Find the value of the expression 12 − 4 + 3 x 2.

Answer:  The slope-intercept form is y = -2x + 10

Step-by-step explanation:

Step 1: The y-intercept is the point where x=0, so that is (0,10)

Step 2: Use the points (-2,14) and (-1,12) to find the slope

Slope (m) = ΔY/ΔX = -2/1 = -2

Step 3: The slope-intercept form is:

y = mx+b

y = (step 2 value) x + (step 1 value)

y = -2x+10

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Answer:

150 handshakes

Step-by-step explanation:

50+50=100 Since the girls shook ONCE to a boy and a girl, we would multiply 100 twice, then add another 50.

Answer:

240 marbles.

Explanation:

Let us call R the number of red marbles, B the number of blue marbles, and N the total number of marbles. Then we know that

Furthermore, we also know that there are 160 blue marbles, meaning B = 160:

We also know that the probability of getting a red marble is 1 / 3, meaning 1 /3 of the total number of marbles is red:

Since N = R + 160, the above becomes

Multiplying both sides by 3 gives

subtracting R from both sides gives

Finally, dividing both sides by 2 gives

Hence, there are 80 marbles in the box.

Therefore, the total number of marbles in the box is

The total number of marbles in the box is 240.

Kevin traveled a total of 315 miles in the journey from Glasgow to Newcastle and then to Nottingham.

To calculate the total distance Kevin traveled, we need to find the distance traveled in each leg of the journey and then add them together.

First, let's calculate the distance from Glasgow to Newcastle.

Kevin drove at an average speed of 60 mph for 2 hours and 30 minutes, which is equivalent to 2.5 hours.

Distance from Glasgow to Newcastle = Speed \(\times\) Time

= 60 mph \(\times\) 2.5 hours.

= 150 miles.

Next, let's calculate the distance from Newcastle to Nottingham.

Kevin drove at an average speed of 55 mph for 3 hours.

Distance from Newcastle to Nottingham = Speed \(\times\) Time.

= 55 mph \(\times\) 3 hours.

= 165 miles.

Finally, to find the total distance traveled, we add the distance from Glasgow to Newcastle and the distance from Newcastle to Nottingham:

Total distance traveled = Distance from Glasgow to Newcastle + Distance from Newcastle to Nottingham

= 150 miles + 165 miles.

= 315 miles.

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Using algebra, the tray C has more pies in it than the trays A and B

To prove that one tray has more pie in it than others, we would need to have information about the amount of pie in each tray.

From the figure, we have

Tray A = x

Tray B = 4x

Tray C = 9x

When the above are compared, we have

9x > 4x > x

This means that tray C has more pies in it

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Answer:

7w-14

7(9)-14

63-14

49

Step-by-step explanation:

Answer:

49

Step-by-step explanation:

since the value of W is given, 9, we have to plug it into the expression to simplify it further.

9 x 7 = 63

63 - 14 = 59

49

The distance from the car to the base of the building is 107.46 feet

From the question We are given the following information

Angle of depression

Height of the building H = 37 feet

Required

distance from the car to the base of the building

Using the SOH CAH TOA identity

tan 19 = opp/hyp

tan 19 = 37/B
B = 37/tan 19
B = 37/0.34432
B = 107.46

Hence the distance from the car to the base of the building is 107.46 feet

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Answer:

28 pages per day

Step-by-step explanation:

126 divided by 4.5 = 28

I hope this helps :3

The given problem concerns a vibrating circular drumhead fixed along the circumference. The following problem needs to be solved for the two-dimensional wave equation to find the displacement for all positive time.

The Bessel functions of the first kind are solutions of the Bessel differential equation, which is the second-order linear ordinary differential equation. The solutions of the Bessel differential equation are periodic, meaning that they repeat themselves after a fixed interval.

A problem was given to determine the displacement of a vibrating circular drumhead fixed along the circumference. The following problem has to be solved for the two-dimensional wave equation 1,0,t)0, a(r, θ, 0) = 1-r2, udT.0, 0) = 1, linn la(r, θ, t)| < oo where (r, ) are polar coordinates on a circle, and V2 denotes the Laplacian in Cartesian coordinates (x, y).

A Fourier-Bessel series was also given.n= where kn is the n-th positive zero of the Bessel function Jo.

To find the displacement of a vibrating circular drumhead fixed along the circumference, the following problem has to be solved for the two-dimensional wave equation.1,0,t)0, a(r, θ, 0) = 1-r2, udT.0, 0) = 1, linn la(r, θ, t)| < oo where (r, ) are polar coordinates on a circle, and V2 denotes the Laplacian in Cartesian coordinates (x, y).The Bessel functions of the first kind are solutions of the Bessel differential equation, which is the second-order linear ordinary differential equation. The solutions of the Bessel differential equation are periodic, meaning that they repeat themselves after a fixed interval.

A Fourier-Bessel series was given by n= where kn is the n-th positive zero of the Bessel function Jo. The Fourier-Bessel series of the problem is given by u(r,θ,t) =  ∑an(t)J0(knr)J0(kn).The problem requires the initial displacement of the drumhead to be radially symmetric along the circle with the maximum displacement taken at the center.

The initial velocity is a positive constant.To solve the given problem for the two-dimensional wave equation, we can use the separation of variables method to separate the solution of the equation into a product of functions of r and θ and a function of t. The general solution of the given problem for the two-dimensional wave equation is given byu

(r, θ, t) =  ∑an(t)J0(knr)J0(kn).

Therefore, we can conclude that to find the displacement of a vibrating circular drumhead fixed along the circumference, the following problem has to be solved for the two-dimensional wave equation. The general solution of the given problem for the two-dimensional wave equation is given by u(r, θ, t) =  ∑an(t)J0(knr)J0(kn).

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The rule of natural deduction that justifies the inference from ( P(0) ) to ( \exists x P(x) ) is the existential introduction ((\exists I)) rule.

The existential introduction rule states that if you have a statement ( P(t) ) where ( t ) is a term or object, then you can introduce an existential quantifier to assert the existence of an object such that ( P ) holds.

In this case, since you have ( P(0) ), which means that ( P ) holds for the value 0, you can introduce an existential quantifier to claim that there exists some ( x ) (in this case, ( x = 0 )) for which ( P(x) ) holds. Therefore, the justification is ( (\exists I) ).

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The correct statement is :David started at 0 instead of 2

A number line is a horizontal line that has equally spread number increments. The numbers included on the line will determine how the number on the line can be answered. The question that goes with the number determines how it will be used, for example, plotting a point.

Given here: In a number line the interval (-5,5) is marked and 2 to 5 is 3

The right steps are

Add 3 to 2 to obtain the required number as there are 3 spaces between 2 and 5

Thus 2+3=5 which is the required answer

but David addes 2-3=-1 which is incorrect.

Hence, David started at 0 instead of 2

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The event can occur (1), and n(T) is the total number of possible outcomes (25).

The probability of selecting the number 13 first is 1/25, since there is only one ball with the number 13 in the container. This can be expressed as a fraction, 1/25, or a decimal, 0.04. To calculate the probability, use the formula P(E) = n(E)/n(T), where P(E) is the probability of the event (in this case, choosing the number 13 first), n(E) is the number of ways the event can occur (1), and n(T) is the total number of possible outcomes (25). Therefore, P(E) = 1/25 = 0.04.

final ans in 50 words

The probability of selecting the number 13 first is 1/25, or 0.04. This can be calculated using the formula P(E) = n(E)/n(T), where n(E) is the number of ways

Therefore, the event can occur (1), and n(T) is the total number of possible outcomes (25).

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Answer:

23 purple marbles

115 yellow marbles

Step-by-step explanation:

Let y represent the yellow marble

Let p represent the purple marbles

So, we have the equations

y = 5p

Therefore, y + p = 138

5p + p = 138

6p = 138

p = 23 marbles

Now let's put 23 in for the p in the equation to find the number of yellow marbles

y = 5(23)

y = 115 marbles

Answer :-The interval of convergence for the given power series is (4, 14).

The power series in question is ∑n=1 to infinity [(x−9)^n]/[n(-5)^n].

To find the interval of convergence, we will use the Ratio Test:

1. Compute the absolute value of the ratio between the (n+1)th term and the nth term:

|(a_(n+1))/a_n| = |[((x-9)^(n+1))/((n+1)(-5)^(n+1))]/[((x-9)^n)/(n(-5)^n)]|

2. Simplify the ratio:

|(a_(n+1))/a_n| = |(x-9)/((-5)(n+1))|

3. Take the limit as n approaches infinity:

lim (n→∞) |(x-9)/((-5)(n+1))|

4. For the Ratio Test, if the limit is less than 1, then the series converges. In this case:

|(x-9)/(-5)| < 1

5. Solve the inequality to find the interval of convergence:

-1 < (x-9)/(-5) < 1

Multiply each side by -5 (and reverse the inequalities since we're multiplying by a negative number):

5 > x-9 > -5

Add 9 to each side:

14 > x > 4

So, the interval of convergence for the given power series is (4, 14).

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The equation of the line of best fit, using the least square method is v = 2.19t + 6.7, making the 2nd option as the right choice.

In the question, we are asked to find the equation of the line of BEST FIT for the given scatter plot.

We let the time be the independent variable x, and velocity is the dependent variable y.

We find the line of best fit using the least square method.

First, we calculate the mean:

Now, we find the slope of the line of best fit, using the formula:

m = {∑(x - μ(x))(y - μ(y))}/{∑(x - μ(x))²}.

Taking value from the tables, which is attached, we get:

m = 239.35/109.2683333 = 2.190479096.

Now, we calculate the y-intercept of the line of best fit, using the formula:

b = μ(y) - m.μ(x),

or, b = 20.5 - 2.190479096*6.283333 = 6.736489681.

Now, the equation of the line of best fit, in the form of y = mx + b, can be written as, y = 2.190479096x + 6.736489681, which on approximation, and making y as v, the velocity, and x as t, the time, we get: v = 2.19t + 6.7.

Thus, the equation of the line of best fit, using the least square method is v = 2.19t + 6.7, making the 2nd option as the right choice.

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The steps of student B are in the correct order but the steps of student A are in the incorrect order.

Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines and the lines that never intersect are known as parallel lines.

We have:

You are given AB and point C. Construct a line parallel to AB that passes through point C

The correct way to draw a parallel line to AB that passes through point C is:

The steps of student B are in the correct order but the steps of student A are in the incorrect order.

Thus, the steps of student B are in the correct order but the steps of student A are in the incorrect order.

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The graph of the parent absolute value function is decreasing over the interval (-∞, 0). The function exhibits a decreasing behavior as x moves from negative infinity towards zero, where the absolute value decreases.

The parent absolute value function is defined as f(x) = |x|. To determine where the graph of this function is decreasing, we need to identify the intervals where the function's slope is negative.

Let's analyze the behavior of the parent absolute value function:

For x < 0, the function can be rewritten as f(x) = -x. In this interval, the function is a linear function with a negative slope of -1. As x decreases, f(x) also decreases, indicating a decreasing behavior.

For x > 0, the function remains f(x) = x. In this interval, the function is a linear function with a positive slope of 1. As x increases, f(x) also increases, indicating an increasing behavior.

At x = 0, the function is not differentiable since the slope changes abruptly from negative to positive. However, it is worth noting that the function does not strictly decrease or increase at x = 0.

Therefore, we can conclude that the graph of the parent absolute value function is decreasing over the interval (-∞, 0).

In this interval, as x moves from negative infinity towards zero, the function values decrease. The farther away x is from zero (in the negative direction), the larger the absolute value, resulting in a decrease in the function values.

On the other hand, the graph of the parent absolute value function is increasing over the interval (0, ∞), as explained earlier.

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Answer:

The value in the hundreds place is 10,000 times greater than the value in the hundredths place

Step-by-step explanation:

Here, we have a digit having same numbers at the hundred and hundredth position.

Now, we want to know how many times greater is the value in the hundred position compared to the value in the hundredth position.

Let’s have the number as follows; Kindly note that we can use any number, we should just make sure that the value at the hundred position is same as that as in the hundredth position.

We should also not make any mistakes identifying the 100 and 100th position

A perfect example for this is below;

768.57

7 is the hundredth position and also on the hundred position.

The value of 7 in the hundred position is 700 while the value of 7 in the hundredth position is 0.07

Now we want to know how many times is 700 greater than 0.07

That would be 700/0.07 = 10,000

Answer:

a:1100....b:11000....c:110000

Step-by-step explanation:

Answer: A= 1100

B= 11000

C= 110000

Step-by-step explanation:

Answer:

d=9.6

Step-by-step explanation:

0.2d+3.14=5.06

                - 3.14

_________________

                   1.92

0.2d=1.92

1.92/0.2= 9.6

The Radical Form (√x)  ,the solutions to the equation √x - 2 + 4 = x are x = 1 and x = 4.

The equation √x - 2 + 4 = x for x, we can follow these steps:

1. Begin by isolating the radical term (√x) on one side of the equation. Move the constant term (-2) and the linear term (+4) to the other side of the equation:

  √x = x - 4 + 2

2. Simplify the expression on the right side of the equation:

  √x = x - 2

3. Square both sides of the equation to eliminate the square root:

  (√x)^2 = (x - 2)^2

4. Simplify the equation further:

  x = (x - 2)^2

5. Expand the right side of the equation using the square of a binomial:

  x = (x - 2)(x - 2)

  x = x^2 - 2x - 2x + 4

  x = x^2 - 4x + 4

6. Move all terms to one side of the equation to set it equal to zero:

  x^2 - 4x + 4 - x = 0

  x^2 - 5x + 4 = 0

7. Factor the quadratic equation:

  (x - 1)(x - 4) = 0

8. Apply the zero product property and set each factor equal to zero:

  x - 1 = 0   or   x - 4 = 0

9. Solve for x in each equation:

  x = 1   or   x = 4

Therefore, the solutions to the equation √x - 2 + 4 = x are x = 1 and x = 4.

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The average time a customer waits in the system is 9 minutes.

To calculate the average time a customer waits in the system, we need to consider the arrival rate of customers and the service rate. In this case, customers arrive at the post office at an average rate of one every 6 minutes, which corresponds to an arrival rate of λ = 1/6 customers per minute.

The average time it takes to process a customer is 3 minutes, which represents the service rate, μ = 1/3 customers per minute.

In queuing theory, the average time a customer waits in the system can be calculated using the formula:

Average waiting time = 1 / (service rate - arrival rate)

In this scenario, the service rate (μ) is 1/3 customers per minute, and the arrival rate (λ) is 1/6 customers per minute. Plugging these values into the formula, we have:

Average waiting time = 1 / (1/3 - 1/6) = 1 / (2/6) = 3/2 = 1.5 minutes.

Therefore, the average time a customer waits in the system is 1.5 minutes, or 9 minutes.

This calculation takes into account the balance between customer arrivals and the processing time, providing an estimate of the average waiting time a customer can expect in the system.

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The function is given by

\(\\ \tt\hookrightarrow D(p)=1500-25p\)

\(\\ \tt\hookrightarrow 1500-25p\geqslant 0\)

\(\\ \tt\hookrightarrow 1500\geqslant 25p\)

\(\\ \tt\hookrightarrow p\leqslant 60\)

Now

\(\\ \tt\hookrightarrow D_f\in (-\infty,60]\)

Answer:

apply distance formula

\( \sqrt{ {(5 - 2)}^{2} + {(1 - 5)}^{2} } \)

u get

\( \sqrt{9 + 16} \)

which is

\( \sqrt{25} \)

which is 5

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Answer:

Step 1: Write down the percent divided by 100 like this: 1200% = 1200 / 100. Step 2: Multiply both top and bottom by 10 for every number after the decimal point: As 1200 is an integer, we don't have numbers after the decimal point. So, we just go to step 3.

Answer:

12/1 or 12

Step-by-step explanation:

Yes, the test in an "if" function must evaluate to either a True or a False value.

An "if" function, also known as a conditional statement, is used to perform specific actions based on whether a certain condition is met or not. The test or condition within the "if" function needs to be evaluated as either True or False in order for the program to decide which action to execute. If the test evaluates to True, the program will perform the action within the "if" block, and if it evaluates to False, it will either execute the action in the "else" block (if present) or simply skip the "if" block.

When using an "if" function in programming, it is essential for the test or condition within the statement to result in a boolean value, which is either True or False. This is because the program needs to determine whether the condition is met or not, so it can decide which set of actions to execute. If the condition evaluates to True, the code within the "if" block will be executed, while if it evaluates to False, the code within the "else" block (if present) will be executed, or the "if" block will be skipped altogether.

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To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

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