if 4a + 6 = 12 - 2a what is 6a
​

Step-by-step explanation:

C. (4,1)

When x=4 and y=1, the equations become,

4 = 3*1 +1

4=4

2*4+4*1 = 8+4 = 12

Answer:

option C

Step-by-step explanation:

x = 3y + 1      equation(i)

2x + 4y =12    equation(ii)

First working for equation (ii)

substituting the value of x in equation (ii)

2(3y + 1) + 4y = 12

6y + 2 + 4y = 12

10y = 12 - 2

y = 10/10

y =1

now substitute the value of y in equation (i)

x = 3*1 = 1

x=3 + 1

x = 4

therefore , answer is (4,1)

Given:

Consider the below figure attached with this question.

To find:

The value of x.

Solution:

We know that, the sum of all exterior angles of a quadrilateral is always 360 degrees.

The below figure represents the four exterior angles of the quadrilateral. So,

\(65^\circ+106^\circ+78^\circ+x^\circ=360^\circ\)

\(249^\circ+x^\circ=360^\circ\)

\(x^\circ=360^\circ -249^\circ\)

\(x^\circ=111^\circ\)

Therefore, the measure of x is \(111^\circ\).

Answer:

I think it's A because 98÷14=7, 63÷9=7, 14÷2=7

Step-by-step explanation:

And all of those can be divided they even get the same numbers when you divide them which is 7.

Suppose A and B are dependent events. If P(A|B) = 0.25 and P(B) = 0.6, then  P(AuB) = 0.2

The probability of an event is described as a number that indicates how likely the event is to occur which is usually  expressed as a number in the range from 0 and 1, or preferably using percentage notation ranging  from 0% to 100%.

The relationship between two dependent events is expressed in the following equation below according to the rules of probability,

P(A|B) = P(A∩B) / P(B)

we then substitute ,

0.25 = P(A∩B) / 0.8

P(A∩B)  = 0.2

In conclusion, If P(A|B) = 0.25 and P(B) = 0.6, then  P(AuB) = 0.2

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Answer:

Top Middle: 2/10 or 1/5 or 4/20

Bottom right: 2/20 or 1/10

Middle right: 2/10 or 1/5

Middle Middle: 7/40

Answer:

The vertex of the graph moves to a point twice as far from the y-axis.

Step-by-step explanation:

How does the graph of y = a(x – h)2 + k change if the value of h is doubled?

The vertex of the graph moves to a point twice as far from the x-axis.

because the role of h is to indicate the distance of the vertex from the y-axis.

The vertex of the graph moves to a point half as far from the x-axis.

The vertex of the graph moves to a point half as far from the y-axis.

Transformation involves changing the position of a function.

When h is doubled in \(\mathbf{y = a(x - h)^2 + k}\), the vertex of the graph moves to a point twice as far from the y-axis.

The function is given as:

\(\mathbf{y = a(x - h)^2 + k}\)

When the value of h is doubled, the new function becomes:

\(\mathbf{y' = a(x - 2h)^2 + k}\)

Rewrite as:

\(\mathbf{y' = a(x - h- h)^2 + k}\)

The above equation means that:

Function y will be translated to the right by h units

Assume the vertex is:

\(\mathbf{Vertex = (2,5)}\)

The new vertex will be:

\(\mathbf{Vertex = (4,5)}\)

Comparing the vertices, it means that:

The new function will have its vertex twice as far from the y-axis

Hence, option (b) is correct.

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Answer:

Answer is 8 - (1.5n) = F

Step-by-step explanation:

1.5 kilos of food eaten every day minus 8 for the amount of food in total will equal the amount of food left.

Answer:

a. 18

b. 45

Step-by-step explanation:

The question states that 2/5 of the class are girls which means 3/5 are boys:

\(\frac{3}{5} = 27\)

Divide this value by 3 to get the value of \(\frac{1}{5}\):

27 ÷ 3 = 9

Multiply this by 5 to find \(\frac{5}{5}\), the total pupils in the class:

9 x 5 = 45

As the number of girls is \(\frac{2}{5}\) of the total pupils:

9 x 2 = 18

So there are 18 girls in the class which has a total pupil size of 45.

Hope this helps!

Step-by-step explanation:

according to question of ⅖ are girls than ⅗ are boys

so let the number of girls be x

so,

→ ⅗ of x = 27

→ x = 27 × 5/3 = 9×5 = 45

→ x = 45

a ) 45 - 27 = 18

than no. of girls is 18.

b) thier are 45 students in total.

hope this answer helps you dear...take care and may u have a great day ahead!

The ratio that correctly models the situations are:

1 to 3 - for every cup of water added to the mixture, there are three drops of food colouring added.

4 : 3 - for every 4 students wearing pants, there are 3 students wearing shorts.

12 : 3 - there 4 times as many boys as there are girls.

A ratio expresses the relationship between two numbers. It shows the number of times that one value is contained in another value. The sign used to represent ratios is :.

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(a) With 10 rectangles using left endpoints, 5 rectangles are contributing negative area values to the estimated net area. This means that the function is below the x-axis in those intervals.

The remaining 5 rectangles are contributing positive area values, as the function is above the x-axis in those intervals.

When using midpoints, the number of positive and negative rectangles may not be the same. It depends on the behavior of the function within each subinterval. The use of midpoints can result in a different distribution of positive and negative rectangles compared to using left endpoints.

(b) The error when using midpoints with 10 subintervals can be determined by calculating the difference between the estimated net area using midpoints and the actual net area.

To calculate the error, we need to evaluate the definite integral of the function over the given interval and subtract the estimated net area using midpoints.

Error = Actual Net Area - Estimated Net Area using Midpoints

Since the exact values are not provided, the specific error value cannot be determined without further information or calculations.

Using left endpoints with 10 rectangles, 5 rectangles contribute negative area values and 5 contribute positive area values. When using midpoints, the distribution of positive and negative rectangles may differ. The error when using midpoints can be calculated by subtracting the estimated net area using midpoints from the actual net area, but the exact error value cannot be determined without further information or calculations.

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The requirement f(x1) * f(x2) < 0 for choosing initial guesses x1 and x2 with opposite signs ensures the validity and convergence of certain numerical root-finding methods such as the bisection method or the regula falsi method.

The statement you provided is true for certain numerical methods used to find roots of equations, such as the bisection method or the regula falsi method. These methods are iterative and require an initial interval or range where the root is expected to be found. To ensure convergence and a valid solution, it is necessary to choose initial guesses x1 and x2 such that the function f(x) evaluated at those points have opposite signs, i.e., f(x1) * f(x2) < 0.

The rationale behind this requirement is based on the Intermediate Value Theorem, which states that if a continuous function f(x) changes sign over an interval [x1, x2], then there exists at least one root within that interval. By ensuring that f(x1) and f(x2) have opposite signs, we guarantee the existence of a root within the interval [x1, x2].

The bisection method works by repeatedly bisecting the interval and selecting a new subinterval that contains the root. At each iteration, the method narrows down the interval by halving it, based on the sign change observed in the function evaluations.

Similarly, the regula falsi (or false position) method also operates by iteratively refining the interval based on the linear interpolation between the function values at the endpoints. The method adjusts the interval based on the sign change of the function, converging to the root.

Both methods rely on the property of opposite signs to guarantee convergence and avoid getting stuck in a non-converging or incorrect solution. If the initial guesses do not satisfy the condition f(x1) * f(x2) < 0, it is possible that the method fails to converge or converges to a different root or solution.

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Option C is correct.  Less than 100  is closest to total deaths resulting from ladder misuse each year.

According to the Consumer Product Safety Commission (CPSC), on average, approximately 300 people die each year in the United States from falls involving ladders.

However, not all of these deaths are due to ladder misuse. In fact, the number of deaths resulting specifically from ladder misuse is likely to be lower. It is estimated that a significant portion of ladder-related fatalities are caused by factors such as overreaching, misusing the ladder, or failing to follow proper safety guidelines.

To reduce the number of deaths and injuries resulting from ladder misuse, it is important to follow safety guidelines and to choose the right ladder for the job, taking into consideration factors such as height, weight, and stability.

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Answer:

Faris' arrival time = 3:30 pm + 3 h 54 mnt = 7:24 pm

Answer:

19.24

Step-by-step explanation:

The probability of rolling a 2 is 1/6. If X is a random variable representing the number of 2s that are obtained after rolling a die 23 times, then X follows a binomial distribution with success probability p = 1/6 across n = 23 trials.

The variance of a binomial distribution with parameters p and n is n p (1 - p), so the standard deviation in this case would be

√(23 • 1/6 • 5/6) ≈ 1.8

Answer:

Equation is;

P = I(1 + r)^n

The population is 328

Step-by-step explanation:

Here we want to model the situation and use the modeled equation to predict population.

This follows an exponential pattern with similarity to the amount paid on a compound interest

Mathematically, we can have the equation as;

P = I(1 + r)^n

Where P is the population we want to calculate

I is the initial population in 1995 = 200 people

r is the rate of increase = 2% = 2/100 = 0.02

n is the difference in the number of years = 2020-1995 = 25

Thus the population would be;

P = 200(1 + 0.02)^25

P = 200(1.02)^25

P = 328.12

which is 328 approximately

The number of boys and girls in a team after the selection of participants are 2 and 3, respectively

The number of boys are girls are given as

Boys = 28

Girls = 42

Sections = 6

To form teams with the same number of boys and girls on each team, we need to determine the greatest common factor (GCF) of the number of girls and the number of boys.

Factors of 28: 1, 2, 4, 7, 14, 28

Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42

The greatest common factor of 28 and 42 is 14.

So, we have

Boys = 28/14 = 2

Girls = 42/14 = 3

This means that each team has 2 boys and 3 girl

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A null space calculator finds the null space of a matrix used in linear algebra.

An invalid space mini-computer is a web-based instrument used to track down the invalid space, otherwise called the portion, of a framework. The invalid space of a framework is the arrangement of all vectors that fulfill the condition Ax= 0, where An is the lattice and x is the vector of questions. The invalid space can be utilized to decide if an arrangement of straight conditions is steady or not, and to find the reason for the arrangement space. An internet based invalid space number cruncher permits clients to enter a network and get the invalid space, as well as different properties like the position, determinant, and eigenvalues of the framework. This can be helpful for understudies and experts in fields like science, physical science, and designing who need to address frameworks of straight conditions and dissect the properties of networks.

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Answer:

2.222.........

Step-by-step explanation:

10 : 90

x : 20

cross multiply

10 x 20 =  90x

200 = 90x

both divide by 90

x = 2.2222.......

Answer:

Step-by-step explanation:

(a) To find the probability that it is raining when you arrive in Oneirabad on a random day, we need to use the law of total probability.

Let A be the event that it is raining, and B be the event that it is the Wet season.

P(A) = P(A|B)P(B) + P(A|B')P(B')

Given that the Wet season lasts for 1/3 of the year, we have P(B) = 1/3. The probability that it is raining during the Wet season is 3/4, so P(A|B) = 3/4.

The Dry season lasts for 2/3 of the year, so P(B') = 2/3. The probability that it is raining during the Dry season is 1/6, so P(A|B') = 1/6.

Now we can calculate the probability that it is raining when you arrive:

P(A) = (3/4)(1/3) + (1/6)(2/3)

= 1/4 + 1/9

= 9/36 + 4/36

= 13/36

Therefore, the probability that it is raining when you arrive in Oneirabad on a random day is 13/36.

(b) Given that it is raining when you arrive, we can use Bayes' theorem to calculate the probability that your visit is during the Wet season.

Let C be the event that your visit is during the Wet season.

P(C|A) = (P(A|C)P(C)) / P(A)

We already know that P(A) = 13/36. The probability that it is raining during the Wet season is 3/4, so P(A|C) = 3/4. The Wet season lasts for 1/3 of the year, so P(C) = 1/3.

Now we can calculate the probability that your visit is during the Wet season:

P(C|A) = (3/4)(1/3) / (13/36)

= 1/4 / (13/36)

= 9/52

Therefore, given that it is raining when you arrive, the probability that your visit is during the Wet season is 9/52.

(c) Given that it is raining when you arrive, the probability that it will be raining when you return to Oneirabad in a year's time depends on the season. If you arrived during the Wet season, the probability of rain will be different from if you arrived during the Dry season.

Let D be the event that it is raining when you return.

If you arrived during the Wet season, the probability of rain when you return is the same as the probability of rain during the Wet season, which is 3/4.

If you arrived during the Dry season, the probability of rain when you return is the same as the probability of rain during the Dry season, which is 1/6.

Since the season you arrived in is independent of the weather when you return, we need to consider the probabilities based on the season you arrived.

Let C' be the event that your visit is during the Dry season.

P(D) = P(D|C)P(C) + P(D|C')P(C')

Since P(C) = 1/3 and P(C') = 2/3, we can calculate:

P(D) = (3/4)(1/3) + (1/6)(2/3)

= 1/4 + 1/9

= 9/36 + 4/36

= 13/36

Therefore, the probability that it will be raining when you return to Oneirabad in a year's time, given that it is raining when you arrive, is 13/36.

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Answer:

x=39.76693372

Step-by-step explanation:

Subtract 2187 from 3.

54.92x−2184=0

Add 2184

to both sides of the equation.

54.92x=2184

Divide each term by 54.92

and simplify.

x=39.76693372

Solving for q will give us the optimal quantity that maximizes the profit,  a function that gives the total profit earned can be written as:

Profit(q) = (Revenue per item - Cost per item) * q

Assuming that the revenue and cost are functions of the quantity sold (q), the total profit can be calculated as follows:

Profit(q) = Revenue(q) - Cost(q)

To find the quantity which maximizes the profit, we can take the derivative of the profit function with respect to q and set it equal to zero, and then solve for q:

Profit'(q) = Revenue'(q) - Cost'(q) = 0

Solving for q will give us the quantity that maximizes the profit. However, without knowing the specific forms of the revenue and cost functions, we cannot write a specific profit function or find the quantity that maximizes the profit.

In general, the profit function can be written as:

Profit(q) = (Revenue per item - Cost per item) * q

where the revenue per item and cost per item are functions of q. To find the quantity that maximizes the profit, we need to differentiate the profit function with respect to q and set it equal to zero:

Profit'(q) = Revenue'(q) - Cost'(q) = 0

Solving for q will give us the optimal quantity that maximizes the profit.

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The relation "r" on the set of all integers, where x = y^2, is not reflexive.

A relation is reflexive if every element in the set is related to itself. In this case, for the relation x = y^2 to be reflexive, every integer "x" should be related to itself, meaning that x = x^2. However, this is not true for all integers.

For example, if we consider x = 2, it is not equal to 2^2 = 4. Similarly, if we consider x = -3, it is not equal to (-3)^2 = 9.

Since there are integers that do not satisfy the condition x = x^2, the relation x = y^2 is not reflexive on the set of all integers.

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Answer:

see explanation

Step-by-step explanation:

let the 2 consecutive numbers be n and n + 1

sum = n + n + 1 = 2n + 1

and

(n + 1)² - n² ← difference of the squares

= n² + 2n + 1 - n²

= 2n + 1 = sum of 2 numbers

Answer:

(0,2)

Step-by-step explanation:

The equations must be derived from the graph:

First, find the slope of f(x):

\(m=\frac{y_2-y_1}{x_2-x_1}\) let \((x_1,y_1)=(-3,3)\) and \((x_2,y_2)=(3,1)\)

\(m=\frac{(1)-(3)}{(3)-(-3)}\\m=\frac{-2}{6}\\m=-\frac{1}{3}\)

Then use \(y-y_1=m(x-x_1)\)

\(y-3=-\frac{1}{3}[x-(-3)]\\y-3=-\frac{1}{3}x-1\\y=-\frac{1}{3}x+2\\f(x)=-\frac{1}{3}x+2\)

For g(x), let:

\((x_1,y_1)=(-3,0)\\(x_2,y_2)=(0,2)\)

\(m=\frac{(2)-(0)}{(0)-(-3)}\\m=\frac{2}{3}\)

\(y-0=\frac{2}{3}[x-(-3)]\\y=\frac{2}{3}x+2\\g(x)=\frac{2}{3}x+2\)

Now, to solve for x, allow the two expressions written in terms of x equal each other.

\(-\frac{1}{3}x+2=\frac{2}{3}x+2\\(-\frac{1}{3}x+2)+\frac{1}{3}x=(\frac{2}{3}x+2)+\frac{1}{3}x\\2=x+2\\(2)-2=(x+2)-2\\x=0\)

To solve for y, substitute 0 for x in f(x):

\(y=-\frac{1}{3}x+2\\y=-\frac{1}{3}(0)+2\\y=0+2\\y=2\)

So, the solution to this system of equations would be the ordered pair (0,2).  This solution is seen on the graph as the intersection of the two lines.

Let's begin by listing out the information given to us:

Principal (P) = 600, interest rate (r) = 1% = 0.01 * 12 = 0.12, componded monthly (n) = 12, time (t) = 3

The formula for compound interest is given by?

We proceed to substitute the values of the variables into the equation, we have:

Applying addition of integers, it is found that this number is of -5.

The addition of these following three pairs is given as follows:

Hence, we got three pairs of values from these cards, all cards are used, and all the additions result in -5, hence, this number is of -5.

The addition of integers used in this problem is as follows:

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1. I based my decision on allocating points to maximize my own score, while also considering the potential benefits of contributing to the group fund.

2. The best outcome for me would be allocating the minimum points required to the GIVE account, while putting the majority in the KEEP account. This would ensure I receive the most points for myself.

3. The best outcome for the group would be if both participants maximized their contributions to the GIVE account. This would create the largest group fund, resulting in the most redistributed points and highest average score.

4. There are parallels with risk management strategies. Individuals may act in their own self-interest, but a larger group benefit could be achieved if more participants contributed to "group" risk management strategies like vaccination, safety protocols, insurance policies, etc. However, some individuals may free ride on others' contributions while benefiting from the overall results. Incentivizing group participation can help align individual and group interests.

Answer:

3/2

Step-by-step explanation:

7 x 3/14 can be simplified to 21/14, which is written in simplest form as 3/2.

Hope can help :)

The simplest form of the fraction of the expression is 3/2.

We have,

The expression:

7 x 3/14

Now,

14 is a multiple of 7.

i.e

7 x 2 = 14

So,

7 x 3/(7 x 2)

7 gets canceled.

= 3/2

Thus,

The simplest form of the fraction of the expression is 3/2.

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