Given the equation 5y = 225, solve for y.

Using the given premises and the valid argument forms, the conclusion is D · G.

To complete the proof using only the eight valid argument forms, we can apply the disjunctive syllogism (DS) and modus ponens (MP) argument forms. Here's the proof:

[(B · ~C) v A] ⊃ D Premise

E v ~C Premise

E ⊃ F Premise

~F Premise

B · G Premise

~C v E Commutation of premise 2

C ⊃ ~E Implication of premise 6

E ⊃ ~E Hypothetical syllogism (HS) using premises 3 and 7

~E Modus ponens (MP) using premises 8 and 5

~(B · ~C) Disjunctive syllogism (DS) using premises 9 and 1

~B v C De Morgan's law using premise 10

C v ~B Commutation of premise 11

D Disjunctive syllogism (DS) using premises 4 and 12

G Simplification of premise 5

D · G Conjunction of premises 13 and 14

Therefore, we have concluded that D · G is a valid conclusion using the given premises and the valid argument forms.

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No, a prime factor of a trinomial is not always a binomial.

A trinomial is a polynomial with three terms, while a binomial is a polynomial with two terms. The factorization of a trinomial may involve both binomial and monomial factors.

For example, consider the trinomial x^2 + 4x + 4. Its factors can be written as (x + 2)(x + 2), which is a binomial squared. In this case, the prime factor of the trinomial is a binomial.

However, there are trinomials whose prime factors include both binomials and monomials. For instance, the trinomial x^2 + 3x + 2 can be factored as (x + 1)(x + 2), where the prime factors are both binomials.

In general, the factorization of a trinomial can involve various combinations of binomials and monomials, and it is not limited to only binomial factors.

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The slope of a line perpendicular to  y=-4x + 16 is (1/4), so the correct option is the first one (counting from the top).

The general linear equation in the slope-intercept form is:

y = a*x + b

Where a is the slope and b is the y-intercept.

Let's say that we have another line:

y = c*x + d

These two lines are perpendicular if and only if the slope of one of the lines is equal to the inverse of the opposite of the other line.

So, the two lines:

y = a*x + b

y = c*x + d

Are perpendicular only if c = -(1/a).

Now, we want to find a line perpendicular to:

y=-4x + 16

Then the slope of that perpendicular line must be:

-(1/-4) = (1/4)

So the slope of a line perpendicular to  y=-4x + 16 is (1/4).

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The mean of X is 3.25, the variance of X is 0.729, and the probability P(X < 2.6) is approximately 0.314.

The mean of X can be found by taking the average of the endpoints of the interval, which is [1.5, 5.0]. Therefore, the mean of X is (1.5 + 5.0) / 2 = 3.25.

The variance of X for a continuous uniform distribution can be calculated using the formula: variance = (b - a)^2 / 12, where a and b are the endpoints of the interval. In this case, a = 1.5 and b = 5.0, so the variance of X is (5.0 - 1.5)^2 / 12 = 0.729.

To find P(X < 2.6), we need to calculate the probability of X falling within the interval [1.5, 2.6]. Since X has a continuous uniform distribution, the probability is equal to the width of the interval divided by the total width of the distribution. In this case, the width of the interval [1.5, 2.6] is 2.6 - 1.5 = 1.1, and the total width of the distribution is 5.0 - 1.5 = 3.5. Therefore, P(X < 2.6) = 1.1 / 3.5 ≈ 0.314.

In summary, the mean of X is 3.25, the variance of X is 0.729, and the probability P(X < 2.6) is approximately 0.314. The continuous uniform distribution ensures that the probability is evenly distributed over the interval [1.5, 5.0], resulting in a constant probability density function within this range.

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The mean of samples 10, 10, 10, 10, 10, and 16 will be 11.

The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.

In a sample of n = 6, five individuals all have scores of x = 10 and the sixth person has a score of x = 16.

Then the data set will be given below.

10, 10, 10, 10, 10, 16

Then the mean of the data set will be

Mean = (10 + 10 + 10 + 10 + 10 + 16) / 6

Mean = 66/6

Mean = 11

Thus, the mean of the sample will be 11.

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Answer: A line straight horizontal on the y value of 2.

Step-by-step explanation:

-------------------------------2-------------------------------------------

Answer:

Shown in the attached image below

Step-by-step explanation:

The graph of y=2 means that any x-value you put in, all of the values are always going to equal 2. That’s why it’s a horizontal line at 2.

Hope this helps! :)

Answer:

pa pic nyou nalang kung may pic plss

Answer:

9 and 29.

Let us denote the older brother’s age 4 years ago by x and the younger brother’s age 4 years ago by y

Their combined ages 4 years ago is 38–8 =30

So we have the equation x+y=30

We also know that x=y^2

X=25 and y=5 will satisfy that condition

So 4 years ago the older was 25 years old and the younger 5.

4 years later the older brother is 29 years old and the younger brother is 9

Answer:

Step-by-step explanation:

The volume formula

Given

Find the volume by substituting the values into formula

Area of base=8.15cm²

Volume

The equation represents the line that passes through (- 6, 7) and (- 3, 6) is  y = -1/3x +5

The slope-intercept form is just a means of formulating a line's equation so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are clearly visible. This form is frequently referred to as the y = mx + b form. This line form is one of the most prevalent in algebra classes.

A line's slope-intercept form is y = mx + b, where m is its slope and b is its y-intercept.

The equation of the line which is passing through two points is:

y₂-y₁ / x₂-x₁

(6-7)/(-3+6)=-1/3

A line's slope-intercept form is y =mx +b, where m is the slope and b is the y intercept.

y = -1/3 x +b. We must now calculate b, the y intercept. To find b, plug one of the given points into the previous equation and solve for b.

6 = -1/3(-3) + b

b = 5

y = -1/3x +5

Therefore, the equation represents the line that passes through (- 6, 7) and (- 3, 6) is  y = -1/3x +5

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The manager should use the percentages of sales split among the four areas: 40% clothing, 40% footwear, 10% housewares, and 10% athletic gear. Using the random digit table, the manager can generate random numbers and assign them to each category based on their respective percentages to simulate the store's sales.

To run a simulation of the store's sales using a random digit table, you will need to assign specific digits to each sales area based on their percentage. Here's a step-by-step explanation:
1. First, determine the digit ranges that correspond to the sales percentages. For this example, you can use:
  - Clothing: 0-3 (40%)
  - Footwear: 4-7 (40%)
  - Housewares: 8 (10%)
  - Athletic gear: 9 (10%)
2. Obtain a random digit table. This is a table filled with random digits, typically from 0 to 9, arranged in a specific order to ensure randomness.
3. Read the random digit table and, for each digit, determine the corresponding sales area using the ranges you established in step 1. For example, if the random digit is 2, it corresponds to clothing; if it's 9, it corresponds to athletic gear.
4. Continue this process for the desired number of trials in your simulation, recording the sales area for each digit to estimate the store's sales distribution.
By following these steps, you'll be able to run a simulation of the store's sales using a random digit table while considering the split among the four sales areas.

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The probability that exactly 10 are yellow out of 9 random selections is 0.

To calculate the probability of exactly 10 jelly beans being yellow out of 9 selected at random, we need to consider the total number of favorable outcomes (selecting exactly 10 yellow jelly beans) divided by the total number of possible outcomes (selecting any 9 jelly beans).

The total number of jelly beans in the box is 23 (yellow) + 33 (green) + 37 (red) = 93.

The number of ways to select exactly 10 yellow jelly beans out of 9 is 0, as we have fewer yellow jelly beans than the required number.

Therefore, the probability of exactly 10 yellow jelly beans is 0.

In this case, it is not possible to have exactly 10 yellow jelly beans out of the 9 selected because there are not enough yellow jelly beans available in the box.

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A box contains 23 yellow, 33 green and 37 red jelly beans. if 9 jelly beans are selected at random, what is the probability that: exactly 10 are yellow?

Answer:

D.

Step-by-step explanation:

a1 = -8

a2 = -8 * 2.5

a3 = -8 * 2.5 * 2.5

a4 = -8 * 2.5^3

an = -8 * 2.5^(n - 1)

The first term is -8. Each subsequent term is 5/2 times the previous term.

Answer: D.

Answer:

Step-by-step explanation:

These are physical measurements, which must be zero or greater.  These restrictions are the reason for your having a total of four inequalities.

Answer:

3

Step-by-step explanation:

Answer:

400 employees

Step-by-step explanation:

Let the total no. of employees be x

From the information we get that,

30% of x= 120

Hence, 30/100x=120

x=120×100/30

x=400

The measure of the complement of the angle is A) 54.

Given:

The ratio of the measure of the supplement of an angle to that of a complement of the angle is 8:3.

Let x be the angle.

supplement of the angle of x is = 180-x

complement of the angle of x is = 90 -x

180 - x / 90 -x = 8/3

3(180-x) = 8(90-x)

3*180 - 3*x = 8*90 - 8*x

540 - 3x = 720 - 8x

-3x+8x = 720 - 540

5x = 180

divide by 5 on both sides

x = 180/5

x = 36

Complement of the angle = 90 - 36

= 54

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The extreme points of the polyhedral set S are {(2, 1), (2, 2), (3, 1), (3, 2), (4, 1), (4, 2)}. There are no extreme directions in this case.

To find the extreme points and extreme directions of the polyhedral set S, we need to analyze the given inequalities.

The inequalities defining the polyhedral set S are:

2x1 + 4x2 > 4

-x1 + x2 < 4

x1 > 0

x2 > 0

Let's solve these inequalities step by step.

2x1 + 4x2 > 4:

Rearranging this inequality, we get x2 > (4 - 2x1) / 4.

This implies that x2 > (2 - x1/2).

-x1 + x2 < 4:

Rearranging this inequality, we get x2 > x1 + 4.

Combining the above two inequalities, we can determine the range of values for x1 and x2. We can draw a graph to visualize this region:

         x2

          ^

          |

     +    |   +

          |

     +----|---------+

          |

     +    |   +

          |

     +----|---------+----> x1

          |

          |

From the graph, we can see that the polyhedral set S is a bounded region with vertices at (2, 1), (2, 2), (3, 1), (3, 2), (4, 1), and (4, 2). These are the extreme points of S.

However, in this case, there are no extreme directions since the polyhedral set S is a finite set with distinct vertices. Extreme directions are typically associated with unbounded regions.

Therefore, the extreme points of S are {(2, 1), (2, 2), (3, 1), (3, 2), (4, 1), (4, 2)}, and there are no extreme directions in this case.

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The inverse Laplace transform of F(s) is:

\(f(t) = e^(-t)\)

To find the inverse Laplace transform of each function, we need to express them in terms of known Laplace transforms. Here are the solutions for each function:

a)

\(F(s) = \large{\frac{2e^{-0.5s}}{s^2-6s+9}}\)

To find the inverse Laplace transform, we first need to factor the denominator of F(s). The denominator factors as (s - 3)². Therefore, we can rewrite F(s) as:

\(F(s) = \large{\frac{2e^{-0.5s}}{(s-3)^2}}\)

Now, we know that the Laplace transform of eᵃᵗ is 1/(s - a). Therefore, the inverse Laplace transform of

\(e^(-0.5s) \: is \: e^(0.5t).\)

Applying this, we get:

\(f(t) = 2e^(0.5t) * t \\

b) F(s) = \large{\frac{s-1}{s^2-3s+2}}\)

We can factor the denominator of F(s) as (s - 1)(s - 2). Now, we rewrite F(s) as:

\(F(s) = \large{\frac{s-1}{(s-1)(s-2)}}\)

Simplifying, we have:

\(F(s) = \large{\frac{1}{s-2}}\)

The Laplace transform of 1 is 1/s. Therefore, the inverse Laplace transform of F(s) is:

\(f(t) = e^(2t) \\

c) F(s) = \large{\frac{s-1}{s^2+s-2}}

\)

We factor the denominator of F(s) as (s - 1)(s + 2). The expression becomes:

\(F(s) = \large{\frac{s-1}{(s-1)(s+2)}}\)

Canceling out the (s - 1) terms, we have:

\(F(s) = \large{\frac{1}{s+2}}\)

The Laplace transform of 1 is 1/s. Therefore, the inverse Laplace transform of F(s) is:

\(f(t) = e^(-2t) \\

d) F(s) = \large{\frac{e^{-s}(s-1)}{s^2+s-2}}\)

We can factor the denominator of F(s) as (s - 1)(s + 2). Now, we rewrite F(s) as:

\(F(s) = \large{\frac{e^{-s}(s-1)}{(s-1)(s+2)}}\)

Canceling out the (s - 1) terms, we have:

\(F(s) = \large{\frac{e^{-s}}{s+2}}\)

The Laplace transform of

\(e^(-s) \: is \: 1/(s + 1).\)

Therefore, the inverse Laplace transform of F(s) is:

\(f(t) = e^(-t)\)

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Answer:

Step-by-step explanation:

1/2*b*h

1/2*4*5

4/2*5

2*5

10

Answer:

Ali's heart rate is 135 times per minute.

Step-by-step explanation:

Let Ali's heart rate be denoted by x times per minute.

It is provided that Ben's heart beats 18 times per minute more than Ali.

The ratio of their heart rates was 15:17.

That is:

\(\frac{15}{17}=\frac{x}{x+18}\)

Solve for x as follows:

\(\frac{15}{17}=\frac{x}{x+18}\)

\(15(x+18)=17x\\15x+270=17x\\2x=270\\x=135\)

Thus, Ali's heart rate is 135 times per minute.

Step-by-step explanation:

the question is not understood plz clarify it

Answer:is 2 over 4|/x

Step-by-step explanation:

the cost of the bike before tax

514.1/106%=$485

Answer:

Area ≈ 314.16 square inches

Step-by-step explanation:

Radius of circle (r) = ½(20) = 10 in.

Formula for area of circle, A = πr²

Plug in the value into the formula

Area = π × 10²

Area = π × 100

Area = 314.159265

Area = 314.16 in.² (nearest hundredth)

(1) The probability that the second ball drawn is yellow is 2/11

(2) The probability of drawing a red ball on the second draw, given that the first ball was not red, is 4/10

To find the probability of drawing a yellow ball on the second draw, we need to consider the possible outcomes of the first draw. There are two possible outcomes: either we draw a yellow ball, or we draw a non-yellow ball.

Therefore, the probability of drawing a yellow ball on the second draw, given that the first ball was yellow, is 2/11, because there are still two yellow balls left in the box out of a total of 11 balls.

To find the probability of drawing a red ball on the second draw, we need to consider the possible outcomes of the first draw again. If we draw a red ball on the first draw, we do not replace it, which means that there are still four red balls left in the box.

If we draw a non-red ball on the first draw, we do not replace it either, which means that there are still four red balls left in the box.

Then it can be written as,

=> 4/10

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Answer:

¹⁴⁵⁸³³³³³³³³⁄₁₀₀₀₀₀₀₀₀₀₀₀

Step-by-step explanation:

lol

Answer: 170

Step-by-step explanation: Like I answered before: Angle G and Angle H are consecutive angles, meaning they both add up to 180 degrees. Thus, if 10 is the value of Angle G, Angle H must be 170.

Answer:

<CDA = 170⁰

Step-by-step explanation:

<A + <D = 180⁰ { Adjacent Angles of an parallelogram are supplementary}

10⁰ + <D = 180⁰

<D = 180⁰ - 10⁰ = 170⁰

<D = x⁰ = 170⁰ = <CDA

Effect size is a measure of the strength of the relationship between two variables. It does not indicate whether one variable causes another. The amount of variance in a set of scores is measured by the variance.

Whether an obtained research finding is valid is determined by statistical significance. Effect size is a quantitative measure of the magnitude of the experimental effect.

It is a way of quantifying the strength of the relationship between two variables. Effect sizes are typically reported on a standardized scale, such as Cohen's d or r.

Effect size does not indicate whether one variable causes another. Causation can only be inferred from a well-designed experiment that controls for confounding variables.

Effect size can be used to assess the strength of the relationship between two variables, but it cannot be used to determine whether one variable causes another.

The amount of variance in a set of scores is measured by the variance. Variance is a measure of how spread out the scores are in a set.

A high variance indicates that the scores are spread out over a wide range, while a low variance indicates that the scores are clustered together.

Whether an obtained research finding is valid is determined by statistical significance. Statistical significance is a measure of how likely it is that the observed results could have occurred by chance. A statistically significant result means that the observed results are unlikely to have occurred by chance alone.

Effect size, variance, and statistical significance are all important concepts in statistics. Effect size measures the strength of the relationship between two variables,

variance measures the spread of scores in a set, and statistical significance measures the likelihood that the observed results could have occurred by chance.

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Answer:

X = 1

Y = 5

Step-by-step explanation:

we have to figure out what x and y = that make both answers correct

3 x 1 = 3

3 + 5 = 8

That means that the first equation is right with X = 1 and Y = 5

Let's see the second equation

5 x 1 = 5

5 + 5 = 10

That means both equations are right so the answer would be

X = 1 and

Y = 5

Method of Elimination:

Given pair of linear equations are:

3x+y = 8 — — —Eqn(i)

On comparing with a₁x+b₁y+c₁ = 0

Where,

5x+y = 10 — ——Eqn(ii)

On comparing with a₂x+b₂y+c2₂ = 0

Where,

a₁/a₂ = 3/5

b₁/b₂ = 1/1= 1

c₁/c₂ = 8/10=4/5

We have,

a₁/a₂ ≠ b₁/b₂ ≠ c₁/c₂

So, Given pair of linear equations in two variables have a unique solution.

Now,

On Subtracting eqn(ii) from eqn(i) then

3x+y = 8

5x+y = 10

(-)

________

-2x+0 = -2

_________

⇛-2x = -2

⇛2x = 2

⇛x = 2/2

⇛x = 1

On Substituting the value of x in eqn(i) then

⇛3(1)+y = 8

⇛3+y = 8

⇛y = 8-3

⇛y = 5

Therefore , The solution = (1,5)

Additional comment:

The product of 32 and 0.9 is 28.8.

The product of a set of numbers is the result of multiplying all the numbers together. For example, the product of 2, 3, and 4 is:

2 x 3 x 4 = 24

In general, if we have n numbers, the product is:

a1 x a2 x a3 x ... x an

where a1, a2, a3, ..., an are the individual numbers.

The product of two negative numbers is positive, while the product of a negative and a positive number is negative. The product of any number and 0 is always 0.

To find the product of 32 and 0.9, you can multiply these two numbers together:

32 x 0.9 = 28.8

Therefore, the product of 32 and 0.9 is 28.8.

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