Consider the following well-formed formulae: Wi (3.)H(x), W2 (Vx)E(x,x), (Vx)(G(x) = ~ H(x)) WA = (5x) (Em) ((x) A GiyAE(x,x)) W4 yG(^ , y (a) Explain why, in any model U for which W3 is true, the predicates G and H, regarded as subsets of U, must be disjoint. (b) Prove that any model in which W1, W2, W3 and W4 are all true must have at least 3 elements. Find one such model with 3 elements.

Step-by-step explanation:

70+1

Steps:

write tens and then ones

The graph for the linear equation y=24x, will be a straight line having coordinate (1,24) i.e. B.

What is a linear equation, exactly?

A linear equation is a first-degree algebraic equation in which each term is either a constant or the product of a constant and a single variable (degree 1). A linear equation is stated as y = mx + b, where y is the dependent variable, x is the independent variable, m is the line's slope, and b= y-intercept .

A linear equation's graph is a straight line. The line's slope decides how steep it is, and the y-intercept indicates where the line crosses the y-axis. Linear equations are used to model relationships between variables that are directly proportional to each other, such as distance and time, or cost and quantity.

Now,

Given equation is y=24x

then for  x,    y is

              1,    24

              2,   48

              3,    72

              4,     96

Hence, the graph will be as represented in option 2.

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Answer:

answers are below

Step-by-step explanation:

5*1.6=8

10*1.6=16

w*1.6=1.6w

15*1.6=24

hope this helps:)

Answer:

4x - 2

Step-by-step explanation:

Given

- 2x + 3 - (5 - 6x) ← distribute parenthesis by - 1

= - 2x + 3 - 5 + 6x ← collect like terms

= 4x - 2

The expression -2x + 3 – (5 – 6x) simplifies to 4x - 2.

The correct way of simplifying expressions is first solving what are inside the brackets.Then solving divisions then multiplications then additions and last subtractions.This way of solving order has a short name which is BODMAS order.

According to the given question we have to simplify the expression

-2x + 3 – (5 – 6x).

First we'll solve what are inside the brackets.

-2x + 3 - 5 + 6x.  (negative sign distributed to get a positive).

= 4x - 2.

= 2(2x - 1).

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The inverse of the function in slope-intercept form is f⁻(x) = -x/2 - 2

What is the inverse function?

A function that can change into another function is referred to as inverse. In other words, the inverse of any function "f" will take y to x if it takes x to y in the first place. If a function is written as "f" or "F," the inverse function is written as "f⁻" or "F⁻."

What is slope-intercept form?

The slope-intercept form of a straight line is used to find the equation of a line.

Here,

A function is given to us and we need to find the inverse of the function in slope-intercept form. The given function is,

f(x)= −2x−4

Let assume that y = f(x), then

y = -2x - 4

Now interchange the positions of x and y, and we get

x = -2y - 4

Solve this equation for y in terms of x,

Adding 4 on both sides, we get

x + 4 = -2y

After, dividing both sides by 2, we get

x/2 + 2 = -y

-x/2 - 2 = y

Now replace y with f⁻(x)

f⁻(x) = -x/2 - 2

Hence, the inverse of the function in slope-intercept form is f⁻(x) = -x/2 - 2

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Answer:

3.5

Step-by-step explanation:

This can be calculatdd by applyinthe g Pythagorean theorem

a^2 + b^2= c^2

12^2 + x^2= 12.5^2

144+ x^2= 156.25

x^2= 156.25-144

x^2= 12.25

x= √12.25

x= 3.5

Hence the distance between the ladder and the house is 3.5 ft

A skewed right distribution is most likely to result in the mean being substantially smaller than the median.

The mean and median are measures of central tendency used to describe the center of a distribution. In a skewed right distribution, the tail of the distribution extends towards the right, indicating a larger number of smaller values and a few extremely large values. This distribution shape is also known as positively skewed.

When a distribution is skewed right, the mean is typically pulled towards the larger values in the tail, making it larger than the median. However, there are scenarios where the mean can be substantially smaller than the median in a skewed right distribution.

This occurs when there are extremely large values in the tail that significantly affect the mean, but the bulk of the distribution remains concentrated on the smaller side. As a result, the mean can be pulled downward, making it smaller than the median.

On the other hand, in a symmetric distribution or a skewed left distribution (negatively skewed), where the tail extends towards the left with a larger number of larger values and a few extremely small values, it is less likely for the mean to be substantially smaller than the median. In these cases, the mean is typically closer to or larger than the median.

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The new coordinates of points M and O is determined as;

M = (0.5, - 1)

O = (2.5, -2).

The new coordinate of points M and O after applying the scale factor is calculated as follows;

The given scale factor = 1/2

The current coordinates of point M and O is;

M = (1, - 2)

O = (5, - 4)

A scale factor can be used to either enlarge a figure or decrease a figure.

When the scale factor is less than 1, it means the new figure will be smaller than the original figure.

However, if the scale factor is greater than 1, the new figure will be greater than the original figure.

The new coordinates of points M and O is determined as follows;

M = (1 x 1/2,  -2 x 1/2) = (0.5, - 1)

O = (5 x 1/2, -4 x 1/2) = (2.5, -2)

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Answer:

(0, 15)

Step-by-step explanation:

y=3x+15

y=mx+b where m=slope and b=y-intercept.

Answer:

Step-by-step explanation:

We know that:

Let's compare the formula and the equation given.

Work:

When we compared, we can say that the slope is 3 and the y-intercept is 15.

Hoped this helped.

\(BrainiacUser1357\)

Therefore, the first four terms of the sequence are 5, 2, -1, and The first four terms of the sequence can be found by substituting the values of n = 1, 2, 3, and 4 into the general term a_n = -3n + 8.

For n = 1:

a_1 = -3(1) + 8 = 5

For n = 2:

a_2 = -3(2) + 8 = 2

For n = 3:

a_3 = -3(3) + 8 = -1

For n = 4:

a_4 = -3(4) + 8 = -4

Therefore, the first four terms of the sequence are 5, 2, -1, and -4. Starting with n = 1, we substitute it into the equation and calculate the value of a_1. Similarly, we repeat this process for n = 2, 3, and 4 to find the corresponding terms of the sequence.

In this case, the general term -3n + 8 represents a linear sequence where the term decreases by 3 each time n increases by 1. The initial value is 8, and the common difference is -3.

As we substitute different values of n, we can observe how the sequence progresses and identify the specific terms. In this example, the first four terms of the sequence are found to be 5, 2, -1, and -4.

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Answer:

0

Step-by-step explanation:

Y-intercept is when the slope touches the y-axis and it touches it at 0.

Answer:

y = 4

its also y = 4 x

Step-by-step explanation:

UPDATE:

the answer was 0 according to some ppl.

The value 0.8 in the equation represents the average height the tree grows each month.

In the equation h = 15 + 0.8m, the constant term 15 represents the height of the tree when it was planted, and the coefficient 0.8 represents the rate of change of the height with respect to time (in this case, months). Since the coefficient is positive, it indicates that the tree is growing taller over time. Specifically, the value of 0.8 means that, on average, the tree is growing 0.8 inches taller each month.

To see why this is the case, we can differentiate the equation with respect to time to get dh/dt = 0.8. This means that the rate of change of the height with respect to time (i.e., the tree's growth rate) is a constant 0.8 inches per month. Therefore, the value 0.8 in the equation represents the average height the tree grows each month.

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Option A) "Cannot be negative" is a correct statement about the F distribution. The F distribution is a probability distribution that is used in statistical hypothesis testing to compare the variances of two populations.

The assertion "cannot be positive" about the F distribution is erroneous. The F distribution can only accept positive values and cannot accept negative values; however, it can accept values greater than zero.

"Is the same as the t distribution" is an error. When the sample size is small or the population standard deviation is unknown, the t distribution is employed for testing hypotheses regarding the population mean.

"Is the same as the z distribution" is similarly erroneous. When the population standard deviation is known and the sample size is large, the z distribution is employed as a probability distribution.

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Answer: 80 children are in the 3rd grade

Step-by-step explanation:

Call the number of children in the 3rd grade = a

=> 64 = \(\frac{4}{5}\) x a

a = 64 : 4/5

a = 80

Answer:

343cm³

Step-by-step explanation:

294:6=49

square root of 49=7

7³= 343cm³

Value of x corresponding to P81 is 59.06.

A normal distribution has a mean u = 67.3 and a standard deviation of o=9.3.

The task is to find P81, which separates the bottom 81% from the top 19%.

For any normally distributed variable z with mean u and standard deviation o, the cumulative distribution function is defined as the probability of a standard normal variable being less than or equal to z.

A standard normal distribution has a mean of 0 and a standard deviation of 1.

That is, the variable z can be calculated as: z = (x - u) / o

The value P(z < z0) can be read off a standard normal table for any value z0.

As the normal distribution is symmetric, we can use the fact that P(z < -z0) = 1 - P(z < z0).

We now calculate z as follows: z0 = (P81 + 1) / 2 = 0.9051

From a standard normal table, we can see that P(z < 0.9051) = 0.8186.

Therefore, P(z < -0.9051) = 1 - P(z < 0.9051) = 0.1814.

Now we calculate the corresponding value of x:

z = (x - u) / o-0.9051 = (x - 67.3) / 9.3x = 59.06

Therefore, P81 corresponds to the value x = 59.06.

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The system of equations that represents the given situation is:

q + d = 35

q*0.25 + d*0.10 = 4.90

Here we want to write a system of equations that represents the given situation.

First, let's define the two variables:

q = number of quarters.

d = number of dimes.

There are 35 coins in total, so the first equation is:

q + d = 35

And the value of these coins is $4.90, then the second equation is:

q*0.25 + d*0.10 = 4.90

Then the system of equations is:

q + d = 35

q*0.25 + d*0.10 = 4.90

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Answer:

8

Step-by-step explanation:

given the areas are equal then equate the areas of both, that is

area of parallelogram = lb ( l is the length and b the breadth )

here b = 2 , then

area = 2l

area of triangle = \(\frac{1}{2}\) bh ( b is the base and h the height )

here b = 8 and h = 4 , then

area = \(\frac{1}{2}\) × 8 × 4 = 4 × 4 = 16 cm²

Now equate the 2 areas

2l = 16 ( divide both sides by 2 )

l = 8 cm

the number in the box is then 8

For the given sequence, the formula for the nth term is a_n = 5^(n-1) / [12 + 3(n-1)] for n is greater than or equal to 1.

The given sequence is: 1/12, 5/15, 5^2/18, 5^3/21, 5^4/24, ....

The sequence has two patterns: the numerators follow a pattern of multiplying by 5 each term, and the denominators increase by 3 each term.

1. First, let's focus on the numerators:

1, 5, 5^2, 5^3, 5^4, ...

To find the formula for the numerators, notice that the exponent of 5 corresponds to n-1, so we have: 5^(n-1).

2. Now, let's focus on the denominators:

12, 15, 18, 21, 24, ...

The denominators increase by 3 each term, and the first term is 12. This is an arithmetic sequence with a common difference of 3, so the formula is: 12 + 3(n-1).

Now, let's combine both formulas to find the formula for the nth term of the sequence:

a_n = 5^(n-1) / [12 + 3(n-1)]

This is the formula for the nth term of the sequence in terms of n for n greater than or equal to 1.

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Answer: mmm

Step-by-step explanation:

mmm

The value of x , given the angle and the lines drawn , would be 142 degrees .

The fact that a straight line was drawn such that x degrees and 38 degrees make up the angles of that line , means that the total angular measure would be 180 degrees because this is the angle of a straight line.

This therefore means that to find the value of x, the formula would be :

x = 180 - 38

x  = 180 - 38

x = 142 degrees

In conclusion, the value of x would be 142 degrees.

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Answer:

$64

Step-by-step explanation:

This would be the answer because if we figure out what needs to be added to -21 to reach 43 we get 64.

(-21+64 - $43.)

Have a blessed day! Also brainliest would be appreciated :)

The actual step response plots would require specific values for time and magnitude scaling, which cannot be accurately depicted in a textual format.

To sketch the pole-zero plots for each system, we first need to identify the poles and zeros of each transfer function.

For G1(s) = (s + 2)^2:

- Pole: s = -2 (double pole)

For G2(s) = (s + 0.5)^0.5:

- Pole: s = -0.5 (single pole)

For G3(s) = (s + 0.5)(s + 2):

- Poles: s = -0.5, s = -2 (single poles)

Now, let's plot the pole-zero plots and the step responses for each system:

Pole-zero plot for G1(s):

- Pole at s = -2 (double pole)

- Zero at s = None (no zero)

Step response of G1(s):

- Time constant: T = 1/2 = 0.5 (from the dominant pole)

- The step response of G1(s) will exhibit an overshoot and multiple oscillations before settling to the steady-state value.

Pole-zero plot for G2(s):

- Pole at s = -0.5 (single pole)

- Zero at s = None (no zero)

Step response of G2(s):

- Time constant: T = 1/0.5 = 2 (from the dominant pole)

- The step response of G2(s) will show a slower rise time and smoother approach to the steady-state value compared to G1(s).

Pole-zero plot for G3(s):

- Poles at s = -0.5, s = -2 (single poles)

- Zero at s = None (no zero)

Step response of G3(s):

- The step response of G3(s) will resemble that of G1(s) since it shares the dominant pole at s = -2. However, the additional pole at s = -0.5 in G3(s) might introduce some damping and affect the transient response.

By observing the step responses of G1(s) and G2(s), we can verify their time constants:

- For G1(s), the time constant T = 0.5, as determined from the dominant pole at s = -2.

- For G2(s), the time constant T = 2, as determined from the dominant pole at s = -0.5.

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Answer:

4329

Step-by-step explanation:

I coan't really explain this sorry.

I hope this helps though!

Also if it's correct could I have a Brainly I need 1 more to level up :3 Thx!

The response is calculated by taking the Laplace transform of the input, multiplying it with the transfer function G(s), and then applying the inverse Laplace transform to obtain the time-domain response.

To calculate the response of the system G(s) to the given input u(t), we first need to find the Laplace transform of the input function u(t). The input function u(t) consists of multiple sinusoidal components, which can be represented in the Laplace domain using complex exponential functions.

Taking the Laplace transform of u(t), we get U(s) = 2/(s^2 + 1) + (-4)/(s^2 + 9) + 2/(s^2 + 25). Now, we multiply U(s) with the transfer function G(s) = (s + 1)/(s^2 + 2s + 2). Multiplying these two expressions, we obtain the product G(s)U(s).

Next, we need to apply the inverse Laplace transform to obtain the time-domain response. By using partial fraction decomposition and considering the inverse Laplace transforms of individual terms, we can calculate the inverse Laplace transform of G(s)U(s).

The final result will be the time-domain response of the system G(s) to the given input u(t). The response will contain the combined effect of the system dynamics and the input signal.

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Answer:

The tickets would have cost Gerallt £150 without the voucher.

Step-by-step explanation:

Set up the equation: 80% of x = £120

Divide both sides of the equation by 80% (which is equivalent to dividing by 0.8):

x = £120 / 0.8

Simplify the right side of the equation:

x = £150

Answer:

6

Step-by-step explanation:

The prime factorization of 12x is 3*2*2x. The prime factorization of 18 is 2*3*3. The same thing that appears in both prime factorizations is 3*2, or 6.

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