prove that 1^3+2^3+3^3+...+n^3=(1+2+3+...+n)^2 by mathematical induction

The area of the triangle is 2√2 square units.

This is a right triangle, and the base (the side opposite the right angle) has a length of 2√2.

We can use the Pythagorean theorem to find the length of the other two sides:

x² + x²  = (2√2)²

2x²  = 8

x²  = 4

x = 2

So the two other sides have a length of 2.

Now we can use the formula for the area of a triangle:

Area = (1/2) × base × height

In this case, the base is 2√2 and the height is 2, so we have:

Area = (1/2)×2√2 ×2

Area = 2√2

Therefore, the area of the triangle is 2√2 square units.

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The domain of the function is (-∞, ∞.)

The range of the function is {3, ∞}.

We have,

From the given quadratic function,

We see that,

The x-values are -∞ to ∞

The y-values are from 3 to ∞

Now,

The x-values are called the domain.

The y-values are called the range.

Thus,

The domain of the function is (-∞, ∞.)

The range of the function is {3, ∞}.

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The image is reflected over the y-axis. Then the correct option is B.

Given that:

Point of the polygon VWXYZ, W(2, 4)

Point of the polygon V'W'X'Y'Z', W'(-2, 4)

The translation does not change the shape and size of the geometry. But changes the location.

The reflection does not change the shape and size of the geometry. But flipped the image.

The point W' can be obtained by reflecting the shape across the y-axis.

Thus, the correct option is B.

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The missing diagram is given below.

When about 60.2 liters of fuel are added to each car, the two vehicles will have the same mass.

Let x be the number of liters of fuel needed for the two vehicles to have the same mass.

The first vehicle's total mass with fuel is: 1295 + 0.737x

The total weight of the second vehicle with gasoline is: 1290 + 0.820x

We want the two masses to be equal so that we may equalize the two expressions and solve for x:

295 + 0.737x = 1290 + 0.820x

0.083x = 5

x = 60.24

Therefore, the two vehicles will have the same mass when approximately 60.2 liters of fuel have been added to each vehicle.

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Answer:

120/30*29*28*27

Step-by-step explanation:

Using a standard normal distribution table or calculator, we can find the p-value associated with z = 4.39 to be less than 0.0001.

For test the claim that half of all teens have made new friends online, we can use a hypothesis test.

Null hypothesis:

The proportion of teens who have made new friends online is equal to 0.5.

Alternative hypothesis:

The proportion of teens who have made new friends online is not equal to 0.5.

We will use a one-sample proportion test with a significance level of 0.01.

For calculate the test statistic, we can use the formula:

z = (p - P₀) / sqrt(P₀ * (1 - P₀) / n)

where p is the sample proportion, P₀ is the hypothesized proportion (0.5), and n is the sample size.

Using the given information, we have:

p = 0.57

P₀ = 0.5

n = 1060

Plugging these values into the formula, we get:

z = (0.57 - 0.5) / sqrt(0.5 x 0.5 / 1060)

z = 4.39

Hence, Using a standard normal distribution table or calculator, we can find the p-value associated with z = 4.39 to be less than 0.0001.

Since the p-value is less than the significance level of 0.01, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that more than half of all teens have made new friends online.

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Step-by-step explanation:

Given the circ , you can find the diameter....then the radius

circ = pi * d

17.584 = pi * d

d = 5.597 in     then radius =   1/2 d = 2.798

AREA = pi r^2 =  pi * 2.798^2 = 24.6 in^2

Answer:480 minutes

Step-by-step explanation:

119-47=72

72/3=24

24*20=480

Null Hypothesis: The average attractiveness rating given by females who read the "great sense of humor" description is not higher than neutral,

μ ≤ 4

Alternative Hypothesis: The average attractiveness rating given by females who read the "great sense of humor" description is higher than neutral, μ > 4.

We have,

The null and alternative hypotheses to determine if the females who read the "great sense of humor" description gave the potential partner an average attractiveness rating that was higher than neutral (μ = 4) can be written as:

Null Hypothesis: The average attractiveness rating given by females who read the "great sense of humor" description is not higher than neutral,

μ ≤ 4

Alternative Hypothesis: The average attractiveness rating given by females who read the "great sense of humor" description is higher than neutral, μ > 4.

Thus,

The null hypothesis states that the mean attractiveness rating of males who are described positively and with a great sense of humor is not significantly different from a neutral rating of 4.

The alternative hypothesis states that the mean attractiveness rating of such males is significantly higher than a neutral rating of 4.

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The upper bound of the volume of water left in the fish tank is 20 liters.

In the given statement is :

A fish tank contains 60 liters of water, rounded to 1 significant figure. 40 liters of water, rounded to 1 significant figure, are removed from the tank.

Work out the upper bound of the volume of water left in the fish tank.

Now, According to the question:

Initial water in tank = 60 liters

Amount of water removed = 40 liters

Hence, To calculate the upper bound of the volume of water left in the fish tank;

= 60 - 40

= 20 liters

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Wyatt paid 1.2422 times the amount of subtotal x, including tax and tip.

We have,

The amount of tax applied to the bill is 6% of the subtotal, or 0.06x.

The total bill (including tax) is.

x + 0.06x = 1.06x

To find the amount of tip Wyatt left on the total bill, we need to multiply the total bill by 17% (or 0.17):

0.17(1.06x) = 0.1802x

The expression in terms of xx that represents the total amount that Wyatt paid is:

= x + 0.06x + 0.1802x

Simplifying the expression by combining like terms.

Total amount = 1.2422x

Thus,

Wyatt paid 1.2422 times the amount of subtotal x, including tax and tip.

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The equation which correctly represents the given situation as required to be determined is; Choice C; w = 5 × 15.

It follows from the task content that the equation which correctly represents the Given situation is to be determined.

Since the intention is to buy 5 tickets in which case; each ticket costs 15 dollars; we have that;

Since the total amount of dollars they have is w dollars; The equation which holds true for the situation is; w = 5 × 15.

Consequently, answer choice C; w = 5 × 15 is correct.

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Answer:

Elena

Step-by-step explanation:

Sorry we have to see the complement first because it is of 90° jjust let the second w go we will do that later we can find the value of w by choosing elena

The slope of a linear function of the table of values given above is calculated as: m = 3.

The slope of a linear function is calculated as change in y over change in x. Note that f(x) is also the same as variable "y".

To calculate the slope, pick any two pairs of values from the table given, i.e. (2, 3) and (3, 6):

Slope of the linear function (m) = change in y / change in x = 6 - 3 / 3 - 2

Slope (m) = 3/1

Slope (m) = 3.

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The requried class average is 83.2 points.

To find the class average, we need to calculate the total number of points earned by all the students and divide by the total number of students.

The 12 students who scored 80 points earned a total of 12 × 80 = 960 points.

The 8 students who scored 88 points earned a total of 8 × 88 = 704 points.

The total number of points earned by all the students is 960 + 704 = 1664 points.

The total number of students is 12 + 8 = 20.

To find the class average, we divide the total number of points by the total number of students:

average = total points / total students

average = 1664 / 20

average = 83.2

Therefore, the class average is 83.2 points.

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The solution is, 7980 times greater is the value represented by the digit 8 in the number 8,342 than the value represented by the digit 8 in the number 284.

Here, we have,

given that,

the value represented by the digit 8 in the number 8,342

and, the value represented by the digit 8 in the number 284.

now, we have to find that how many times greater is the value.

so, we have to differentiate the value represented by the digit 8 in the number 8,342 with the value represented by the digit 8 in the number 284.

so, we get,

the value represented by the digit 8 in the number 8,342  is 8000

and, the value represented by the digit 8 in the number 284 is 80

so, difference between them is:

8000 - 80

=7980

Hence, The solution is, 7980 times greater is the value represented by the digit 8 in the number 8,342 than the value represented by the digit 8 in the number 284.

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the domain and range of the inequality are,

x ≥ 1 and y ≥ - 4

The inequality is:

⇒ y ≤ √(x - 1) - 4

Now, To find:

The domain and range of the given inequality.

Solution:

We have,

⇒ y ≤ √(x - 1) - 4

The related equation is:

⇒ y ≤ √(x - 1) - 4

This equation is defined if:

√x - 1 ≥ 0

x ≥ 1

In the given inequality, the sign of inequality is <, it means the points on the boundary line are not included in the solution set.

So, the domain of the given inequality is, x ≥ 1

We know that,

√(x - 1)  ≥ 0

√(x - 1) - 4 ≥ - 4

y ≥ - 4

So, the range of the given inequality is, y ≥ - 4

Therefore, the correct option is C.

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Answer:

A

Step-by-step explanation:

The opposite of an integer is the number on the opposite side of the number line with the same distance from zero. So, the integers that are opposites are 14 and -14, 17 and -17, 32 and -32, and 15 and -15. This is because these pairs have the same absolute value but different signs. For instance, the absolute value of 14 is 14, and the absolute value of -14 is also 14. Therefore, -14 is the opposite of 14. Similarly, -17 is the opposite of 17 and so on.

Answer:

a

Step-by-step explanation:

got it right on edge

The requried, justification for the given function has been shown below.

(a) Yes, R₁ defines a function. Each element in the domain is mapped to a unique element in the codomain, which is 0 in this case.

(b) No, R₂ does not define a function. For some values of n, there may be multiple animals with n legs, so there is no unique output for each input.

(c) Yes, R₃ defines a function. Each element in the domain is mapped to a unique element in the codomain, which is the remainder of n divided by 5.

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Answer:

The answer is (d) 10 lbs.

Step-by-step explanation:

Let's start by using the weighted average formula:

weighted average price = (price of first item x weight of first item + price of second item x weight of second item) / total weight

Let x be the number of pounds of walnuts needed.

The total weight of the mixture is x + 8 pounds.

The price of the walnuts is $0.80 per pound, and the price of the cashews is $1.25 per pound.

We want the mixture to cost $1.00 per pound.

Using the formula, we get:

1.00 = (0.80x + 1.25(8)) / (x + 8)

Simplifying, we get:

1.00(x + 8) = 0.80x + 10

1.00x + 8.00 = 0.80x + 10.00

0.20x = 2.00

x = 10

Therefore, Jordan needs to mix 10 pounds of walnuts with 8 pounds of cashews to make a mixture that costs $1.00 per pound.

Step-by-step explanation:

how many ways can the coach make out the batting order? 9! = 9 · 8 · 7 · 6 · 5 ·4 · 3 · 2 · 1 = 362,880 .

The graph of f(x) = x(x+5)(x+3) / (x+3)(x+5) bears resemblance to the line y=x since both plots share similar linear characteristics.

Both the numerator and denominator of f(x) = x(x+5)(x+3) / (x+3)(x+5) cancel out the factors (x+3) and (x+5), giving us a simplified expression for the function, f(x) = x.

A line with a slope of 1 passes through the origin in an upward direction. When we examine the graph of y=x, which is a straight line passing through the origin with a slope of 1, it becomes apparent that adding 1 to x also adds 1 to y.

Since the simplified expression is merely f(x) = x, we can deduce that the graph of this function follows a linear path passing through the origin with a slope of 1.

In conclusion, the graph of f(x) = x(x+5)(x+3) / (x+3)(x+5) bears resemblance to the line y=x since both plots share similar linear characteristics.

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The answers are explained in the solution.

Given are lines drawn in a coordinate plane, we need to identify the equations,

So, we have,

y = 2x – 4 = r

y = 2x + 4 = p

This is because these lines are parallel and have same slope, also the y-intercept is -4 and 4,

y = x = n

y = -x = s

This is also because, the line of y = x passes from origin.

b) We can use a translation to map the line p or r onto the line r or p.

c) We can use an axial symmetry in the y-axis to map the line n or s onto the line s or n.

d) The line s or n is mapped onto itself under central symmetry in the point (0, 0).

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The number of coupon codes that can be generated is given as follows:

247,808 coupon codes.

The Fundamental Counting Theorem states that if there are m ways to do one thing and n ways to do another, then there are m x n ways to do both.

This can be extended to more than two events, where the number of ways to do all the events is the product of the number of ways to do each individual event, according to the equation presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

The codes are composed as follows:

Thus the total number of codes is obtained as follows:

N = 22² x 8³

N = 247,808 coupon codes.

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The volumes of smaller container and larger container are 10.6 in³ and 166.22 in³ respectively.

Given that are two containers in a conical shape and cylindrical shape,

Volume of conical shape = 1/3 × π × radius² × height

= 1/3 × 3.14 × 1.5² × 4.5

= 10.6 in³

Volume of cylindrical shape = π × radius² × height

= 3.14 × 2.75² × 7

= 166.22 in²

When we pour water from smaller container to larger container = 10.6 / 166.22 × 100 = 6.4 % of larger container will be filled.

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Answer: 18º

Step-by-step explanation:

a + 126º = 180º (adj.  ∠s on st. line)

a = 54º

Let the adjacent angle next to b be c.

a + c = 180º (int. ∠, AB//CD)

54º + c = 180º

c = 126º

108º + x = 126º (ext. ∠ of Δ)

x = 18º

The measure of arc and angle in the given circle are as follow,

Measure of arc CA = 144°

Measure of arc AD  = 98°

Measure of ∠C = 90°

In the circle ,

Center of the circle = Q

m∠ABC = 72°

Measure of arc CD = 46°

Measure of arc CA

Measure of ∠ABC = 72°

In a circle angle at the center is double of angle at the circumference of the circle in the same arc.

Measure of ∠CQA = 2 ×∠ABC

                               =  2× 72°

                               = 144°

measure of arc CA = measure of ∠CQA

                                = 144°

Measure of arc AD ,

m ∠AQD + m ∠CQD = m ∠CQA

⇒m ∠AQD  = 144° - 46°

⇒m ∠AQD  =  98°

⇒ Measure of arc AD  = 98°

Measure of angle C = ( 1/2) times of measure of BQD

                                 = ( 1/2) × 180°

                                 = 90°

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Answer:

7

Step-by-step explanation:

7, 7, 7, 11, 15, 18

The mode is the number that appears most.

Answer: 7

Answer:

7

Step-by-step explanation:

The mode is the most frequently occurring value in a set of data. In this case, the number 7 occurs twice, which is more than any other number, so the mode is 7. It is worth noting that if there were no values that occurred more than once, then there would be no mode for the data set. In this case, the data set has a single mode, but it is possible for a data set to have multiple modes if there are multiple values that occur with the same highest frequency.

x at the vertex would help Charlie to find out how long it takes his basketball to reach the highest point.

When a quadratic function is in vertex form, the vertex (h, k) represents the highest or lowest point of the parabola.

In this case, the time it takes for the basketball to reach the highest point can be found by finding the x-value of the vertex of the function that represents the height of the basketball over time.

Therefore, option (A) x at the vertex would help Charlie to find the time at which the basketball reaches the highest point.

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