/00)

Now, We can simplify as;

⇒ (8 × 10) + (4 × 1) + (5 × 1/100)

⇒ 80 + 4 + (5 × 0.01)

⇒ 84 + 0.05

⇒ 84.05

Thus, the value of solution of the expressions are,

⇒ 84.05

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Answer:

The last one

Step-by-step explanation:

Answer:

C. AB = 5.8 cm

Step-by-step explanation:

In trapezoid ABCD, EF is Midsegment.

\( \therefore EF =\frac{1}{2} (AB + CD) \)

\( \therefore 9.2 =\frac{1}{2} (AB + 12.6) \)

\( \therefore 9.2\times 2= AB + 12.6\)

\( \therefore 18.4= AB + 12.6\)

\( \therefore 18.4-12.6= AB \)

\( \therefore AB= 5.8 \: cm \)

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Have a great day!!!

Answer:

7, since it is the number that pops up the most in the set of data given here

Hope that helps! :)

-Aphrodite

Step-by-step explanation:

Answer:

(-2,6) and (-2,-6)

Step-by-step explanation:

According to the United States Census Bureau, the average number of cars per household in America is 1.84. Therefore, the correct answer is option (d) 1.84.

The expected number of cars in a randomly selected American household can be calculated by finding the mean number of cars per household in America. The mean is calculated by summing up all the number of cars in all households and dividing the total by the number of households. According to the most recent data available from the United States Census Bureau, the total number of households in America is approximately 128 million, and the total number of cars is approximately 236 million.

Mean = Total number of cars / Total number of households

Mean = 236,000,000 / 128,000,000

Mean = 1.84

Therefore, the expected number of cars in a randomly selected American household is 1.84, which corresponds to option (d) in the given options.

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The given statement "When the limit of f(x) exists, it always equals f(a)" is true, and the correct option is D.

The limit of a function f(x) as x approaches a is the value that the function approaches as x approaches a. If the limit exists, it signifies that the function is coming arbitrarily near to a given value as x approaches a. That is the function's limit at a.

When we evaluate the function when x = a, we obtain f(a). So, if the function's limit exists as x approaches a, and if that limit is L, then f(a) = L. This is because the function approaches L arbitrarily close as x approaches a, implying that the function's value at an is also L.

Therefore, we can conclude that the statement "When the limit of f(x) exists, it always equals f(a)" is true, and the correct option is D.

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Answer:

  x = 7

Step-by-step explanation:

The sum of the interior angles is 90°, so you have ...

  (7x +8) +(5x -2) = 90

  12x = 84 . . . . subtract 6; next, divide by 12

  x = 7

Answer:

each card cost = $3.5

Step-by-step explanation:

to spent $15 = $8 + 2cards

$15 = $8 + 2C

$15 - $8 = 2C

$7 = 2C

C = $7 / 2

C = $3.5

therefore each card cost = $3.5

Answer:

$3.50 per card

Step-by-step explanation:

15 = 8 + 2x

x = 7 / 2

x = 3.50

Answer:

her grade is 90

Step-by-step explanation:

The mean number of miles the hiker walked for the 6 days was 6.5 miles.

To calculate the mean or average of a set of numbers, we add up all the numbers and then divide the sum by the number of items in the set. In this case, we have the number of miles the hiker walked on each of the six days. To find the total number of miles the hiker walked, we simply add up all the numbers

8 + 5 + 7 + 2 + 9 + 8 = 39

Next, we divide the total number of miles by the number of days (which is 6) to get the average or mean number of miles the hiker walked per day:

Mean number of miles = Total number of miles / Number of days

= 39 / 6

= 6.5

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Answer:

-7

Step-by-step explanation:

arithmetic sequences are consistant sequences by adding or subtracting a constant term, in this case to get from -6 to -13, you subtract 7. And to get from -13 to -20 you subtract 7 again. The next number in the sequence would be -27 as -20-7= -27

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The common difference of the arithmetic sequence -6, -13, -20 is -7.

To find the common difference of an arithmetic sequence, we subtract any term from the term that follows it.

In the given sequence -6, -13, -20, the common difference can be found by subtracting each term from the term that follows it as:

-13 - (-6) = -13 + 6 = -7

-20 - (-13) = -20 + 13 = -7

From the calculations above, we can see that the common difference of the arithmetic sequence -6, -13, -20 is -7.

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By using the Pythagoras theorem, AC + AD = BC is proved.

The relationship between the sides of a triangle can be proven using the properties of triangles.

Let us denote the length of AC as a and the length of AD as b. Since the triangle is right angled at A, the lengths of its sides must adhere to the Pythagorean theorem, that is a² + b² = (AB)². Additionally, since the bisector of ∠ C intersects the side AB at D, the length of AC must equal the length of AD, that is a = b.

Using the two equations above, we can substitute b for a in the equation a² + b² = (AB)² and solve for a. This results in a = AB/2. Substituting a for AB/2, we get

=> (AB/2)² + b² = (AB)².

Finally, multiplying by 2, we can get AB + 2b² = 2(AB)², which can be simplified to AB + 2b² = 2a².

Since a = b, this can be simplified to

=> AB + 2b² = 4b²,

resulting in AB = 2b².

Therefore, AC + AD = AB = 2b² = 2(AC) = BC, proving that the statement AC + AD = BC holds true for any right triangle right angled at A such that AB = AC and the bisector of ∠ C intersects the side AB at D

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Complete Question:

△ ABC is a right triangle right angled at A such that AB = AC and bisector of ∠ C intersects the side AB at D. Prove that AC + AD = BC.

From the given Venn diagram, the value of  M∩N={4,7}.

A Venn diagram is a prominent diagram type that depicts the logical relationship between sets. It was popularized in the 1880s by John Venn (1834-1923). The diagrams are used to teach elementary set theory and to show simple set relationships in probability, logic, statistics, linguistics, and computer science. To depict sets, a Venn diagram uses basic closed curves drawn on a plane. These curves are almost often circles or ellipses.

Before Venn, similar concepts had been presented. Similar ideas were proposed by Christian Weise in 1712 and Leonhard Euler (Letters to a German Princess) in 1768. Venn popularized the concept in Symbolic Logic, Chapter V "Diagrammatic Representation," 1881.

The intersection of two sets is the set of all the elements that are shared by both.

M={4,7,9,3}

N={4,7,6}

Because M and N share the numbers 4 and 7, M∩N={4,7}.

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The solution of the trigonometric equation is x = 6.49°

A trigonometric equation is an equation that contains the trigonometric ratios.

Given the trigonometric equation 2cot²3x = 7cosec3x -5 (1),  

To solve the trigonometic equation, we use the trigonometric identity

1 + cot²Ф = cosec²Ф

⇒ cot²Ф = cosec²Ф - 1

Substituting Ф = 3x into the equation, we have

⇒ cot²3x = cosec²3x - 1  (2)

So, substituting (2) into the trigonometric equation (1), we have

2cot²3x = 7cosec3x - 5

2(cosec²3x - 1) = 7cosec3x - 5

Expanding the bracket, we have

2cosec²3x - 2 = 7cosec3x - 5

Collecting like terms, we have

2cosec²3x - 7cosec3x + 5 - 2 = 0

2cosec²3x - 7cosec3x + 3 = 0

Let cosec3x = y

2y² - 7y + 3 = 0

Factorizing, we have

2y² - y - 6y + 3 = 0

y(2y - 1) - 3(2y - 1) = 0

(y - 3)(2y - 1) = 0

y - 3 = 0 or 2y - 1 = 0

y = 3 or 2y = 1

y = 3 or y = 1/2

cosec3x = 3 or cosec3x = 1/2

1/sin3x = 3 or 1/sin3x = 1/2 (since cosecФ = 1/sinФ)

sin3x = 1/3 or sin3x = 2

Since sinФ cannot be greater than 1, we ignore the second answer.

So, sin3x = 1/3

Taking inverse sine, we have

3x = sin⁻¹(1/3)

3x = 19.47°

x = 19.47°/3

x = 6.49°

So, the solution is x = 6.49°

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Answer:

3, 7, 20, 1, -4, 9

Step-by-step explanation:

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As per the addition formula, the value of the trigonometric function is -0.809.

In statistics, function is defined as a relationship between inputs where each input is related to exactly one output.

Here we have to find the value of the trigonometric function cos(13/15)cos(-/5)-sin(13/15)sin(-/5)  by using the addition and subtraction formula.

Here we have the following trigonometric function:

=> cos(13/15)cos(-/5)-sin(13/15)sin(-/5)

Now, we have to use the trigonometric addition formula,

=> Cos (A+B) = Cos A Cos B - Sin A Sin B

To solve the given function,

Here let us rewrite the given function based on the addition formula, then we get,

=> Cos ( 13π/15 + (-π/5) )

=> Cos( 12π/5)

=> Cos(144°)

=> -0.809

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Answer:

D n/2 = 9

Step-by-step explanation:

14 + (18) = 32 not 29

6(18)= 108 NOT 3

18 - 7 = 11 NOT 25

The only answer is D because 18 divided by 2 = 9

The mean of X, or the expected value of X, is 9. This means that if we were to conduct the same experiment numerous times, on average, we would expect to observe 9 successes per 15 trials.

In probability theory, a binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials with a constant probability of success. In this case, we have a random variable X that has a binomial distribution with parameters n = 15 and p = 0.6. We are required to find the mean of X, denoted as E(X).

The mean of a binomial distribution is given by the formula E(X) = np, where n is the number of trials and p is the probability of success in each trial. Substituting the given values, we get E(X) = 15 x 0.6 = 9.

It's worth noting that the mean of a binomial distribution represents a measure of central tendency and can be used to make predictions about the likely number of successes in future trials. Additionally, the variance and standard deviation of the binomial distribution can also be calculated using formulas, and these measures provide information about the spread or dispersion of the distribution.

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The mean of X or the expected value of X is 9. This means that if we run the same test many times, on average, we expect to observe 9 successes each time experiment 15.

In probability theory, the binomial distribution is a probability variable that describes the number of successes of a fixed number of experiments. In this case, we have a random variable X that follows a binomial distribution with parameters n = 15 and p = 0.6.

We need to find the mean of X, the mean of E(X).

The mean of the binomial distribution is given by the formula E(X) = np; where n is the number of trials and p is the probability for each trial. Substituting the given values, we get E(X) = 15 x 0.6 = 9.

The binomial distribution represents a measure of central tendency and validity for predicting the number of future successes. trials.

In addition, the model can be used to calculate the variance and standard deviation of the binomial distribution, and these measures provide information about the distribution of the distribution.

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It will take a minimum of 10 clock hours (not driving hours) for the truck driver to travel 450 miles from Charlotte, NC to Pittsburgh, PA.

The current Hours of Service (HOS) rules for truck drivers stipulate that a truck driver cannot drive for more than 11 hours after 10 consecutive hours off duty.

Additionally, the driver is not allowed to drive beyond 14 hours after coming on duty.

The driver's shift includes both driving and non-driving time.

Therefore, it is necessary to consider the total amount of time spent on the job.

The truck driver will have to stop for rest breaks, refueling, or other reasons during the 450-mile journey to Pittsburgh, Pennsylvania. The driver is required to take a 30-minute break after eight hours of driving.

Therefore, the minimum number of clock hours (not driving hours) it will take the truck driver to travel the 450-mile distance from Charlotte, NC to Pittsburgh, PA is calculated as follows:

Time for the trip = (Distance ÷ Average Speed) + Breaks

Time for the trip = (450 ÷ 50) + (30 ÷ 60) × 2

Time for the trip = 9 + 1

Time for the trip = 10 clock hours

Therefore, it will take a minimum of 10 clock hours (not driving hours) for the truck driver to travel 450 miles from Charlotte, NC to Pittsburgh, PA.

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The approximate range is [1,900, infinity), since the population started at 1,900 and will never decrease to a lower

value.

To determine the weekly factor of growth for the insect population, we need to look at the increase in y-values as well

as the increase in x-values. We can find the weekly factor of growth by dividing the y-value of a point by the y-value of

the previous point. For example, to find the weekly factor of growth from week 1 to week 2, we divide 1,900 by 1,000.

To find the weekly factor of growth from week 2 to week 3, we divide 3,8100 by 1,900. Doing this for each interval, we

get: 1,900 ÷ 1,000 ≈ 1.9; 3,8100 ÷ 1,900 ≈ 2.005; The weekly factor of growth for the insect population is approximately

1.9 for the first interval and approximately 2.005 for the second interval.

2. The point (1, 900) represents the population  when it was first measured. Therefore, the population when it was first

measured was 1,900.3. To write an equation relating p and w, we can use the general form of an exponential function:

y = abx, where a is the initial amount (when x = 0), b is the factor of growth (if b > 1) or decay (if 0 < b < 1), and x is the

number of time periods. In this case, we have p = abw, where a = 1,900 and b is the factor of growth. We found in the

first part that the factor of growth for the first interval is approximately 1.9 and for the second interval is approximately

2.005. Therefore, we can write two equations: p = 1900(1.9)w for 0 ≤ w < 3, and p = 1900(2.005)(w - 3) for w ≥ 3.4. To

find p(4), we use the equation for the first interval: p = 1900(1.9)4 ≈ 25,520. This represents the population of the insects

after 4 weeks.5. The approximate domain for this situation is [0, infinity), since the population will continue to increase

over time. The approximate range is [1,900, infinity), since the population started at 1,900 and will never decrease to a

lower value.

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Answer:

B works it satisfies the equation to both 1 ⅔ i = 1 ⅔ i

Answer:

i. false

ii. true

iii. true

iv. false

When comparing negative numbers, if you disregard the negative sign, the apparent greater value will actually be the smaller.

Answer:

22 - 4x

Step-by-step explanation:

4(3-x) + 10  Distribute the 4

4(3) - 4x +10

12 - 4x +10

22 - 4x

Answer:

RATIONAL

Step-by-step explanation:

Answer:

NOT RATIONAL

Step-by-step explanation:

The total amount of time spent on practicing is 3 minutes

To obtain the total practice time, we multiply the time taken by its respective frequency as seen on the plot.

From the plot:

(\((1 * 0) + (1 * 1/4) + (2 * 1/2) + (1 * 3/4) + (1 * 1)\\(0 + 1/4 + 1 + 3/4 + 1)\\= 3\)

Hence, the total amount of time spent is 3 minutes as obtained from the dot plot given.

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