Prove that the line joining the midpoint of a median to a vertex of the triangle trisects

the side opposite the vertex considered.​

Sure! Here's a block diagram representation of a 5-to-32 line decoder using four 3-to-8 line decoders with enable (3:8 decoder with enable) and a 2-to-4 line decoder.

     _________       _________       _________       _________

    |         |     |         |     |         |     |         |

IN[4] | 5:32    |     | 3:8     |     | 3:8     |     | 3:8     |

----->| Decoder |---->| Decoder |---->| Decoder |---->| Decoder |----> Y[31]

    |_________|     |_________|     |_________|     |_________|

    |                           | |                           |

IN[3] |                           | |                           |

----->|                           | |                           |

    |          3:8 Decoder       | |          3:8 Decoder       |

    |___________________________| |___________________________|

    |                           | |                           |

IN[2] |                           | |                           |

----->|                           | |                           |

    |          3:8 Decoder       | |          3:8 Decoder       |

    |___________________________| |___________________________|

    |                           | |                           |

IN[1] |                           | |                           |

----->|                           | |                           |

    |          3:8 Decoder       | |          3:8 Decoder       |

    |___________________________| |___________________________|

    |                           | |                           |

IN[0] |                           | |                           |

----->|          2:4 Decoder       | |                           |

    |___________________________| |          3:8 Decoder       |

                                   |___________________________|

Inputs:

IN[4:0]: 5-bit input lines

Outputs:

Y[31:0]: 32 output lines

The 5-to-32 line decoder takes a 5-bit input (IN[4:0]) and produces 32 output lines (Y[31:0]). It uses four 3-to-8 line decoders with enable (3:8 Decoder) to decode the input bits and generate intermediate outputs. The intermediate outputs are then connected to a 2-to-4 line decoder (2:4 Decoder) to produce the final 32 output lines (Y[31:0]).

Note: The enable lines for the 3-to-8 line decoders are not shown in the diagram for simplicity. Each 3-to-8 line decoder will have its own enable input, which can be used to enable or disable the decoder's functionality.

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(a) Negation: ¬(∀x∀yF(x,y))

Applying De Morgan's law: ∃x∃y¬F(x,y)

English: There exist two people such that one is not a friend of the other.

(b) Negation: ¬(∃x∃yF(x,y))

Applying De Morgan's law: ∀x∀y¬F(x,y)

English: For every pair of people, they are not friends.

(c) Negation: ¬(∃x∀yF(x,y))

Applying De Morgan's law: ∀x∃y¬F(x,y)

English: For every person, there is someone who is not their friend.

(d) Negation: ¬(∀x∃yF(x,y))

Applying De Morgan's law: ∃x∀y¬F(x,y)

English: There exists a person such that they are not a friend of anyone.

(a) Everyone is a friend of everyone.

Logical expression: ∀x∀yF(x,y)

In this statement, the expression ∀x∀yF(x,y) asserts that for every person x and every person y, x is a friend of y. It claims that every person in the domain is friends with every other person.

Negation: ¬(∀x∀yF(x,y))

To negate the statement, we add a negation operation at the beginning.

Applying De Morgan's law: ∃x∃y¬F(x,y)

By applying De Morgan's law, we distribute the negation over the conjunction (∀x∀y) and change it to a disjunction (∃x∃y). We also negate the predicate F(x,y) to ¬F(x,y).

English translation: Someone is an enemy of someone.

The negated statement, ∃x∃y¬F(x,y), implies that there exists at least one person x and one person y such that x is an enemy of y. It states that there is a case where someone is not a friend of someone else, suggesting the existence of an enemy relationship.

(b) Someone is a friend of someone.

Logical expression: ∃x∃yF(x,y)

This statement asserts the existence of at least one person x and one person y such that x is a friend of y. It claims that there is a pair of individuals in the domain who are friends.

Negation: ¬(∃x∃yF(x,y))

To negate the statement, we add a negation operation at the beginning.

Applying De Morgan's law: ∀x∀y¬F(x,y)

By applying De Morgan's law, we distribute the negation over the disjunction (∃x∃y) and change it to a conjunction (∀x∀y). We also negate the predicate F(x,y) to ¬F(x,y).

English translation: For every pair of people, they are not friends.

The negated statement, ∀x∀y¬F(x,y), states that for every person x and every person y, x is not a friend of y. It implies that there is no pair of individuals in the domain who are friends.

(c) Someone is a friend of everyone.

Logical expression: ∃x∀yF(x,y)

This statement claims that there exists at least one person x such that x is a friend of every person y. It suggests the existence of an individual who is friends with everyone in the domain.

Negation: ¬(∃x∀yF(x,y))

To negate the statement, we add a negation operation at the beginning.

Applying De Morgan's law: ∀x∃y¬F(x,y)

By applying De Morgan's law, we distribute the negation over the conjunction (∃x∀y) and change it to a disjunction (∀x∃y). We also negate the predicate F(x,y) to ¬F(x,y).

English translation: For every person, there is someone who is not their friend.

The negated statement, ∀x∃y¬F(x,y), asserts that for every person x, there exists at least one person y who is not a friend of x. It states that for each individual, there is someone who is not their friend.

(d) Everyone is a friend of someone.

Logical expression: ∀x∃yF(x,y)

This statement asserts that for every person x, there exists at least one person y such that x is a friend of y. It claims that every individual in the domain has at least one friend.

Negation: ¬(∀x∃yF(x,y))

To negate the statement, we add a negation operation at the beginning.

Applying De Morgan's law: ∃x∀y¬F(x,y)

By applying De Morgan's law, we distribute the negation over the conjunction (∀x∃y) and change it to a disjunction (∃x∀y). We also negate the predicate F(x,y) to ¬F(x,y).

English translation: There exists a person such that they are not a friend of anyone.

The negated statement, ∃x∀y¬F(x,y), states that there exists at least one person x such that for every person y, x is not a friend of y. It suggests the existence of an individual who is not a friend of anyone in the domain.

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Answer:

- 9,800,000,000

Step-by-step explanation:

9.8 * \(10^{-9}\)

Simplify 10 with exponent

\({10}^{-9}\) = -10 with 9 zeroes

Rewrite

\({10}^{-9}\) = -1,000,000,000

Place back into expression

9.8 * -1,000,000,000

Simplify by multiplying

- 9,800,000,000

Let me know if you have any questions!

The solution is\(sin x 2 = ±1/10, cos x 2 = ± (√19) / 2(√5)\), and tan x 2 = ± 1/√19.

We are given that sec(x) = 109 ,Using the formula of sec(x), we get:\(sec(x) = 1/cos(x)10/9 = 1/cos(x)cos(x) = 9/10sin^2(x) + cos^2(x) = 1\)

Using the value of cos(x) we get:\(sin^2(x) + (9/10)^2 = 1sin^2(x) = 1 - (9/10)^2sin^2(x) = 19/100sin(x) = ± √(19/100)sin(x) = ± ( √19 ) / 10\)

Now, 270° < x < 360° lies in the fourth quadrant of the coordinate plane. In this quadrant, only the sine of the angle is positive.

Hence, \(sin(x) = √19 / 10sin(x) = √19 / 10sin(x/2) = ± √[(1 - cos(x))/2]sin(x/2) = ± √[(1 - cos(x))/2] = ± √[(1 - 9/10)/2] = ± √(1/100) = ± 1/10cos(x/2) = ± √[(1 + cos(x))/2] = ± √[(1 + 9/10)/2] = ± √(19/20) = ± (√19) / 2(√5)tan(x/2) = (1-cos(x))/sin(x) = (1 - 9/10)/(√19 / 10) = ± 1/√19So, sin x 2 = ±1/10cos x 2 = ± (√19) / 2(√5)tan x 2 = ± 1/√19\)

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Answer:

144/441

Step-by-step explanation:

There are 18+24=42 total socks

There are 24 black socks

So the probability is (24/42)*(24/42)=12/21 * 12/21 = 144/441

Answer:

189

Step-by-step explanation:

By using the equation for the perimeter, we will see that the width is 11 inches and the length 8 inches.

The frame is a rectangle. Remember that for a rectangle of length L and width W, the perimeter is:

P = 2*(W + L)

In this case we know that the perimeter is 38 inches, and the length is 3 inches shorter than the width, then we can write two equations:

38in = 2*(W + L)

L = W - 3in

Replacing the second equation in the first one we get:

38in = 2*(W + W - 3in)

38in = 4*W - 6in

38in + 6in = 4*W

44in = 4*W

44in/4 = W

11in = W

The width is 11 inches, and the length is 11in - 3in = 8 in.

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Answer:

13,160

Step-by-step explanation:

\(si \: = \frac{pnr}{100} \)

P = principle amount

n = no.of years

r = rate(%)

\( = \frac{5600 \times 45 \times 3}{100} \)

= 56 × 45× 3

= 7560

The final answer is 5600 + 7560 = 13160

pls like and mark as brainliest if it helped!

Answer:

x=16

Step-by-step explanation:

(16*3)-2

48-2

46

134+46=180

Answer:

the answer is c hope it help

Answer: D

Step-by-step explanation:

1. movethe constanat to the right

2. Calculate

3.The statement is false

Answer:

An equation in the form y = mx + b is in the 'slope y-intercept' form where m is the slope and b is the y-intercept. We can rewrite our equation, y = 4, in slope y-intercept form as follows: y = 0x + 4. Here, it is clear that the slope, or m, is zero. Therefore, the slope of the horizontal line y = 4 is zero

Answer:

x = 11

Step-by-step explanation:

Raising both sides to the fifth power, we get:

27(x - 2) = 3⁵

x - 2 = 3⁵ / 27

x - 2 = 3⁵ / 3³

x - 2 = 3⁽⁵⁻³⁾ = 3² = 9

x = 11

Answer:

C

Step-by-step explanation:

BECAUSE HE IS Alexander the Great, was King of Macedonia, Hegemon of Greece, Pharaoh of Egypt, Great King of Media and Persia, until the date of his death

Answer:

Option B DEfeating Persia

Step-by-step explanation:

He wanted to defeat the Persian Empire. But to do that, he needed to increase Macedonia's strength. Philip trained his army to fight like the Greek hoplites. Then, one by one, he took over the Greek city-states.

Hope you understand.

Please mark as the brainliest

Answer:

D. 3 1/12

Explanation:

\(\rightarrow \sf 4\dfrac{1}{3} -1\dfrac{1}{4}\)

convert into improper fraction

\(\rightarrow \sf \dfrac{13}{3} -\dfrac{5}{4}\)

make the denominators same. 12 is the common factor of both 3 and 4

\(\rightarrow \sf \dfrac{13(4)}{12} -\dfrac{5(3)}{12}\)

simplify

\(\rightarrow \sf \dfrac{52}{12} -\dfrac{15}{12}\)

join both fraction

\(\rightarrow \sf \dfrac{52-15}{12}\)

simplify

\(\rightarrow \sf \dfrac{37}{12}\)

convert into mixed fraction

\(\rightarrow \sf 3\dfrac{1}{12}\)

Answer:

Step-by-step explanation:

as x+6 is the quotient, you need to use -6

-6 |  4   -3   +5       6

x         -24  +162 -1002

add

       4  -27  167  -996

f(x)= 4x^2 -27x +167 - 996/(x+6)

Lets check

(x+6)(4x^2 -27x +167)= 4x^3 -27x^2 +167x + 24x^2 - 162x + 1002 =

= 4x^3 - 3x^2 +5x +1002

1002-996= 6

So we have the correct solution: 4x^2 -27x +167 - 996/(x+6)

Answer:

The answer is D

Step-by-step explanation:

The expansion of the trinomial 10x² - 61 x + 72 is (2x - 9) (5x - 8).

An algebraic expression known as a trinomial has three non-zero terms and more than one variable. An example of a trinomial is a polynomial having three terms. An algebraic expression with one or more terms is called a polynomial.

Given:

10x² - 61 x + 72

Calculate the roots of the trinomial as shown below,

10x² - 16 x - 45 x + 72

2x  (5x - 8) - 9(5x - 8)

(2x - 9) (5x - 8)

Thus, the expansion of the trinomial is (2x - 9) (5x - 8).

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Answer:

She used 9 tiles which are 3 cm long

Step-by-step explanation:

cuz 3x9=27 and yea

Answer:

(4 x 14) + 10 = 66

Step-by-step explanation:

(4 x 14) + 10 = ?

56 + 10 = 66

Answer:

\(f(8) = - 42\)

Step-by-step explanation:

Hi there!

You have to substitute x = 8 into:

\(f(x) = 6(1 - x)\)

It then becomes:

\(f(8) = 6(1 - 8)\)

Calculate the above

\(f(8) = - 42\)

While a common rule of thumb is to have a minimum sample size of 100 for continuous data to be statistically significant, the actual appropriate sample size may vary depending on the specific study design and research question. Option(D)

In statistics, the term "statistical significance" refers to whether an observed effect or relationship in the data is likely to be real and not just due to random chance. To determine statistical significance, we often perform hypothesis testing.

The sample size is a crucial factor in hypothesis testing. A larger sample size generally provides more reliable and precise estimates of population parameters and increases the statistical power of the test. With a larger sample size, even smaller effects or differences between groups can become statistically significant.

While there is no hard and fast rule for the minimum sample size to achieve statistical significance, a common guideline is to aim for at least 30 samples. This guideline is often used in the context of the Central Limit Theorem, which states that the sampling distribution of the sample mean becomes approximately normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

In practice, the appropriate sample size depends on various factors, including the nature of the data, the effect size being studied, the desired level of confidence, and the statistical test used. Researchers often conduct sample size calculations based on these factors before conducting their studies to ensure they have an adequate sample size to achieve meaningful results and detect significant effects if they exist.

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Answer:

hard

Step-by-step explanation:

I have never seen this before

Answer:

n + (n + 1) = -33

Step-by-step explanation:

First integer = n (given)

Therefore, second integer = (n + 1)

According to the given information:

n + (n + 1) = - 33

To calculate the percent change from phytoplankton to smelt, you would first need to find the difference between the two concentrations. Then, you would divide the difference by the original concentration and multiply by 100%.

For example, if the concentration of phytoplankton is 100 parts per million (ppm) and the concentration of smelt is 150 ppm, then the difference between the two concentrations is 50 ppm.

Dividing 50 ppm by 100 ppm and multiplying by 100% gives us a percent change of 50%. This means that the concentration of PCBs in smelt is 50% higher than the concentration of PCBs in phytoplankton.

To calculate the percent change from phytoplankton to smelt, you can use the following formula:

Percent change = \(\frac{(new value - old value)}{old value } *100%\)

In this case, the new value is the concentration of PCBs in smelt and the old value is the concentration of PCBs in phytoplankton.

Once you have calculated the percent change, you can interpret it by comparing it to a reference value. For example, a percent change of 50% is considered to be a large change. This means that the concentration of PCBs in smelt is much higher than the concentration of PCBs in phytoplankton.

It is important to note that the percent change is only a measure of the relative change between two values. It does not take into account the absolute values of the two values. For example, a percent change of 50% is the same whether the original value is 100 or 1000.

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If buses arrive at stop at "15-minute" intervals, then the probability that he waits more than 10 minutes for a bus is "1/3".

Let us denote the arrival-time of the passenger by X, where X is uniformly distributed between 7am and 7:30am. hence, the probability-density-function (pdf) of "X" is written as :

f(x) = 1/30, for 7am ≤ x ≤ 7:30am

f(x) = 0, otherwise

We observe that, the passenger will wait for more than 10 minutes for a bus only if he arrives between 7:00 a.m. and 7:05 a.m. , or between 7:15 a.m. and 7:20 a.m.

So, the probability for waiting time can be written as ;

⇒ \(\int\limits^5_0 {\frac{1}{30} } \, dx\) + \(\int\limits^{20}_{15} {\frac{1}{30} } \, dx\),

⇒ (1/30)(5 - 0) + (1/30)(20 - 15);

⇒ 1/3.

Therefore, the required probability is 1/3.

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The given question is incomplete, the complete question is

Buses arrive at a specified stop at 15-minute intervals starting at 7am. If a passenger arrives at the stop at a time that is uniformly distributed between 7am and 7:30am, find the probability that he waits more than 10 minutes.

Answer:2.25 m/s^2

Step-by-step explanation:

a = (v-u)/t = 27/12 = 2.25 m/s^2

The coordinates of the point that is 2/5 of the way from A to B is (-1,-2).

Given, points are A = (-4, -2) and B = (11, -2).

We want to find the coordinates of the point that is 2/5 of the way from A to B.

According to distance rule,

Now distance of A and B =

\( \sqrt{ {( - 4 - 11)}^{2} + {( - 2 + 2)}^{2} } = \sqrt{ {15}^{2} } = 15 \: unit\)

Now required co-ordinate is away 2/5 th distance

from A to B.

So, the distance

\( = 15 \times \frac{2}{5} = 3 \: unit\)

Let, required co-ordinate be (x,y)

Now, distance between (x,y) and (-4,-2) = 3

\( \sqrt{ {(x + 4)}^{2} + {(y + 2)}^{2} } = 3....(1)\)

We are putting first point (5,0) in equation (1) and get \( \sqrt{ {(5 + 2)}^{2} + {(0 + 2)}^{2} } \ne3\)

Again putting (-1,-2) in equation (1), and get \( \sqrt{ {( - 1 + 4)}^{2} + {( - 2 + 2)}^{2} } = 3\)

Therefore, it is clear that required co-ordinate is (-1,-2).

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Answer:

r≈12mi

Step-by-step explanation:

mark brainiest and Im 100% correct

Answer:

Answer:

4 m

Step-by-step explanation:

I took the test

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The volume of a cone (V) is calculated as

V = \(\frac{1}{3}\) πr²h ( r is the radius and h the height )

Here V = 151 and r = diameter ÷ 2 = 12 ÷ 2 = 6 , then

\(\frac{1}{3}\) πr²h = 151 ( multiply both sides by 3 to clear the fraction )

πr²h = 453 , that is

3.14 × 6² × h = 453

3.14 × 36h = 453

113.04h = 453 ( divide both sides by 113.04 )

h  ≈ 4 m ( to the nearest metre ) → B

The mean of Kalil's second data set does not change in comparison to the mean of the data set in his original survey. The change in the means is 0.

To determine the change in the means without calculating the mean of either data set, we need to consider the information given in the question. The original survey had a data set of 1313 classmates who had been surveyed and some of them had been to a grocery store. The second survey had the same data set of 1313 classmates, but this time none of them had been to a grocery store since the last survey.

From this information, we can conclude that the mean of the second data set would be lower than the mean of the original data set. This is because in the original data set, some classmates had been to a grocery store which would have increased the mean. But in the second data set, none of the classmates had been to a grocery store, which means there would be no increase in the mean.

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The answer to the equation (e^x) + (2^-x) + 2 cos(x) - 6 = 0 accurate to within 10^-5 for 1 ≤ x ≤ 2 is approximately x ≈ 1.3907, obtained using the Secant method.

Secant method to find the solutions to the equation (e^x) + (2^-x) + 2 cos(x) - 6 = 0 for 1 ≤ x ≤ 2.

Step 1:

Choose initial guesses x0 = 1 and x1 = 2.

Step 2:

Calculate f(x0) and f(x1):

f(x0) = (e^1) + (2^-1) + 2 cos(1) - 6 ≈ -3.4687

f(x1) = (e^2) + (2^-2) + 2 cos(2) - 6 ≈ 2.1086

Step 3:

Calculate the next approximation, xn:

xn = x1 - (f(x1) * (x1 - x0)) / (f(x1) - f(x0))

    = 2 - (2.1086 * (2 - 1)) / (2.1086 - (-3.4687))

    ≈ 1.3907

Step 4:

Update the values of x0 and x1:

x0 = x1 = 2

x1 = xn = 1.3907

Repeat steps 2-4 until the desired accuracy is achieved.

Let's perform one more iteration.

Step 2:

Calculate f(x0) and f(x1):

f(x0) = (e^2) + (2^-2) + 2 cos(2) - 6 ≈ 2.1086

f(x1) = (e^1.3907) + (2^-1.3907) + 2 cos(1.3907) - 6 ≈ -0.00001754

Step 3:

Calculate the next approximation, xn:

xn = x1 - (f(x1) * (x1 - x0)) / (f(x1) - f(x0))

    = 1.3907 - (-0.00001754 * (1.3907 - 2)) / (-0.00001754 - 2.1086)

    ≈ 1.3907

Since the calculated xn is the same as the previous iteration, we can conclude that the solution has converged.

Therefore, the solution to the equation (e^x) + (2^-x) + 2 cos(x) - 6 = 0 accurate to within 10^-5 for 1 ≤ x ≤ 2 is approximately x ≈ 1.3907.

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After simplifying the expression we get the answer as ₋3x²/8¹³.

Given the expression is (₋8)³ 6x (1/2)²2x(₋8)⁻¹⁶

expand the powers.

(₋8×₋8×₋8) 6x (1/2 × 1/2)2x × 1/8¹⁶

we get:

(₋512) 6x (1/4) 2x × 1/8¹⁶

(₋8)³ 6x (1/4) × 2x × 1/8¹⁶

cancel 8 from numerator and denominator.

₋6x × 1/4 × 2x × 1/8¹³

divide the numbers.

₋3x² × 1/8¹³

₋3x²/8¹³

Hence we get the simplified answer as ₋3x²/8¹³.

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The cash price of one radio after a 14% discount is $4644.

The price of a radio is $5400. After giving a 14% discount for each radio, what will be the cash price?

Solution: The given price of the radio is $5400. The discount given on each radio is 14%.

Let's calculate the discount: Discount% = 14% Discount = (Discount%/100%) × Selling Price Discount = (14/100) × $5400 Discount = $756 Therefore, the discount on one radio is $756.

The cash price of one radio after a 14% discount is: Cash Price = Selling Price - Discount Cash Price = $5400 - $756Cash Price = $4644 Therefore, the cash price of one radio after a 14% discount is $4644.

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