Translate the sentence into an inequality.

A number w divided by 5 is less then 20.

The polar form of the complex number -3√3 - 3i is: z = 6(cos(π/3) - i sin(π/3))

To write the complex number -3√3 - 3i in polar form, we first need to find its modulus and argument.

The modulus (or absolute value) of a complex number is the distance from the origin to the point representing the number in the complex plane. It can be found using the formula:

|z| = sqrt(x² + y²)

where z = x + yi is the complex number.

Applying this formula, we get:

|z| = sqrt((-3√3)² + (-3)²) = \(\sqrt{27 + 9}\)= \(\sqrt{36}\) = 6

The argument (or angle) of a complex number is the angle between the positive real axis and the line connecting the origin to the point representing the number in the complex plane. It can be found using the formula:

arg(z) = atan(y/x)

where z = x + yi is the complex number.

Applying this formula, we get:

arg(z) = atan((-3)/(-3√3)) = atan(√3) = π/3 radians (since tan(π/3) = √3)

Therefore, the polar form of the complex number -3√3 - 3i is:

z = 6(cos(π/3) - i sin(π/3))

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Answer:

a = 12 years

Step-by-step explanation:

Mark is 6 years older than his brother Sam. Now, we are asked to represent Sam’s age by a. This means that if Sam is a years old, Mark is (a + 6) years old.

The sum of their ages is 30, this means that when we add their ages together, we get the sum of thirty.

Mathematically this means a + a + 6 = 30

2a + 6 = 30

This is the equation needed to get a. To get a , we proceed to solve the equation to completion.

2a = 30 - 6

2a = 24

a = 24/2

a = 12

Step-by-step explanation:

Using absolute value to tell wether the sum of two integers is positive or negative.

Suppose we have a positive integer,

x and a negative interger, -x and we want to find their sum, we take the absolute values of each of the integers, that is |x| and |-x|. Then we subtract these values: |x| - |-x|. If the larger integer is positive, the result of the difference is positive, but if the larger number is negative, the result of the difference is negative.

For any integer x, x + (-x) = 0

Answer:

both yes

Step-by-step explanation:

from my understanding an order pair means the x values from all must never match so

Answer:

no is not pairs function

Answer:

4544

Step-by-step explanation:

1136 *4 = 4544

The probability that extra unleaded gas was requested is 35%.

To find the probability that the next customer requested extra unleaded gas, we need to first find the total probability that any customer requests extra unleaded gas.

Since 35% of customers request extra unleaded gas, the probability that a customer requests it is 35%. Of those customers, 30% fill their tanks, so the probability that a customer requesting extra unleaded gas fills their tank is 30%.

Therefore, the probability that a customer requesting extra unleaded gas fills their tank is (35%) * (30%) = 0.105, or about 10.5%.

This is the probability that the next customer requested extra unleaded gas and fills their tank. To find the probability that the next customer simply requested extra unleaded gas, regardless of whether they fill their tank or not, we need to add the probabilities of them requesting extra unleaded gas and either filling or not filling their tank.

The probability that the next customer requested extra unleaded gas and filled their tank is 0.105, as we calculated above. The probability that the next customer requested extra unleaded gas and did not fill their tank is (35%) * (70%) = 0.245, or about 24.5%.

To find the total probability that the next customer requested extra unleaded gas, we need to add these two probabilities: 0.105 + 0.245 = 0.35, or 35%. This is the probability that the next customer requested extra unleaded gas.

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Answer:

a₁₅ = 30

Step-by-step explanation:

The nth term of an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₅ = 10 and a₁₀ = 20 , then

a₁ + 4d = 10 → (1)

a₁ + 9d = 20 → (2)

Subtract (1) from (2) term by term to eliminate a₁

5d = 10 ( divide both sides by 5 )

d = 2

Substitute d = 2 into (1) and solve for a₁

a₁ + 4(2) = 10

a₁ + 8 = 10 ( subtract 8 from both sides )

a₁ = 2

Then

a₁₅ = 2 + (14 × 2) = 2 + 28 = 30

Answer:

  30

Step-by-step explanation:

Evenly-spaced terms of an arithmetic sequence are an arithmetic sequence. You are given terms 5 and 10 and asked to find term 15. The difference between term 15 and term 10 will be the same as the difference between term 10 and term 5.

  5d = a10 -a5 = 20 -10 = 10 . . . . . . . this is 5 times the common difference (d)

  a15 = a10 +5d = 20 +10 = 30

The 15th term is 30.

_____

Additional comment

Another way to look at this is that a10 is the midpoint between a15 and a5. That means ...

  a10 = (a15 +a5)/2

  a15 = 2(a10) -a5 = 2(20) -10 = 30

Answer:

I think it is 7

Step-by-step explanation:

Because 3*4= 12 and 3+4=7 and those are the numbers that make the smallest sum that I can think of

Please Mark Brainlest

Answer:

3/7

Step-by-step explanation:

The expression for the volume of a closed box with a square base of side x and height h is V = x^2 * h, and the expression for the total surface area of the box is A = 4xh + 2x^2.

(a) The expression for the volume, V, of the closed box is given by V = x^2 * h. This expression represents the product of the area of the square base, x^2, and the height, h, of the box. The unit of measurement for the volume would be cubic units, such as cubic meters or cubic feet, depending on the context.

(b) The expression for the total surface area, A, of the closed box can be obtained by adding the areas of all six faces of the box. The box has four identical rectangular faces, each with an area of x * h, and two identical square faces, each with an area of x^2. Therefore, the total surface area can be expressed as A = 4xh + 2x^2. This expression represents the sum of the areas of all six faces of the box. The unit of measurement for the surface area would be square units, such as square meters or square feet, depending on the context.

In summary, the volume and surface area of a closed box with a square base of side x and height h can be expressed as V = x^2 * h and A = 4xh + 2x^2, respectively. These expressions can be useful in various applications, such as calculating the amount of space needed to store objects or materials or determining the amount of material needed to construct the box.

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The depth of the 84 inches wide satellite dish that has the receiver located 15 inches above the vertex is 29.4 inches.

The location of the receiver = 15 inches above the vertex

Width of the dish = 84 inches

The receiver of a satellite dish is normally located at the focus (focal point).

Taking the shape of the satellite dish as a parabola, and writing the equation of the parabola as x² = 4•a•y, we have;

Coordinates of the focus = (0, a)

Where;

a = The distance of the focus above the vertex

Therefore;

a = 15 inches

The dish is horizontally spaced equally about the vertex.

The farthest point horizontally from the vertex, X, of the dish corresponds to the furthest vertically from the vertex, which is the maximum depth or height, Y.

At the maximum height, from the vertex, Y, (farthest point, vertically from the vertex), we have;

X = 84 ÷ 2 = 42

Which gives;

42² = 4 × 15 × Y

Y = 42² ÷ (4 × 15) = 29.4

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An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.

In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.

Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors

.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).

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Answer:

There are 59,049 different ways of answering the exam.

Step-by-step explanation:

The first thing we need to count is the total number of selections, then we need to count the number of options for each one of these selections. The total number of combinations will be equal to the product between all the numbers of options.

Here, the selections are each one of the 10 questions, so we have 10 selections.

And each one of these selections has 3 options (true, false, blank)

So, we have 10 selections with 3 options each, then the total number of combinations will be:

C = 3*3*3*3*3*3*3*3*3*3 = 3^10

C = 59,049

There are 59,049 different ways of answering the exam.

The constraints for the company are -

70<x<130, 50<y<110 and 150<x + y<220

The objective function for maximizing profit is z = 65x + 45y.

What are business constraints?

Constraints can be business or technical in nature and are defined as restrictions or limitations on possible solutions.

Considering that x is the number of laptops and y is the number of tablets.

According to the information provided, there are between 70 and 130 laptops.

Additionally, there are between 50 and 110 tablets.

Specifically, 70<x<130 and 50<y<110.

Between 150 and 220 devices make up the total number of x + y.

This equals 150<x + y<220.

These are all limitations on daily production.

Since each laptop makes $65 in profit and each tablet makes $45.

As a result, the overall profit for laptops is $65x and for tablets it is $45y.

Consequently, the objective function z for calculating total profit is -

z = 65x + 45y

Maximize z = 65x + 45y to make the most profit.

Therefore, the constraints and maximum profit is obtained.

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A company makes two types of electronic devices: laptops and tablets. Its business plan says that it must produce from 70 to 130 laptops, and from 50 to 110 tablets, per day. The total number of devices it must make per day according to the plan ranges from 150 to 220. Given that x is the number of laptops made per day, and y is the number of tablets made, what are the daily constraints that the plan places on the company? The company sells all the electronic devices it makes. Its profit is $65 for every laptop sold and $45 for every tablet sold. What is the objective function for maximizing profit?

If we employ the law of cosines, for C= mi; assuming LA is opposite side a, ZB is opposite side b, and ZC is opposite side c, c ≈ 1.821 miles.

To determine c, let's employ the law of cosines, which is given by:c² = a² + b² - 2ab cos(C)

Here, c is the length of the side opposite angle C, a is the length of the side opposite angle A, b is the length of the side opposite angle B, and C is the angle opposite side c.

Now we'll plug in the provided values and solve for c. c² = (2.82)² + (3.23)² - 2(2.82)(3.23)cos(40.2

)c² = 7.9529 + 10.4329 - 18.3001cos(40.2)

c² = 17.3858 - 14.0662

c² = 3.3196

c ≈ 1.821

Therefore, c ≈ 1.821 miles when rounded to three decimal places.

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Answer: 9x + 6y = 234

Step-by-step explanation:

Answer:

234

Step-by-step explanation:

it makes more sense then the others

Answer:

36 Degrees

Step-by-step explanation:

First the entire angle of BAC is 71 degrees, so all you have to do is subtract the known angle (2) by the entire angle. 71-35= 36. So that means the measure of angle 1 is 36 degrees.

The graph of g(x) is the graph of f(x) stretched vertically and reflected over the axis.

The correct option is C.

We can compare the graphs of two functions f(x)=x² and g(x)=-2/3 x² by determining their vertices, domain, range, axis of symmetry, and shape of the graphs. The vertex of f(x)=x² is at the origin (0,0), which means that the parabola opens upward and is symmetrical around the y-axis.

The domain is all real numbers, and the range is y≥0. The axis of symmetry is the y-axis. On the other hand, the vertex of g(x)=-2/3 x² is also at the origin, and it opens downward. It is also symmetrical around the y-axis. The domain is all real numbers, and the range is y≤0.

The axis of symmetry is the y-axis, just like f(x).It is important to remember that g(x) is the negative of f(x), which indicates that g(x) is reflected across the x-axis. Furthermore, the stretch factor is 2/3, which makes the graph of g(x) flatter than the graph of f(x) and it is  stretched vertically and reflects over x axis(option c).

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Answer: m=5

Step-by-step explanation:

Answer: 5

Step-by-step explanation:

Answer: D) Increase the sample size and decrease the confidence level.

Step-by-step explanation:

A reduced interval width means that the data is more accurate. This can only be achieved if the sample size is increased because a larger sample size is able to capture more of the characteristics of the variables being tested.

A smaller confidence interval will also lead to a reduced interval width because it means that the chances of the prediction being correct have increased.

Answer: 6

Step-by-step explanation: Area = 1/2 (a+b) x h, divide both side by 1/2(a+b), we have Area : (1/2 (a+b)) = h. Now, replace A = 24, a=5.8, b= 2.2. We got h = 6.

On assuming the given Hexagons are similar then the changes that will result in pair of Non Similar Hexagons is :

(c) adding 15° to angles G, H, and I and subtracting 15° from angles J, K and L .

The Hexagons are said to be similar if they have matching sides in the same proportion .

If the same operation is performed on every side of the hexagon , then the hexagon will remain similar ,

So , from the given operation , the operation that is not performed on each side or on each hexagon , it will result in  Non similar hexagon .

The operation performed in option (c) performs addition on G, H, I and subtraction on angles J, K, L .

Therefore , it will result in Non Similar Hexagons .

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Answer:

26.6666666667

Step-by-step explanation:

3/4 of a hour is 45 minutes 12 ÷ by 0.45 would equal 26.6666666667

The first 5 terms of the sequence are: 5, 15, 25, 35, 45.

To find the first 5 terms of the sequence given by A(n) = 5 + (n - 1) * 10, we substitute the values of n from 1 to 5 into the formula.

A(1) = 5 + (1 - 1) * 10 = 5 + 0 = 5

A(2) = 5 + (2 - 1) * 10 = 5 + 10 = 15

A(3) = 5 + (3 - 1) * 10 = 5 + 20 = 25

A(4) = 5 + (4 - 1) * 10 = 5 + 30 = 35

A(5) = 5 + (5 - 1) * 10 = 5 + 40 = 45

Therefore, the first 5 terms of the sequence are: 5, 15, 25, 35, 45.

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There are 144 ways to form a five-digit number that is divisible by 5 using the numerals 0, 1, 2, 3, 4, and 5 without repetition.

For the number to be divisible by 5, its units digit must be either 0 or 5. Since we cannot repeat digits, we have two cases to consider:

Case 1: The units digit is 0.

In this case, we have 5 choices for the units digit (0, 1, 2, 3, or 4). For the remaining four digits, we can choose them in 4! ways (i.e., 4 choices for the first digit, 3 choices for the second digit, 2 choices for the third digit, and 1 choice for the fourth digit).

Therefore, the total number of five-digit numbers that are divisible by 5 and have a units digit of 0 is:

5 × 4! = 120

Case 2: The units digit is 5.

In this case, we have only one choice for the units digit, which is 5. For the remaining four digits, we can choose them in 4! ways as before.

Therefore, the total number of five-digit numbers that are divisible by 5 and have a units digit of 5 is:

1 × 4! = 24

The total number of ways to form a five-digit number that is divisible by 5 without repeating digits is the sum of the numbers from both cases:

120 + 24 = 144

Therefore, there are 144 ways to form a five-digit number that is divisible by 5 using the numerals 0, 1, 2, 3, 4, and 5 without repetition.

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The scatter plot shows the results of the survey and yes, there is an outlier in the data set which is the lowest time value of grade 11 and it is an outlier because it is an extremely low data point relative to the nearest data point.

This is referred to as an extremely high or extremely low data point relative to the nearest data point and the rest of the neighboring co-existing values in a data graph.

The outlier is at the lowest time value if grade 11 and it falls under such category because it is an extremely low data point relative to the nearest data point in the given graph.

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Rounding to the nearest whole number, she will have run a total distance of 13 kilometers after 16 days.

To find out how far she will have run in total after 16 days, we can use the formula for calculating compound interest:

A = P(1 + r/100)^n

Where:

A = Total distance run after n days

P = Initial distance (4.8 kilometers)

r = Rate of increase per day (6.9%)

n = Number of days (16)

Plugging in the given values, we can calculate the total distance:

A = 4.8(1 + 6.9/100)^16

Using a calculator or performing the calculations step by step, we get:

A ≈ 4.8(1.069)^16 ≈ 4.8(2.092473)^16 ≈ 4.8(2.628)

A ≈ 12.6144

Rounding to the nearest whole number, she will have run a total distance of 13 kilometers after 16 days.

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