Which of the following proportions is false?

To provide Logical Proofs with line-by-line justifications for the following arguments,

Let's use the first 4 rules of inference.

Given below is the justification for each step of the proof with the applicable rule of Inference.

E > M1. A > (E > ~F) Premise2. H v (~F > M) Premise3. A Premise4. ~H  Premise5. A > E > ~F 1, Hypothetical syllogism6.

E > ~F 5,3 Modus Ponens 7 .

~F > M 2,3 Disjunctive Syllogism 8.

E > M 6,7 Hypothetical SyllogismIf

A is true, then E must be true because A > E > ~F.

Also, if ~H is true, then ~F must be true because H v (~F > M). And if ~F is true,

Then M must be true because ~F > M. Therefore, E > M is a valid  based on the given premises using the first four rules of inference.

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1. The remainder when dividing \(x^2\) by x - 1 is 1.

2. The simplified expression for \(x + 3 - 3x^2 - 4x - 12\ is\ -3x - 3x^2 - 9\).

3. Factors of 20 in pairs: 1 and 20, 2 and 10, 4 and 5.

4. Factors of 60: 1 and 6\(x + 3 - 3x^2 - 4x - 12\) 30, 3 and 20, 4 and 15, 5 and 12, 6 and 10.

5. Factors of 26: 1 and 26, 2 and 13.

6. Factors of 43: 1 and 43.

1. To divide \(x^2\) by x - 1, you can use polynomial long division. The remainder would be 1 because \(x^2\) divided by x - 1 leaves a remainder of 1.

2. The expression can be simplified by combining like terms. Combining the x and -4x terms, we have:

\(x - 4x + 3 - 3x^2 - 12 = -3x - 3x^2 - 9\)

So, the simplified expression is \(-3x - 3x^2 - 9\)

3. Factors of 20 in pairs are:

  - 1 and 20

  - 2 and 10

  - 4 and 5

4. Factors of 60 are:

  - 1 and 60

  - 2 and 30

  - 3 and 20

  - 4 and 15

  - 5 and 12

  - 6 and 10

5. Factors of 26 are:

  - 1 and 26

  - 2 and 13

6. Factors of 43 are:

  - 1 and 43

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The probability of a vanilla taffy is given as follows:

P(vanilla) = 0.31.

Hence the probability of a vanilla or banana taffy is given as follows:

P(vanilla or banana) = 0.52.

The two parameters that are needed to calculate a probability are listed as follows:

Then the probability is then calculated as the division of the number of desired outcomes by the number of total outcomes.

When we are given the relative frequencies, we must simply identify the desired outcomes, as follows:

Hence the probability is given as follows:

P(vanilla or banana) = P(vanilla) + P(banana) = 0.52.

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a. The mean will not change. When considering the effect of sample size on the mean of the sampling distribution,

it's important to understand the concept of the Central Limit Theorem (CLT) and the properties of sampling distributions.

The Central Limit Theorem states that for a large enough sample size, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution. Additionally, the mean of the sampling distribution will be equal to the population mean.

As the sample size increases, the sampling distribution becomes more representative of the population distribution, and the variability of the sample means decreases. However, the mean of the sampling distribution remains the same as the population mean.

This is an important property of the Central Limit Theorem. It means that increasing the sample size does not change the mean of the sampling distribution. The mean of the sampling distribution is solely determined by the population mean, not the sample size.

To put it simply, the mean of the sampling distribution represents the average of all possible sample means that could be obtained from a population. It is not influenced by the sample size but rather reflects the underlying population parameter.

Therefore, when the sample size increases, the mean of the sampling distribution will not change. It will remain the same as the population mean.

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Answer:

To find -134 + 53, add the ones place (4+3=7) and the tens place (5+3=8), giving you -81.

Answer: -81.

Answer:

-81

Step-by-step explanation:

You subtract the absolute values and take the sign of the larger absolute value.

Absolute value is the distance from zero.  This will be a positive number

134 - 53 = 81

The sign will be negative because the sign of the higher absolute value number is negative.  134 has a larger absolute value than 53 and it is negative, so our answer is negative.

Helping in the name of Jesus.

Answer:
-7x + 5

Step-by-step explanation:

2(4x + 1) - 3(5x - 1)

8x + 2 - 3(5x-1)
8x + 2 - 15x + 3
8x + 5 - 15x
-7x + 5

Hope it helped !
Adriel

Answer:

f^-1 (x) = x^2 + 5

Step-by-step explanation:

f(x) = √x - 5

replace x with y

x= √y - 5

solve for y,

x =√y-5

x^2 + 5

Answer -

f^-1(x) = x^2 + 5

HOPES THIS HELPS :)

Given:

The function is:

\(h(x)=x^2-3x+5\)

To find:

The value of \(h(2x+1)\).

Solution:

We have,

\(h(x)=x^2-3x+5\)

Putting \(x=2x+1\), we get

\(h(2x+1)=(2x+1)^2-3(2x+1)+5\)

\(h(2x+1)=(2x)^2+2(2x)(1)+(1)^2-3(2x)-3(1)+5\)

\(h(2x+1)=4x^2+4x+1-6x-3+5\)

On combining like terms, we get

\(h(2x+1)=4x^2+(4x-6x)+(1-3+5)\)

\(h(2x+1)=4x^2-2x+3\)

Therefore, the required function is \(h(2x+1)=4x^2-2x+3\).

Given:

Point = (1,-4), Slope - 8

Point = (1,5), Slope =1

To find:

The slope-intercept forms of the given lines.

Solution:

The slope intercept form of a line is:

\(y=mx+b\)

The point slope form is:

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

where, m is the slope of the line.

We have, Point = (1,-4), Slope - 8. So, the equation of the line is:

\(y-(-4)=-8(x-1)\)

\(y+4=-8x+8\)

\(y=-8x+8-4\)

\(y=-8x+4\)

Therefore, the correct option is B.

We have, Point = (1,5), Slope =1. So, the equation of the line is:

\(y-5=1(x-1)\)

\(y-5=x-1\)

\(y=x-1+5\)

\(y=x+4\)

Therefore, the correct option is D.

Answer: B. ( 3x + 4) ( 3x + 4)   or   (3x+4)^2

Step-by-step explanation:

Solve by factoring

9x^2 + 24x + 16       Find two numbers that  their product is 144 and their sum is 24.   The numbers  12 and 12 works out because 12 times 12 is 144 and 12 plus 12 is 24.

Rewrite the expression in a new way like,

9x^2 + 12x + 12x  + 16         Now factor by grouping them into two groups

(9x^2 + 12x) ( 12x + 16)     Now factor each group by using the greatest GCF

3x ( 3x + 4) 4( 3x + 4)     Factor out 3x +4  

(3x + 4) ( 3x + 4)

The solution to the integral ∫cot(x) dx is ln|sin(x)| + C, where C is the constant of integration.

The integral of cot(x) dx can be evaluated by rewriting cot(x) in terms of sine and cosine.

To evaluate the integral ∫cot(x) dx, we start by expressing cot(x) in terms of sine and cosine.

The identity cot(x) = cos(x)/sin(x) allows us to rewrite the integral as ∫cos(x)/sin(x) dx.

Next, we can apply a substitution to simplify the integral. Let u = sin(x), then du = cos(x) dx.

Rewriting the integral using u, we have ∫du/u.

The integral of du/u is ln|u| + C, where C is the constant of integration.

Substituting back u = sin(x), we obtain ln|sin(x)| + C.

Therefore, the solution to the integral ∫cot(x) dx is ln|sin(x)| + C, where C is the constant of integration. This represents the antiderivative of cot(x).

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Answer: =248x

Step-by-step explanation: Hope this help :D

Let's simplify step-by-step.

4x(10)+2x(104)

=40x+208x

Combine Like Terms:

=40x+208x

=(40x+208x)

=248x

Variables would make each algebraic equation a true statement is;

d² = 36 is true for d = ±6.4s = 2s - 2 + 3s is true for s = 2.b + 25 = b - 25 is true for no value of b will make the equation true.

The given algebraic equations will be true if the following values of the given variables are used:

d² = 36 is true for, d = ±6

We know that the square of a number gives us a positive value only.

So, d = ±6.4s = 2s - 2 + 3s is true for.

Since both sides of the equation have terms with s in them, let's simplify it:

4s = 2s + 3s - 2⇒ 4s = 5s - 2⇒ 4s - 5s = -2⇒ -s = -2⇒ s = 2.

Thus, 4(2) = 2(2) - 2 + 3(2) is true for b + 25 = b - 25 is true for

Let's simplify the given equation

b + 25 = b - 25⇒ b - b = -25 - 25⇒ 0 = -50

The given equation is always false.

There is no value of b that will make it true.

Complete the following statements by determining which value(s) of the given variables would make each algebraic equation a true statement:

d² = 36 is true for d = ±6.4s = 2s - 2 + 3s is true for s = 2.b + 25 = b - 25 is true for no value of b will make the equation true.

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Answer:

A

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

Each time you divide or multiply by a negative number, you must change the direction of the inequality symbol.

Answer:

C and D are same options

(D)\( f(x) = x^2 \)

Step-by-step explanation:

\(f(x) = {x}^{2} \\ plug \: x = - x \\ f( - x) = {( - x)}^{2} = {x}^{2} \\ f( - x) = f(x)\)

Answer:

√

8

≈

3

Explanation:

Note that:

2

2

=

4

<

8

<

9

=

3

2

Hence the (positive) square root of  

8

is somewhere between  

2

and  

3

. Since  

8

is much closer to  

9

=

3

2

than  

4

=

2

2

, we can deduce that the closest integer to the square root is  

3

.

We can use this proximity of the square root of  

8

to  

3

to derive an efficient method for finding approximations.

Consider a quadratic with zeros  

3

+

√

8

and  

3

−

√

8

:

(

x

−

3

−

√

8

)

(

x

−

3

+

√

8

)

=

(

x

−

3

)

2

−

8

=

x

2

−

6

x

+

1

From this quadratic, we can define a sequence of integers recursively as follows:

⎧

⎪

⎨

⎪

⎩

a

0

=

0

a

1

=

1

a

n

+

2

=

6

a

n

+

1

−

a

n

The first few terms are:

0

,

1

,

6

,

35

,

204

,

1189

,

6930

,

...

The ratio between successive terms will tend very quickly towards  

3

+

√

8

.

So:

√

8

≈

6930

1189

−

3

=

3363

1189

≈

2.828427

Answer:

a person who fortells an event is called

Answer:

1/4

Step-by-step explanation:

It takes the line 4 horizontal unitz to get to the next vertical unit.

Answer:

C 1/4

Step-by-step explanation:

Answer:

Option B is tge right answer.

3.07/10⁴= 0.000307

Answer:

a. 0.00307

Step-by-step explanation:

1)  XY' + Z + X'Z' + YZ'

2) equation 2 is correct.

3) equation 3 is incorrect .

1)

Simplifying algebraically,

XY' +Z+ (X' + Y)Z'

So,

XY' + Z + X'Z' + YZ'

2)

D(A + B)(A + B')C

Simplifying,

(AD + DB) (A + B')C

Further,

ADC + AB'CD + ABCD + BB'CD

ACD + ABCD + AB'CD

= ACD

Thus equation 2 is correct .

Hence proved .

3)

(a + b)(b + c)(c + a) = f1

Simplifying further,

abc + ab + bc + ac = f1

Let f2 = (a'+ b')(b' + c')(c' + a')

Simplify further,

f2 = a'b'c' + a'b' + b'c' + a'c'

Here,

f1 ≠ f2

Thus we disprove equation 3 .

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At year 2, you will have approximately $25,915.13 in your bank account, assuming an initial investment with a 5% interest rate compounded annually. The correct answer is (a).


To find out how much money you will have in your bank account at year 2, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (in this case, $30,000)
P = Principal amount (initial investment)
R = Annual interest rate (5% or 0.05)
N = Number of times interest is compounded per year (assumed to be once per year)
T = Number of years (in this case, 3)
Let’s solve for P, the principal amount at year 0:
30,000 = P(1 + 0.05/1)^(1*3)
30,000 = P(1.05)^3
Dividing both sides of the equation by (1.05)^3:
P = 30,000 / (1.05)^3
P ≈ 25,915.13
Therefore, at year 2, you will have approximately $25,915.13 in your bank account.
The correct answer is (a) $25,915.13.

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The types of systems of linear equations are as follows:

Dependent: The system has infinitely many solutions. The graphs of the equations represent the same lines.

Independent: The system has exactly one solution. The graphs of the equations intersect at a single point.

Inconsistent: The system has no solution. The graphs of the equations are parallel lines.

Linear equations are mathematical equations that describe a linear relationship between two or more variables. These equations have the form of y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.

The solutions to linear equations form a straight line when plotted on a graph.

By plotting the equations on the graph we get:

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The minimum probability that an outcome falls between 42 and 98, according to Chebyshev's inequality, is at least 0.9184 (or 91.84% when expressed as a percentage).

Chebyshev's inequality states that for any probability distribution, the minimum proportion of values within k standard deviations of the mean is at least 1 - 1/k^2.

In this case, we are given that the mean (μ) of the distribution is 70 and the standard deviation (σ) is 8. We want to find the minimum probability that an outcome falls between 42 and 98, which corresponds to a range of 56 units.

To apply Chebyshev's inequality, we need to determine the value of k. Since we want to find the minimum probability, we want to maximize the range by setting k to its minimum value.

We can use the formula k = (x - μ) / σ, where x is the range we are interested in. Substituting the values, we have:

k = (98 - 70) / 8 = 3.5

Now we can use Chebyshev's inequality to find the minimum probability:

P(|X - μ| ≤ kσ) ≥ 1 - 1/k^2

P(42 ≤ X ≤ 98) ≥ 1 - 1/(3.5)^2

P(42 ≤ X ≤ 98) ≥ 1 - 1/12.25

P(42 ≤ X ≤ 98) ≥ 1 - 0.0816

P(42 ≤ X ≤ 98) ≥ 0.9184

Therefore, the minimum probability that an outcome falls between 42 and 98, according to Chebyshev's inequality, is at least 0.9184 (or 91.84% when expressed as a percentage).

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Answer:

8 inches

Step-by-step explanation:

The volume of a hemisphere is half the volume of a sphere.

Therefore, the sum of the volumes of the two hemisphere-shaped scoops of ice cream (with diameters of 4 inches), is equal to the volume of a sphere with diameter of 4 inches.

If the melted ice cream fills the cone exactly to the top without overflowing, the volume of the cone with diameter of 4 inches must be equal to the volume of a sphere with diameter of 4 inches.

As the diameter of a circle is twice its radius, then the radius of the sphere and cone is r = 2 inches.

The formulas for the volume of a cone and the volume of a sphere are:

\(\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}\)   \(\boxed{\begin{minipage}{4 cm}\underline{Volume of a sphere}\\\\$V=\dfrac{4}{3} \pi r^3$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius.\\\\\end{minipage}}\)

The depth of the cone is its height.

Therefore, to calculate how deep the cone must be so that the melted ice cream will fill the cone exactly to the top without overflowing, set the two equations equal to each other, substitute r = 2, and solve for h (the depth of the cone).

\(\begin{aligned}\textsf{Volume of a cone}&=\textsf{Volume of a sphere}\\\\\dfrac{1}{3} \pi (2)^2 h & = \dfrac{4}{3} \pi (2)^3\\\\\dfrac{1}{3} \pi \cdot 4 h & = \dfrac{4}{3} \pi \cdot 8\\\\\dfrac{4}{3} \pi h& = \dfrac{32}{3} \pi \\\\\dfrac{4}{3} h& = \dfrac{32}{3} \\\\4 h& = 32 \\\\h&=\dfrac{32}{4}\\\\h&=8\; \sf inches\end{aligned}\)

Therefore, the depth of the cone must be 8 inches.

The cone must be at least 8 inches deep in order for the melted ice cream to fill the cone exactly to the top without overflowing.

1. The opening of the ice cream cone has a diameter of 4 inches. This means that the radius of the cone's opening is 4/2 = 2 inches.

2. The two hemisphere-shaped scoops of ice cream have diameters of 4 inches each. This means that the radius of each scoop is 4/2 = 2 inches.

3. When the ice cream melts, it will take up the space between the scoops and fill the cone. In order for the melted ice cream to fill the cone exactly to the top without overflowing, the depth of the cone must be equal to the combined height of the two ice cream scoops.

4. The height of each hemisphere-shaped scoop can be calculated using the formula for the volume of a sphere, which is (4/3)πr³, where r is the radius.

  - For each scoop, the radius is 2 inches, so the height of each scoop is (4/3)π(2)³ = (4/3)π(8) = (32/3)π.

5. Since there are two scoops, the combined height of the two scoops is 2 * (32/3)π = (64/3)π.

6. Therefore, the cone must be at least (64/3)π inches deep in order for the melted ice cream to fill the cone exactly to the top without overflowing. This is approximately equal to 67.03 inches.

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Answer:

5h

Step-by-step explanation:

To earn $25, she would have to work a total of 5 hours, to get $30. Although 30 is over 25, 4 hours, or $24 is not enough. H represents hours, so 5 hours, or 5h.

Answer: 5 hours

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The graph of function y = 2x - 4 is shown in figure.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Equation of line is,

⇒ y = 2x - 4

Now, WE know that;

Standard form of equation of line is,

y = mx + c

Where, m is slope and c is y - intercept.

Here, Function is,

y = 2x - 4

Hence, y - intercept = - 4

Thus, The graph of function y = 2x - 4 is shown in figure with y - intercept (0, - 4).

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Answer:

The length of the missing side is 18yd

Step-by-step explanation:

Sq30 - Sq 24 = Sq (x)

Yes. I've received grades that follow the "curve" for many of my classes. After a test or assignment, student scores are adjusted when grading is done on a curve. The curve typically improves both the overall average grade and individual student scores. Some professors fully avoid curves while others utilize a variety of techniques.

By combining numerous payment cards through a mobile app, Curve (also known as the Curve card) is a payment card that enables users to make purchases and withdrawals with just one card. After each transaction is over, you can "swap the bank card you paid with." This function was dubbed "Back in time" by Curve. Shachar Bialick launched Curve in 2015; it is the company that issues the card as well as owns and runs the business. In December 2015, the business obtained $2 million in startup capital. In February 2016, an open beta for iOS users in the "enterprise community" was released. Customers were informed by Curve in May 2016 that Curve will no longer be able to support American Express after May 31, 2016, and they were given refunds.

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P(X = 7), λ = 6: The Poisson probability of X = 7, with a parameter (λ) value of 6, is 0.1446. P(X = 11), λ = 12: The Poisson probability of X = 11, with a parameter (λ) value of 12, is 0.0946. P(X = 6), λ = 8: The Poisson probability of X = 6, with a parameter (λ) value of 8, is 0.1206.

The Poisson probability is used to calculate the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence (parameter λ). The formula for Poisson probability is P(X = k) = (e^-λ * λ^k) / k!, where X is the random variable representing the number of events and k is the desired number of events.

To calculate the Poisson probabilities in this case, we substitute the given values of λ and k into the formula. For example, for the first case (a), we have λ = 6 and k = 7: P(X = 7) = (e^-6 * 6^7) / 7!

Using a calculator, we can evaluate this expression to find that the probability is approximately 0.1446. Similarly, for case (b) with λ = 12 and k = 11, and for case (c) with λ = 8 and k = 6, we can apply the same formula to find the respective Poisson probabilities.

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Answer:

  x = 16

Step-by-step explanation:

The two angles marked with x-terms are "alternate exterior angles", hence, congruent.

  8x -14 = 5x +34

  3x = 48 . . . . . . . . . add 14-5x

  x = 16