The function f(x) = x2 4 is defined over the interval [-2, 2]. if the interval is divided into n equal parts, what is the height of the right endpoint of the kth rectangle?

It’s discriminant is zero, so it has one real solution statement is true for  x²-2x +1=0.

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The given quadratic equation is x²+1=2x

This can also be written as x²-2x +1=0

a=1, b=-2 and c=1

The expression b² − 4ac is called the discriminant, and can be used to determine whether the solutions are real, repeated, or complex.

(-2)² − 4(1)(1)=4-4

b² − 4ac= 0

A discriminant of zero indicates that the quadratic has a repeated real number solution.

It’s discriminant is zero, so it has one real solution.

Hence, It’s discriminant is zero, so it has one real solution statement is true for  x²-2x +1=0.

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Answer:

Yes because Bob' total would cost $13 and Maria's would cost $14 which would both be less than the $21 they had to spend.

Evaluation of the equation is \(\frac{y^{-14} }{6718464}\)

Here from the question, we get the evaluation

                     \([(2y)^{-3} (3y)^{-2} (6y)^{-2}]^{2}\)

Now evaluate it in the simple form we have

                   \([(\frac{1}{2y} )^{3} (\frac{1}{3y} )^{2} (\frac{1}{6y} )^{2} ]^{2}\)

                   \([\frac{1}{8y^{3} } \frac{1}{9y^{2} } \frac{1}{36y^{2} } ]^{2}\)

                  \([\frac{1}{2592y^{7} } ]^{2}\)

                  \(\frac{1}{6718464y^{14} }\)

                   \(\frac{y^{-14} }{6718464}\)

Therefore we get the simplest form of the evaluation.

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x= 15

Hi there !

x - y = - 11

replace y = 26

x - 26 = - 11

x = 26 - 11

x = 15

Good luck !

Answer:

The blue point is at -15.

Step-by-step explanation:

It's counting by 3's. 3, 6, 9, 12, 15...

Answer: Let's call Sarah's original amount of money as x. Then, Christine had 0.8x.

After they spent $684 altogether, Christine had 0.8x - 0.25(0.8x) = 0.8x - 0.2x = 0.6x left.

Sarah had x - 684.

Since Christine had thrice as much money left as Sarah, we can write an equation:

0.6x = 3(x - 684)

Expanding the right side of the equation:

0.6x = 3x - 2052

Solving for x:

2.6x = 2052

x = 787.69

So Sarah originally had 787.69 dollars and spent 787.69 - 684 = 103.69 dollars.

Step-by-step explanation:

225125₆/101₆ = 2225₆

One way to arrive at this is to convert both given numbers to base 10, compute the quotient in base 10, then convert back to base 6.

101₆ = 1×6² + 0×6¹ + 1×6⁰ = 37

225125₆ = 2×6⁵ + 2×6⁴ + 5×6³ + 1×6² + 2×6¹ + 5×6⁰ = 19,277

So we have

225125₆/101₆ = 19,277/37 = 521

Next,

521 = 2×216 + 89 = 2×6³ + 89

89 = 2×36 + 17 = 2×6² + 17

17 = 2×12 + 5 = 2×6¹ + 5×6⁰

and so

521 = 2×6³ + 2×6² + 2×6¹ + 5×6⁰ = 2225₆

Or you can use the long division algorithm. Division in base 6 is the same as in base 10, except numerals range from 0 to 5 instead of 0 to 9. See if you can follow this diagram (replaced with an attachment)

Answer: 40 degrees

Step-by-step explanation:

There are 9 sides in a nonagon and 360 degrees make the shape up.

360 degrees divided by  9 EQUAL SIDES of a nonagon = 40 degrees

Answer:

Step-by-step explanation:

The formula for the circumference of a circle is 2 * π * r, where r is the radius of the circle.

Given that the radius of the circle is 13 millimeters, the circumference of the circle is:

2 * π * 13 = 26 * π millimeters

Since the value of π is approximately 3.14, the approximate circumference of the circle is:

26 * 3.14 = 81.64 millimeters.

Answer:

The expression (2n)(2n + 1)(4n + 1)/6 - 2n(2n + 1) + 2n is equivalent to ∑i=1 to 2n (i-1)².

Step-by-step explanation:

The expression ∑i=1 to 2n (i-1)² represents the sum of (i-1)² for values of i ranging from 1 to 2n. We can simplify and rewrite this expression using properties of summation:

∑i=1 to 2n (i-1)² = ∑i=1 to 2n (i² - 2i + 1)

= ∑i=1 to 2n i² - ∑i=1 to 2n 2i + ∑i=1 to 2n 1

Now let's evaluate each term separately:

∑i=1 to 2n i²:

This represents the sum of the squares of i for values of i ranging from 1 to 2n. This can be expressed as the formula for the sum of squares:

∑i=1 to 2n i² = (2n)(2n + 1)(4n + 1)/6

∑i=1 to 2n 2i:

This represents the sum of 2i for values of i ranging from 1 to 2n. We can factor out the 2 and use the formula for the sum of the first n positive integers:

∑i=1 to 2n 2i = 2(2n)(2n + 1)/2 = 2n(2n + 1)

∑i=1 to 2n 1:

This represents the sum of 1 for values of i ranging from 1 to 2n. Since we are summing 1 a total of 2n times, this is simply 2n.

Putting it all together, we have:

∑i=1 to 2n (i-1)² = ∑i=1 to 2n i² - ∑i=1 to 2n 2i + ∑i=1 to 2n 1

= (2n)(2n + 1)(4n + 1)/6 - 2n(2n + 1) + 2n

= (2n)(2n + 1)(4n + 1)/6 - 2n(2n + 1) + 2n

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The lower confidence bound for the percentage of all such homes that have electrical/environmental problems is 12.8% (rounded to one decimal place). This means we can be 99% confident that the true percentage of all homes with electrical/environmental problems is at least 12.8%.

To calculate the lower confidence bound using a confidence level of 99%, we need to use the formula:
Lower Bound = Sample Proportion - Z-score * Square Root[(Sample Proportion * (1 - Sample Proportion)) / Sample Size]
Here, we need to know the sample proportion, which is the percentage of homes that have electrical/environmental problems. Let's assume that the sample size is 500 and 85 homes out of those have electrical/environmental problems. Then the sample proportion would be:
Sample Proportion = 85/500 = 0.17
Next, we need to find the Z-score for a 99% confidence level. From the Z-tables, we can find that the Z-score for a 99% confidence level is 2.576.
Putting these values in the formula, we get:
Lower Bound = 0.17 - 2.576 * Square Root[(0.17 * (1 - 0.17)) / 500] = 0.128

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The total amount of blood drawn is 3.025 mL.

The given condition is that;

The amount of red blood cells in a blood sample is equal to the total amount of in the sample minus the amount of plasma.

From above condition we can assume following factors as;

Total amount of blood plasma in the sample = 5.5 mL

Amount of red blood cells = 45% = 45/100 = 0.45 mL

To find the total amount of blood drawn ( x );

From the above condition, the amount of red blood cells in a blood sample is equal to the total amount of in the sample minus the amount of plasma.

x = 5.5 - [5.5 * 0.45]

x = 5.5 - 2.475

x = 3.025

Hence, the total amount of blood drawn is 3.025 mL.

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\(\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}\)

Actually Welcome to the Concept of the Straight lines.

Since there are more than one lines that can land plane safely, we take one of it,

When, X = 10 and Y = 7, so the equation we get as,

y-7 = m(x-10) + c

lets find slope, that is value of m,

y2-y1/x2-x1 = m

so, 9-7/ 7-10 = 2/-3

so, m= -2/3

so the final Equation is,

=> y-7 =(-2/3)(x-10) +c

The required measure of length of the box is 2.9 inches. Option A is correct.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
according to the question,
h = 3l - 2.5
w = 3/4l
The volume of the box,
40 = l × w × h
40  = l × 3/4l × [3l-2.5]
40 = 3/4l²[3l - 2.5]
40 = 9/4l³ - 7.5/4l²

9/4l³ - 7.5/4l² - 40 = 0
t = 2.91932
t ≈ 2.9 inches

Thus, the length of the box must be at least 2.9 inches. Option A is the right answer.

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Answer:198.447

Step-by-step explanation:

just search 7 ounces to grams

Answer:

\(g(f(x)) = gof(x) =( x - 7)^{2} \\ = {x}^{2} - 14x + 49 \\ g(f(4) )\times g(f(4)) = (4^{2} - 14 \times 4 + 49 )\times( 4 ^{2} - 14 \times 4 + 49) \\ = 9 \times 9 \\ = 81\)

The chi-square test of independence is typically used to analyze the relationship between two variables when both variables are nominal, the two variables have been measured on different individuals and the observations on each variable are within-subjects in nature. The answer is  D. all of the above

The chi-square test of independence is a statistical test that is used to determine if there is a significant association between two categorical variables. It is commonly used when both variables are nominal, meaning they consist of categories or groups rather than numerical values.

When conducting the chi-square test of independence, the data is typically collected by measuring the two variables on different individuals or units.

For example, researchers may collect data on the gender (nominal variable) and political affiliation (nominal variable) of different individuals and analyze whether there is a relationship between the two variables.

The test examines the observed frequencies of the different categories in a contingency table and compares them to the expected frequencies under the assumption of independence. If the observed and expected frequencies significantly differ, it suggests that there is an association between the two variables.

Therefore, the chi-square test of independence is applicable when both variables are nominal and the data is collected on different individuals. This allows researchers to investigate the relationship between the variables and determine if they are associated or independent.

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Answer:

i believe its 5/10 or 1/2

Step-by-step explanation:

Answer:

Parallelogram S: b = 7, h = 6

Parallelogram T: b = 3, h = 6

Area of Parallelogram S = 42

Area of Parallelogram T = 18

Step-by-step explanation:

The bases and heights of each parallelogram are given by the arrows, just count the number of boxes you see.

Area = base × height, so you just multiply these numbers. Area of parallelograms is found the same way as area for squares/rectangles.

7 × 6 = 42 and 3 × 6 = 18

The second wheel has a smaller circumference compared to the first wheel. The second wheel completes a revolution when the wheel turns 75.40 inches, but the odometer reads 84.82 inches.

There are two types of odometers

In the case of a mechanical odometer, the worm gear is used to make the gear train, and the overall gear ratio is 1690:1, which means that when the vehicle travels a distance of 1 mile, the mechanical odometer input shaft makes 1690 revolutions during this time. In the case of a digital odometer, a magnetic sensor is used to receive pulses, each of which counts as one revolution. We now have a bicycle odometer designed for 27 wheels. Thus, d₁ = 27 inches is the diameter of the first wheel

d₂= 24 inches is the diameter of the second wheel

The odometer is the distance traveled by the vehicle, given as the number of revolutions of the wheel multiplied by the circumference of the wheel. So for the first wheel, Therefore, in case of first

wheel, \(C_1 = πd_1 \)

= π × 27

= 84.82 inches

In case of second wheel,

\(C_2 = π × d_2\)

= π × 24 inches

= 75.40 inches

So, \(C_1 - C_2 = \) 84.82 inches - 75.40 inches

= 9.42 inches

So we can see that the second wheel has circumference is less as compared to the first wheel.

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Complete question:

bicycle odometer is designed for 27 wheels. what happens if you use it on a bicycle with 24 wheels?

Answer:

the triangle is not right-angled

Step-by-step explanation:

First of all, we are told that the perimeter of the triangle is 22 and the two sides are given, 8cm and 5cm respectively. This means that the third side is: 22-(8+5) = 9cm

From this as see that 9cm is the highest length we have and if it were a right-angled triangle, this could be the hypotenuse. Now, to be sure of the initial response we use the Pythagoras theorem. We know that the hypotenuse² = adjacent² + opposite²

let's use the measurements we are given in the question

8²+5²=AC²

64+25=89

AC=√89

AC=9.433981132

AC =9.43cm

and when we add 8+5+9.43 to calculate the perimeter we get 22.43 which is not the initial perimeter, this the triangle isn't right-angled

Answer:

D. Negative

Step-by-step explanation:

Always read the graph from left to right

The graph is going down thus it is negative

Answer: Negative.

Step-by-step explanation: The graph of the line falls from left to right which makes it negative.

The answer will be x squared over 4 plus y squared over 8 equals 1.

An ellipse is an oval shape geometry having two focuses and the curve is equidistant from the focus.

The general equation of the ellipse is given as;

(x²/a²) + (y²/b²) = 1

The coordinates of a foci are: (±c, 0) where;

c² = b² - a²

However, we know that equation of directrix is; x = ±a/e

Now, Directrix is given ±4

Thus, a/e = 4

a = 4e

We also know that c = ae from ellipse foci coordinates.

Thus, ae = 2

since ae = 2, then (4e)e = 2

4e² = 2

e² = 2/4

e = 1/2

Thus;

a = 4 × 1/2

a = 2

Since c² = b² - a²;

2² = b² - 2²

4 = b² - 4

b² = 8

From (x²/a²) + (y²/b²) = 1, we can put our values to get;

x²/4 + y²/8 = 1

Hence the answer will be x squared over 4 plus y squared over 8 equals 1.

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Answer:

To calculate the fish population in 2020, we need to first find the fish population in 2018, 2019, and then use that to find the population in 2020.

In 2018, the fish population would be:

36,000 - (10% of 36,000) = 36,000 - 3,600 = 32,400

In 2019, the fish population would be:

32,400 - (10% of 32,400) = 32,400 - 3,240 = 29,160

Finally, to find the fish population in 2020, we can repeat the same process:

29,160 - (10% of 29,160) = 29,160 - 2,916 = 26,244

Therefore, the fish population in 2020 was approximately 26,244.

Step-by-step explanation:

Answer:

1.09 seconds

Step-by-step explanation:

I need the image that I am going to attach to solve the exercise.

We have the following information:

Confetti height from the ground is 25 feet

Person's height is 6 feet

So, the distance that the confetti would fall would be the subtraction of these heights, that is:

25-6 = 19 feet

d = 19 feet

We use the 5th equation of the attached image:

t = d ^ (1/2) / 4

replacing:

t = 19 ^ (1/2) / 4

t = 1.09 seconds

The volume of the 'scooped' pyramid is approximately 26.6667 cubic units.

To find the volume of the 'scooped' pyramid, we first need to determine the area of its base. Since the cross-sectional area of the pyramid is x 4 at a distance x from the tip, we can assume that the area at the tip is zero. This means that the area of the base is 4 times the area at a distance of 5 from the tip (since the distance from tip to base is 5).

Therefore, the area of the base is 4x4 = 16 square units. To find the volume, we can use the formula for the volume of a pyramid, which is:

Volume = (1/3) x Base Area x Height

In this case, the height of the pyramid is 5 units. So, we can substitute the values we have:

Volume = (1/3) x 16 x 5

Volume = 26.6667 cubic units

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Reduction formula for ∫(tanⁿ x) dx is Iₙ = x tanⁿ x - n Iₙ₋₁

To obtain a reduction formula for ∫(tanⁿ x) dx, where n is a positive integer, we can use integration by parts.

Let's denote the integral as Iₙ:

Iₙ = ∫(tanⁿ x) dx

Using the integration by parts formula ∫u dv = uv - ∫v du, we choose:

u = tanⁿ x     (differential of u: du = n(tanⁿ⁻¹ x sec² x) dx)

dv = dx         (v = x)

Applying integration by parts, we have:

Iₙ = ∫u dv

  = uv - ∫v du

  = x tanⁿ x - ∫x (n tanⁿ⁻¹ x sec² x) dx

  = x tanⁿ x - n ∫(x tanⁿ⁻¹ x sec² x) dx

Now, we can rewrite the integral on the right-hand side in terms of Iₙ₋₁:

Iₙ = x tanⁿ x - n Iₙ₋₁

This is our reduction formula for ∫(tanⁿ x) dx.

To show that f(n) + f(n - 2) = ..., where f(n) = ∫(tanⁿ x) dx, we can apply the reduction formula repeatedly:

f(n) = x tanⁿ x - n f(n - 1)

f(n - 1) = x tanⁿ⁻¹ x - (n - 1) f(n - 2)

By substituting f(n - 1) into the expression for f(n), we get:

f(n) = x tanⁿ x - n(x tanⁿ⁻¹ x - (n - 1) f(n - 2))

    = x tanⁿ x - n x tanⁿ⁻¹ x + n(n - 1) f(n - 2)

Therefore, we have shown that f(n) + f(n - 2) = x tanⁿ x - n x tanⁿ⁻¹ x + n(n - 1) f(n - 2).

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