Using Ohm’s law, work out the following basic formula’s. V = 2
Amps × 6 Ohms I = 12V ÷ 6R R = 12V ÷ 4I

The parametric equations for the line passing through (-4, 7) and parallel to the vector <6, -9> are x = -4 + 6t and y = 7 - 9t, where t is the parameter determining the position on the line.

To find the parametric equations for the line passing through the point (-4, 7) and parallel to the vector <6, -9>, we can use the point-slope form of a line.

Let's denote the parametric equations as x = x₀ + at and y = y₀ + bt, where (x₀, y₀) is the given point and (a, b) is the direction vector.

Since the line is parallel to the vector <6, -9>, we can set a = 6 and b = -9.

Substituting the values, we have:

x = -4 + 6t

y = 7 - 9t

Therefore, the parametric equations for the line are x = -4 + 6t and y = 7 - 9t.

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Answer:

output = 8

Step-by-step explanation:

1. To solve for the output of the equation, we plug in the value of the input, 18, and simplify.

2. (Solving)

Therefore, the output is 8.

An equation is formed when two equal expressions. The output of y= 2/3x −4 when the input is 18 is 8.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The output of y= (2/3)x −4 when the input is 18 are,

y = (2/3)x - 4

y = (2/3)18 - 4

y = 12 - 4

y = 8

Hence, the output of y= 2/3x −4 when the input is 18 is 8.

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Answer:

   -3/2

Step-by-step explanation:

Slope = y2 - y1 over x2 - x1

-5 - (-2) = -3

-1 - (-3) = 2

Answer: - 3/2

Answer:

No, No, Yes, Yes, Yes.

Step-by-step explanation:

A integer is a whole number. 1, 2, 3, etc.

Answer:

Only -46 is an integer number and others are not.

Step-by-step explanation:

An integer is a whole number but not a fractional number that can be positive, negative, or zero.

In this chart -46 is an integer cause it is a whole number and -1/2, 57.68, 24/6, 9/3 are not integers cause they are a fraction.

Answer:

True,True,3=8-5 (y=3),E,39

Step-by-step explanation:

The sum of the 3rd triangular, 4th square, 5th pentagonal, 6th hexagonal, 7th heptagonal, and 8th octagonal numbers is 384.

What is triangle ?

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted triangle ABC.

The nth triangular number is given by the formula: n(n+1)/2

The nth square number is given by the formula: n^2

The nth pentagonal number is given by the formula: n(3n-1)/2

The nth hexagonal number is given by the formula: n(2n-1)

The nth heptagonal number is given by the formula: n(5n-3)/2

The nth octagonal number is given by the formula: n(3n-2)

So, the sum of the 3rd triangular number, 4th square number, 5th pentagonal number, 6th hexagonal number, 7th heptagonal number and 8th octagonal number can be calculated as follows:

Triangular number: 3 * (3 + 1) / 2 = 6

Square number: 4^2 = 16

Pentagonal number: 5 * (3 * 5 - 1) / 2 = 35

Hexagonal number: 6 * (2 * 6 - 1) = 91

Heptagonal number: 7 * (5 * 7 - 3) / 2 = 98

Octagonal number: 8 * (3 * 8 - 2) = 128

The sum of these numbers is: 6 + 16 + 35 + 91 + 98 + 128 = 384.

So, the sum of the 3rd triangular, 4th square, 5th pentagonal, 6th hexagonal, 7th heptagonal, and 8th octagonal numbers is 384.

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The sum of the 3rd triangular, 4th square, 5th pentagonal, 6th hexagonal, 7th heptagonal, and 8th octagonal numbers is 384.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted triangle ABC.

The nth triangular number is given by the formula: n(n+1)/2

The nth square number is given by the formula: n^2

The nth pentagonal number is given by the formula: n(3n-1)/2

The nth hexagonal number is given by the formula: n(2n-1)

The nth heptagonal number is given by the formula: n(5n-3)/2

The nth octagonal number is given by the formula: n(3n-2)

So, the sum of the 3rd triangular number, 4th square number, 5th pentagonal number, 6th hexagonal number, 7th heptagonal number and 8th octagonal number can be calculated as follows:

Triangular number: 3 * (3 + 1) / 2 = 6

Square number: 4² = 16

Pentagonal number: 5 * (3 * 5 - 1) / 2 = 35

Hexagonal number: 6 * (2 * 6 - 1) = 91

Heptagonal number: 7 * (5 * 7 - 3) / 2 = 98

Octagonal number: 8 * (3 * 8 - 2) = 128

The sum of these numbers is: 6 + 16 + 35 + 91 + 98 + 128 = 384.

So, the sum of the 3rd triangular, 4th square, 5th pentagonal, 6th hexagonal, 7th heptagonal, and 8th octagonal numbers is 384.

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Answer:

k=30

Step-by-step explanation:

The formula for calculating the mean from a frequency table is:

\( \displaystyle \overline{x} = \frac{ \sum \: fx}{ \sum f} \)

we have

So our equation is

\( \displaystyle 7= \frac{ 120 + 3k}{30} \\ \implies \dfrac{120 + 3k}{30} = 7\)

Solving the equation yields:

\(\implies 120 + 3k = 210 \\ \implies 3k = 90 \\ \implies \boxed{k = 30}\)

Answer:

k = 30

Step-by-step explanation:

The formula for the mean is:

\(\boxed{\displaystyle \text{Mean}=\overline{x}=\dfrac{\sum fx}{\sum f}}\)

where:

Given:

  \(\displaystyle \sum f=30\)

  \(\displaystyle \sum fx=120+3k\)

  \(\overline{x}=7\)

Substitute the given values into the formula and solve for k:

\(\implies 7=\dfrac{120+3k}{30}\)

Multiply both sides by 30 to eliminate the denominator on the right side:

\(\implies 210=120+3k\)

Subtract 120 from both sides:

\(\implies 90=3k\)

Divide both sides by 3:

\(\implies k=30\)

Therefore, k = 30.

Answer:

Step-by-step explanation:

As per diagram, the triangles have 3 congruent sides:

So they are congruent by SSS criteria

The number of combinations of random samples of 5 students can be 792.

Given, 12 groups of students

We have to select random samples of 5 students,

Here we will use the combination formula,

Cₙ,ₓ = n! / x! (n - x)!

Here n=12 and x=5

Cₙ,ₓ = 12! / 5! (7!)

Cₙ,ₓ = 479,001,600 / (120) × (5040)

Cₙ,ₓ = 792

Therefore the possible ways of selecting the random samples of 5 students are 792.

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Answer:

Step-by-step explanation:

Answer:5 rational numbers are 19/27, 20/27, 21/27, 22/27, 23/27

Step-by-step explanation:

Answer:

(A.) & (D.) are your answers i hope you have a great day

Step-by-step explanation:

Answer:

no solutions

Step-by-step explanation:

-7 does not equal 7, so there are no solutions.

Infinite solutions would be if it was two equal values, for example, 7 = 7.

Answer:

-1/125

Step-by-step explanation:

1/(-5)^3

evaluate

1/-125

Answer:

\(\displaystyle [-1, 2]\)

Step-by-step explanation:

\(\displaystyle -2x + [1 - x] = 4 → 4 = 1 - 3x → \frac{3}{3} = \frac{-3x}{3}; -1 = x, 2 = y \\ \\ [-1, 2]\)

I am joyous to assist you at any time.

Answer:

Function 1 rate of change: 1/2

Function 2: 5/6

Function 2 has the greatest rate of change

Step-by-step explanation:

For an exam next week, Julietta spends 2 hours studying each night for 7 nights, while Mark crams his sessions into 2 blocks of 7 hours, hence based on spacing effect, it can be predicted that Julietta’s memory would be stronger than Mark.

Spacing effect refers to an observation that repetitions that is spaced in time (spaced learning) can produce stronger long-term memories than repetitions massed closer together in time (massed learning). According to research, spaced learning has demonstrated consistently to offer benefit memory as opposed to massed learning. Spaced learning can lead to enhanced long-term memory and recollection of information learn becomes more easier than in massed learning.

In this case, Julietta opted for spaced learning, spend two hour each night studying for seven nights (the repetition of subject topic spaced over a period of week).  Mark opted for massed learning, cram his session in two blocks of seven hours straight (repetition of subject topic contracted over a short period of two blocks). Hence, Julietta will be enabled to remember the material more easily than Mark

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The statement "As long as N is significantly less than K, logistic growth is indistinguishable from exponential" is false. If dN/dt > 0, then N increases.

The statement "As long as N is significantly less than K, logistic growth is indistinguishable from exponential" is false. Logistic growth takes into account the carrying capacity of the environment, represented by K, which limits the growth of a population as it approaches this limit. In contrast, exponential growth assumes an unlimited supply of resources and no constraints on population growth. Therefore, as N approaches K, logistic growth begins to level off, while exponential growth continues to increase indefinitely.
If dN/dt > 0, then N increases. This means that the population size is growing at a positive rate. If dN/dt is equal to zero, then N remains stable, indicating that the population size is not changing. Finally, if dN/dt is negative, then N decreases, indicating that the population size is shrinking. Therefore, the correct answer to this question is "increases."

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In positive exponents, the simplified form of the above polynomial is s⁷/t¹¹.

A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables. x2 4x + 7 is an example of a polynomial with a single indeterminate x. A polynomial is an expression in mathematics that consists of variables (also known as indeterminates) and coefficients and includes only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Here,

=4s⁵*t⁻⁷/-2s⁻²*-2t⁴

=s⁷/t¹¹

The simplified form of given polynomial is s⁷/t¹¹ in positive exponents.

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Answer:

Angle IAJ

Step-by-step explanation:

X idea again. They are opposite to each other in the immediate area around them.

The question is about linear transformation. T[3] is equal to [6/7], and T[5] is equal to [18/7, -11].

In the given linear transformation T:\(R^{2}\) -> \(R^{3}\), we are given that T[7] = [2] and T[3a+b] = [18, -11]. From the information T[7] = [2], we can deduce that T[1] = (1/7)T[7] = (1/7)[2] = [2/7].

To find T[3a+b], we can write it as T[3a] + T[b]. Since T is a linear transformation, we have T[3a+b] = 3T[a] + T[b].

From the given equation T[3a+b] = [18, -11], we can equate the corresponding components: 3T[a] + T[b] = [18, -11].

Using the previously found value of T[1] = [2/7], we can rewrite the equation as: 3(a/7)[2] + T[b] = [18, -11].

Simplifying, we have (6/7)a + T[b] = [18, -11]. Comparing the components, we get: (6/7)a = 18 and T[b] = -11.

Solving the first equation, we find a = 21. Therefore, T[3] = 3T[1] = 3[2/7] = [6/7] and T[5] = 3T[1] + T[2] = 3[2/7] + [-11] = [18/7, -11].

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A parametric description of the solution set of a linear system is the same as solving the system is the false statement.

If a linear system has at least one solution, only then can the solution set be stated using a parametric description. The set of ordered pairs that make up the solution to an equation with two variables is referred to as the solution set. You'll discover what a solution set is in this tutorial and witness an example. By combining two equations with two variables into one equation with one variable, we can solve a system of equations. Since there are two variables in each equation in the system, replacing a variable with an expression can help minimize the number of variables in an equation.

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m∠FHG is given as 120 degrees

100 + ∠FJG = 180 degrees

∠FJG = 80 degrees

∠BGD = ∠AGJ They are vertically opposite

∠HGI + ∠GIH + ∠IHG = 180

40 + 80 + ∠IHG = 180

∠IHG = 60 degrees

∠IHG + m∠FHG = 180 degrees

60 + m∠FHG = 180

m∠FHG = 120 degrees

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Answer:

Step-by-step explanation:

(a) The center of the circle is also the circumcenter of the triangle PQR.

Since ΔPQR is equilateral, all sides are equal, therefore opposite angles are also congruent:

Sum of the three angles is 360° as cover the full circle.

Each angle measure is:

(b) Each side is 16 cm and the radius is 12 cm.

The distance of the midpoint M of PQ from the center O is perpendicular bisector of ΔPOQ.

The segment MO is:

ΔXYZ is isosceles with:

(a) The altitude of ΔXYZ is a perpendicular bisector of YZ. h = XM is the altitude

Find h:

(b) Note the ∠ZXM is half of the ∠ZOM as both the angles intercept half of the arc ZY and ∠ZOM is a central angle.

Find ∠ZXM:

Find ∠ZOM:

Find the measure of the radius:

Find the measure of the diameter:

Answer:

2•(y +1) - 2y = 2 [2] 0 = 0 => Infinitely many solutions

Step-by-step explanation:

The system of equations representing the given situation is:

b + p = 2.

4b + 5p = 8.

In the question, we are given that Courtney walked from her house to the beach at a constant speed of 4 kilometers per hour, and then walked from the beach to the park at a constant speed of 5 kilometers per hour. The entire walk took 2 hours and the total distance Courtney walked was 8 kilometers.

We are asked to represent the situation using a system of equations where b is the number of hours it took Courtney to walk from her house to the beach, and p the number of hours it took her to walk from the beach to the park.

Courtney's journey from house to beach:

Time = b hours.

Speed = 4 kilometers per hour.

Distance = Speed*Time = 4b kilometers.

Courtney's journey from beach to park:

Time = p hours.

Speed = 5 kilometers per hour.

Distance = Speed*Time = 5p kilometers.

Courtney's complete journey:

Time = b + p hours

Distance = 4b + 5p kilometers.

Now, we are given that Courtney took 2 hours to complete the entire walk and total distance was 8 kilometers.

So, we can write the situation as:

b + p = 2.

4b + 5p = 8.

Thus, the system of equations representing the given situation is:

b + p = 2.

4b + 5p = 8.

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The provided question is incomplete. The complete question is:

"Courtney walked from her house to the beach at a constant speed of 4 kilometers per hour, and then walked from the beach to the park at a constant speed of 5 kilometers per hour. The entire walk took 2 hours and the total distance Courtney walked was 8 kilometers.

Let b be the number of hours it took Courtney to walk from her house to the beach, and p the number of hours it took her to walk from the beach to the park.

Which system of equations represents this situation?"

Answer: 56 785 is written as fifty six thousand, seven hundred and eight five. The number 406 090 is written as four hundred and six thousand and ninety. Numbers with seven, eight or nine digits, are millions. 46 758 442 is forty six million, seven hundred and fifty eight thousand, four hundred and forty two.

Step-by-step explanation:

The number would be 794 in figure form which represents seven hundred and ninety-four.

A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9. Based on the basic value of its digits, different types of number systems exist.

Calculating the number of quantities for an object or the Number of things left in the container are only two examples of the types of mathematical operations that utilize the Number System.

We have to write the number seven hundred and ninety-four in figures

As per the given statement, the expression would be:

⇒ 700 + 94

⇒ 794

Therefore, the number seven hundred and ninety-four in figure form would be 794.

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In your given situation, the distribution of grades is left-skewed, which indicates that the majority of the students scored higher grades, with fewer students receiving lower grades.

If the distribution of grades was left-skewed, it means that there were more students who scored higher grades than those who scored lower grades. This would result in a longer tail on the left side of the distribution curve. However, despite the skewness, the mean, median, and mode were all the same. This suggests that the majority of the grades fell around the same value, which is the central tendency of the distribution. The fact that the mean and median are the same suggests that the skewness was not significant enough to pull the mean away from the median. Therefore, in this case, the mean and median can be considered as representative of the typical grade achieved by the students.
. However, the mean, median, and mode are all the same, suggesting that the central tendency of the grades is consistent, and the overall distribution might be only slightly skewed.

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To find the probability of either event occurring, we can use the formula for the union of two events: P(A or B) = P(A) + P(B) - P(A and B).

Given that P(A) = 0.6, P(B) = 0.5, and P(A and B) = 0.25, we can substitute these values into the formula.

\(P(A or B) = P(A) + P(B) - P(A and B)\)
\(P(A or B) = 0.6 + 0.5 - 0.25\)
\(P(A or B) = 0.85 - 0.25\)
\(P(A or B) = 0.60\)
The probability of either event occurring is 0.60 or 60%.

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The probability of either event occurring can be found by adding the probabilities of the individual events and subtracting the probability of both events happening together. In this case, the probability of either event A or event B occurring is 0.6.

The probability of either event occurring can be calculated using the principle of addition. To find the probability of either event happening, we need to sum the individual probabilities of the events and subtract the probability of both events happening together.

Given:

p(a) = 0.6 (probability of event A occurring)
p(b) = 0.5 (probability of event B occurring)
p(a and b) = 0.25 (probability of both events happening together)

To calculate the probability of either event occurring, we can use the formula:

p(a or b) = p(a) + p(b) - p(a and b)

Substituting the given values into the formula:

p(a or b) = 0.6 + 0.5 - 0.25

p(a or b) = 0.85 - 0.25

p(a or b) = 0.6

Therefore, the probability of either event A or event B occurring is 0.6.

To understand this concept better, let's consider an example. Suppose event A represents rolling a fair six-sided die and getting an even number (2, 4, or 6). The probability of event A occurring would be 0.5. Now, let event B represent flipping a fair coin and getting heads. The probability of event B occurring would be 0.5.

If we want to find the probability of either rolling an even number or flipping heads, we can use the formula mentioned earlier. The probability of rolling an even number is 0.5, the probability of flipping heads is 0.5, and the probability of both happening together is 0.25. Plugging these values into the formula, we get:

p(A or B) = 0.5 + 0.5 - 0.25

              = 0.75

Therefore, the probability of either rolling an even number or flipping heads is 0.75.

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Answer:

49th term = 225

Step-by-step explanation:

The following sequence: -15, -10, -5, 0, -5... is an example of an arithmetic progression.

An arithmetic progression or AP for short, is a sequence in which the difference between successive terms is constant. This difference is known as the common difference, and can be found by subtracting a term by its preceding term.

The general formula, for the nth term of an arithmetic progression, is thus:

Tn = a + (n - 1)d, where a = first term, and d = common difference.

In the sequence: -15, -10, -5, 0, 5...,

a = -15, and d = -10--15 = 5

T49 = -15 + (49 - 1)5 = 225

∴ 49th term = 225