PLEASE HELP I WILL GIVE BRAINLIEST FOR THE CORRECT ANSWER!!

Use mathematical induction to prove that 1 + 2 + 3 + … + n = (1/2) n (a1 + an).

Use the result to find the sum of 1 + 2 + 3 + ... + 500.

Answer:

B

Step-by-step explanation:

the longest side of a triangle is opposite the largest angle.

∠ Y = 180° - 60° - 43° = 180° - 103° = 77°

then ∠ Y is the largest angle in the triangle , so

side opposite ∠ Y is the longest , that is XZ

XZ is the longest side of the given triangle XYZ.

A triangle is a three-sided polygon that consists of three edges and three vertices.

The given triangle is XYZ.

We have to find the longest side.

Angle X and angle Z are given

∠X = 60 and ∠Z = 43

Now let us find ∠Y by angle sum property

∠X+∠Y+∠Z=180

60+43+∠Y=180

103+∠Y=180

Subtract 103 from both sides

∠Y=180-103

∠Y=77

The side which is opposite to the greatest angle is longest side

Hence, XZ is the longest side of the given triangle XYZ.

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The value of (f- g)(x) is  2x - 26.

This is a question of subtraction of functions.

Subtraction of functions

The subtraction of function involves the creation of a new function through the addition of two other functions.

Subtraction of one real-valued function from another.

Let h: X → and p: X → be any two real functions, where X ⊆ Real numbers. Then, we can define h - p: X → by h - p x = h(x) – p(x), for all x ∈ X.

Given that:-

f(x) = 2x + 1

g(x) = 27

We have to find the value of (f- g)(x)

We know that,

(f- g)(x) = f(x) - g(x)

Hence, we can write,

(f- g)(x) = 2x + 1 - 27 = 2x - 26

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Answer:

34

Step-by-step explanation:

Answer:

34

Step-by-step explanation:

Because 612 quarts divided by 18 quarts for each plant is 34. So, it's 34 plants.

The independent set in a graph is a set of vertices that contain no edges. So, no neighboring vertices are included. The max independent set problem is to get an independent set of maximum size in graph G.

The solution for this question is discussed below:

a) The integer linear program for the max independent set problem is as follows:

maximize ∑x_i Subject to: x_i+x_j ≤ 1 {i,j} ∈ E;x_i ∈ {0, 1} ∀i. The variable x_i can represent whether the ith vertex is in the independent set. It can take on two values, either 0 or 1.

b) The LP relaxation for the max independent set problem is as follows:

Maximize ∑x_iSubject to:

xi+xj ≤ 1 ∀ {i, j} ∈ E;xi ≥ 0 ∀i. The variable xi can take on fractional values in the LP relaxation.

c) The family of graphs is as follows:

Consider a family of graphs G = (V, E) defined as follows. The vertex set V has n = 2^k vertices, where k is a positive integer. The set of edges E is defined as {uv:u, v ∈ {0, 1}^k and u≠v and u, v differ in precisely one coordinate}. It can be shown that the size of the max independent set is n/2. Using LP, the value can be determined. LP provides a value of approximately n/4. Therefore, the ratio LP-OPT/OPT is at least c/4. Therefore, the ratio is in for a constant c>0.

d) The size of a max-independent set is equivalent to the number of vertices minus the minimum vertex cover size.

e) The 2-approximation algorithm for vertex cover implies a 2-approximation algorithm for the max independent set.

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Answer:

Answer for this one is second one (-8,-7,5)

Step-by-step explanation:

Hope it will help you :)

The cost of 1.20 kg of carrots is $2.09.

to convert the weight of carrots from pounds to kilograms. There are approximately 2.20462 pounds in 1 kilogram. Therefore, 1.20 kg of carrots is equivalent to 2.64555 pounds.

Next, we can use the given price of $0.79 per pound to calculate the cost of 2.64555 pounds of carrots.

Cost of 2.64555 pounds of carrots = 2.64555 x $0.79

Cost of 2.64555 pounds of carrots = $2.09 (rounded to the nearest cent)

Therefore, the cost of 1.20 kg of carrots is $2.09.

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To calculate the magnitude and direction of the electric field at the center of the square, we need to consider the contributions from each charge.

To calculate the electric field at the center of the square, we'll use the principle of superposition, which states that the total electric field is the vector sum of the electric fields due to each individual charge.

Given:

Charge at the corners of the square:

q1, q2, q3, q4 (each in multiples of 6.00×10⁽⁻⁶⁾ C)

Charge at the midpoints of the sides:

q5, q6, q7, q8 (each in multiples of 6.00×10⁽⁻⁶⁾ C)

Distance between adjacent charges on the perimeter of the square:

d = 6.90×10⁻⁽⁻²⁾ m

The electric field due to a point charge q at a distance r is given by Coulomb's law:

E = k × (q / r²)

where:

E is the electric field,

k is Coulomb's constant (approximately 8.99 × 10⁹ N·m²/C²),

q is the charge, and

r is the distance between the charge and the point where the electric field is being calculated.

Since the charges are arranged symmetrically, we can observe that charges q1, q2, q3, and q4 will contribute electric fields along the x and y axes. Charges q5, q6, q7, and q8 will contribute only to the x or y component of the electric field due to their positions at the midpoints of the sides.

Let's calculate the electric field components due to each charge and sum them up to find the net electric field at the center of the square.

Electric field components due to charges at the corners:

Charges q1 and q3 are equidistant from the center along the x-axis, so they contribute equally to the x-component of the electric field.

Charges q2 and q4 are equidistant from the center along the y-axis, so they contribute equally to the y-component of the electric field.

E_x1 = E_x3 = k × (q1 / (d/2)²)

E_y2 = E_y4 = k × (q2 / (d/2)²)

Electric field components due to charges at the midpoints:

Charges q5 and q7 lie on the x-axis and are equidistant from the center, so they contribute equally to the x-component of the electric field.

Charges q6 and q8 lie on the y-axis and are equidistant from the center, so they contribute equally to the y-component of the electric field.

E_x5 = E_x7 = k × (q5 / d²)

E_y6 = E_y8 = k × (q6 / d²)

Net electric field components at the center of the square:

Sum up the x-components and y-components of the electric field contributions due to each charge.

E_x = E_x1 + E_x3 + E_x5 + E_x7

E_y = E_y2 + E_y4 + E_y6 + E_y8

Magnitude and direction of the net electric field:

Calculate the magnitude using the Pythagorean theorem:

E = sqrt(E_x² + E_y²)

Determine the direction of the electric field using the arctan function: θ = atan(E_y / E_x)

Now let's calculate the electric field at the center of the square.

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Answer:

i thought it is 18 since 4 x3 =12 then 6x3 =18 I am not sure 100%

Answer:

I- where is the graph

Step-by-step explanation:

Answer:

It's A the first graph

Step-by-step explanation:

Answer:

The answer is A

Step-by-step explanation:

Answer: A and C

Step-by-step explanation:

So the largest rectangle has sides of 5 length and 2+4 width or 6 right. so 5*6=30 Now we have to find which of these expressions solve to get 30. I would just solve them all but the answer is

A and C

the total number of squares that contain the black center square is\($1 + 4 + 9 + 16 + 1 = \boxed{31}$.\)

To solve this problem, we need to count the number of squares of each size that contain the black center square.

There is only one square of size\($5\times 5$\), which is the entire grid and obviously contains the black center square.

For squares of size\($4\times 4$\), there are \($4$\)possible squares that contain the black center square (one for each corner).

For squares of size\($3\times 3$,\) there are 9 possible squares that contain the black center square (one for each position that the center square could occupy, and then each of those squares could be oriented in three different ways).

For squares of size $2\times 2$, there are $16$ possible squares that contain the black center square (one for each pair of adjacent squares).

For squares of size \($1\times 1$\), there is only one possible square that contains the black center square (the center square itself).

Therefore, the total number of squares that contain the black center square is\($1 + 4 + 9 + 16 + 1 = \boxed{31}$.\)

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There are 11 squares containing the black center square in the 5x5 grid.

To find the number of squares that contain the black center square, we'll consider the sizes of the squares and their positions in the 5x5 grid.
The black center square is a 1x1 square itself, so that's 1 square.
For 2 x 2 squares containing the center square, there are 4 possible positions (the center square can be in any corner). So, that's 4 squares.
For 3x3 squares containing the center square, there is only 1 possible position (the center square is exactly in the middle). So, that's 1 square.
4. For 4x4 squares containing the center square, there are 4 possible positions (the center square can be in any corner). So, that's 4 squares.
5. For 5x5 squares containing the center square, there is only 1 possible position (the center square is exactly in the middle).

So, that's 1 square.
Now, we'll add up the number of squares we found in each step:
1 + 4 + 1 + 4 + 1 = 11.

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The values of x and y are given as follows:

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

In this problem, we have that the right angle is bisected, and thus it is divided into two angles of 45º.

As the angle of 45º has the same value for the sine and the cosine, the sides of the triangle BDC have the same length, hence the value of x is given as follows:

x = 3.

Applying the Pythagorean Theorem, the value of y will be given as follows:

y² = 3² + 3²

y² = 2 x 9

\(y = 3\sqrt{2}\)

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Answer:

\(x=\dfrac{9}{4}=2.25\)

\(y=\dfrac{15}{4}=3.75\)

Step-by-step explanation:

The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the altitude to one segment is equal to the ratio of the other segment to the altitude.

\(\boxed{\sf \dfrac{altitude}{segment\:1}=\dfrac{segment\:2}{altitude}}\)

From inspection of the given right triangle:

Therefore:

\(\implies \dfrac{BD}{CD}=\dfrac{AD}{BD}\)

\(\implies \dfrac{3}{x}=\dfrac{4}{3}\)

\(\implies 3 \cdot 3 = 4 \cdot x\)

\(\implies9 = 4x\)

\(\implies x=\dfrac{9}{4}\)

The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the hypotenuse to one leg is equal to the ratio of the same leg and the segment segment directly opposite the leg.

\(\boxed{\sf \dfrac{hypotenuse}{leg\:1}=\dfrac{leg\:1}{segment\;1}}\quad \sf and \quad \boxed{\sf \dfrac{hypotenuse}{leg\:2}=\dfrac{leg\:2}{segment\;2}}\)

From inspection of the given right triangle:

Therefore:

\(\implies \dfrac{AC}{BC}=\dfrac{BC}{CD}\)

\(\implies \dfrac{4+x}{y}=\dfrac{y}{x}\)

\(\implies x(4+x)=y^2\)

Substitute the found value of x:

\(\implies \dfrac{9}{4}\left(4+\dfrac{9}{4}\right)=y^2\)

\(\implies y^2=\dfrac{225}{16}\)

\(\implies y=\sqrt{\dfrac{225}{16}}\)

\(\implies y=\dfrac{\sqrt{225}}{\sqrt{16}}\)

\(\implies y=\dfrac{15}{4}\)

The value are give below:

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

Using Pythagoras theorem in FPO

FO²= FP²+ OP²

FO²=12.5²+19²

FO²=39.75

FO= 22.74

Now In OQR

OR²=OQ²+QR²

517.25= x² +14²

x²= 321.25sx

x=17.9

31. Now, given triangle

    H² = 5²+10²

    H²=125

    H=11.18

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The value of x in the figure is 17.9

Considering the triangle FOP, where:

From the question, we have:

OP = 19

FG = 25

Where:

FP = 0.5 * FG

FP = 0.5 * 25 = 12.5

Using Pythagoras theorem, we have:

FO² = FP² + OP²

Substitute known values

FO² = 12.5² + 19²

Evaluate the sum of squares

FO² = 517.25

Considering the triangle ROQ, where:

From the question, we have:

OQ = x

RS = 28

Where:

RQ = 0.5 * RS

RQ = 0.5 * 28 = 14

Using Pythagoras theorem, we have:

OR² = OQ² + RQ²

Recall that

OR = FO

Square both sides

OR² = FO²

This means that:

FO² = OQ² + RQ²

Substitute known values

517.25 = x² + 14²

Collect like terms

x² = 517.25 - 14²

Evaluate

x² = 321.25

Take the square root of both sides

x = 17.9

Hence, the value of x is 17.9

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By using the simulated results and the law of large numbers, we can estimate that the probability of answering exactly 15 questions correct on a 30-question exam with a 35% chance of getting each question correct is approximately 7.2%.

Based on the simulated results, we can estimate the probability of answering exactly 15 questions correct on a 30-question exam with a 35% chance of getting each question correct. To do this, we first need to look at the histogram or table of the simulated results to see how many of the 1000 exams scored 15.

If we look at the histogram or table, we can see that there were 72 out of 1000 exams that scored exactly 15. This means that the proportion of exams that scored 15 is 72/1000 or 0.072.

Using the law of large numbers, we can estimate that this proportion is the same as the probability of answering exactly 15 questions correctly on a 30-question exam with a 35% chance of getting each question correct. Therefore, the estimated probability of answering exactly 15 questions correct is 0.072 or 7.2%.

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Step-by-step explanation:

That symbol is sigma, which is the sum of that equation from k = 1 to n = 4

Equation is 2(3^n-1)

Since we're going 1 to 4, the sum would be as follows (replacing n with 1, 2, 3, and 4

\(2( {3}^{1 - 1}) + 2( {3}^{2 - 1}) + 2( {3}^{3 - 1}) + 2( {3}^{4 - 1}) = {?}\)

\(2(1) + 2(3) + 2(9) + 2(27) = \)

\(2 + 6 + 8 + 54 = 70\)

Answer:

a. The answers obtained are as follows:

Frequency for flossing 7 times per week = 24

Relative frequency for flossing 4 times per week = 0.1231

Cumulative Frequency at flossing 1 time per week = 22

b. The Cumulative Relative Frequency at flossing 7 time per week is 100%.

Step-by-step explanation:

Note: This question is not complete and the data in it are merged together. The complete question is therefore provided with the sorted data before answering the question. See the attached pdf file for the complete question.

The explanation to the answers is now provided as follows:

a. Complete the table (Use 4 decimal places when applicable)

Note: See part a of the attached excel for the complete table (answers are in bold red color)

Frequency is the rate at which something or an event occurs in a particular sample.

Since we already have frequency for others flossing times per week and we have 130 adults as the sample, the frequency for flossing 7 times per week is calculated by deducting the frequencies of others from 130 as follows:

Frequency for flossing 7 times per week = 130 – 10 – 12 – 14 – 18 – 16 – 21 – 15 = 24

Relative Frequency refers to the fraction of times an event occurs. The relative frequencies in this question are calculated by dividing each frequency by the total number of adults in the sample, i.e. 130. The relative frequency for flossing 4 times per week is therefore calculated as follows:

Relative frequency for flossing 4 times per week = Frequency for flossing 4 times per week / Total number of adults in the sample = 16 / 130 = 0.1231

Cumulative Frequency is calculated by adding the current frequency to the previous Cumulative Frequency. The Cumulative Frequency at flossing 1 time per week is therefore calculated as follows:

Cumulative Frequency at flossing 1 time per week = Cumulative Frequency at flossing 0 time per week + Frequency at flossing 1 time per week = 10 + 12 = 22

b. What is the cumulative relative frequency for flossing 7 times per week? %

Note: See part b of the attached excel for the complete table (answer is in bold red color)

The cumulative relative frequency refers to the accumulation of the previous relative frequencies.

Cumulative Relative Frequency is calculated by adding the current relative frequency to the previous Cumulative Relative Frequency. It should be noted that the first cumulative relative frequency equal to the first relative frequency.

The Cumulative Relative Frequency at flossing 7 time per week is therefore calculated in the attached excel file as follows:

Cumulative Relative Frequency at flossing 1 time per week = Cumulative Relative Frequency at flossing 6 times per week + Relative Frequency at flossing 7 times per week = 0.8154 + 0.1846 = 1.0000

Since the question indicates that the Cumulative Relative Frequency at flossing 7 time per week should be stated in percentage term, we therrefore have:

Cumulative Relative Frequency at flossing 7 time per week = 1.0000 * 100 = 100%.

Answer:

4.44%

Step-by-step explanation:

%Error = \(\frac{E-T}{T}\) x 100

E = experiment

T = Theoretical

E = 86

T = 90

What is the percent error?​

We Take

\(\frac{86-90}{90}\) x 100 ≈ 4.44%

So, the percent error is about 4.44%

Answer:

im pretty sure its right

Step-by-step explanation:

We want to see underline the correct part in each statement.

So, Jean and Jericho are playing on a seesaw.

Jean is heavier than Jericho.

Now, notice that a seesaw is a lever. So it "amplificates" the force that you apply in one end to lift the weight that is on the other end. Depending on the form of the lever and the weights, the force that you need to do changes.

If we define:

We must have:

W₁*d₁ = W₂*d₂

Then:

1) This situation illustrates (direct, inverse) variation.

d₁, the position of Jean, varies inversely with respect to Jean's weight.

2) The two quantities that must vary in this situation are (weight and

distance from the center, height and weight).

(by the equation above)

3) The heavier the kid, the (closer, farther) he/she should be at the

center to balance the seesaw?

By the given equation, we see that d₁ must be smaller than d₂.

And the last two are trivial:

4) When Jean moves farther from the center, Jericho tends to go (up,

down).

5) If Jericho moves closer to the center, Jean tends to go (up, down).

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Answer:

\(18+0.08B\geq 75\)

Step-by-step explanation:

there is a flat fee of $18

there is an incremental fee of $0.08 per ball which can be shown as \(0.08B\)

so the amount that Carolina will spend would be \(18+0.08B\)

the promotion only applies if Carolina spends $75 or more. the greater than or equal to symbol is \(\geq\)

so the inequality would be \(18+0.08B\geq 75\)

however, we could simplify this to \(0.08B\geq 57\) but it is not necessary

Answer:

See below

Step-by-step explanation:

Use prime number factoring of the number you have within the cubed root equation.....216.

Start with 216 and find a prime number that can divide into 216 evely.

2 x 108 the 2 is a prime number

now find another prime to divide into 108 evenly.

2 x 54 again the 2 is a prime number

find another prime number that will divide into 54

2 x 27 again the 2 is a prime number

another prime that divides into 27 evenly

3 x 9 and the 3 is prime

lastly, another prime to divide into 9

3 x 3 and other of these are primes.

So if you line up these prime numbers you have 222333

Take the numbers that you have in groups of 3s.  You have 1 group of 2s and 1 group of 3s.  Multiply those two numbers together.

2 x 3 = 6

So the cubed root of 216 is 6.

Answer:

On average, 2 out of 10 adults visited the museum most frequently

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want the measures of the angles marked x° and y° in the given diagram.

The measure of an inscribed angle is half the measure of the arc it intercepts. This means any inscribed angles that intercept the same arc will have the same measure.

The inscribed angles with vertices J and K both intercept arc FH, so both have the marked measure of 56°.

  x = 56

The angle where the chords cross (y°) will be half the sum of the arcs those chords intercept. Here, those are arcs FH and JK.

Given that half the arc measure is the measure of the intercepting inscribed angle, we can simply sum the inscribed angles to get y°:

  y° = 56° +19° = 75°

  y = 75

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Answer:

1/4

Step-by-step explanation:

The scale Factor is nothing but the times It has either increased or got diminished

Here in this case you can see that

The side 40m has been diminished to 10m

Hence the scale factor is 1/4

The scale factor is 1/4

The scale factor is the mathematical term used to represent a shape being multiplied a certain amount of times to create a bigger shape. Scale factor can also be a ratio.

Answer:

4/9

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

To solve this place an imaginary decimal point right before the 8 now going one number value at a time move it to where its original place was and count the number of time you had to move it.

Answers:

x = 16

MB = 31

==================================================

Work Shown:

M is the midpoint of AB

This means AM is half as long as AB and AM = MB

Put another way, AB is twice as long as AM

AB = 2*AM

3x+14 = 2*(2x-1)

3x+14 = 4x-2

14+2 = 4x-3x

16 = x

x = 16

AM = MB

MB = AM

MB = 2x-1

MB = 2*16-1

MB = 32-1

MB = 31

Answer:

9pi

Or

28.278

Step-by-step explanation:

If you need the exact answer just type in 3.142x3 Squared then it will give you the exact answer but if not just find the pi button on the calculator and put in pi x 3 squared