the function f is continuous and ∫80f(u)du=6. what is the value of ∫31xf(x2−1)dx?

The date which is 100 days ago from 12 February 2023  is equal to

November 04, 2022 .

Present date is equal to 12 February 2023.

Date which is 100 days is written as :

January month has 31 days.

December month has 31 days.

November month has 26 days.

Total days equal to :

( 31 + 31 + 26 + 12 ) days = 100 days

100 days ago from 12 February 2023 is equal to :

12 February 2023  minus 100 days is 04 days 2022.

Therefore, the day which is 100 days ago from 12 February 2023 is given by   November 04, 2022 .

The above question is incomplete , the complete question :

What is 100 days ago from 12 February 2023 ?

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Therefore , the solution of the given problem of linear equation comes out to be  129 sodas were sold.

The formula y=mx+b is used to produce a simple regression curve. The slope is B, and the y-intercept is m. The preceding line indicates independent components, yet is commonly referred to as a "math equation combining many variables". In bivariate linear equations, there are just two variables. Application problems involving linear equations have no known solutions. Y=mx+b.

Here,

Let's start by defining some variables. Let s be the number of sodas sold and h be the number of hot dogs sold.

We know from the problem that:

s + h = 172 (the total number of sodas and hot dogs sold)

s = 3h (the number of sodas sold is three times the number of hot dogs sold)

We can substitute the second equation into the first equation to eliminate s and get an equation in terms of h:

3h + h = 172

4h = 172

h = 43

So, 43 hot dogs were sold. We can then use the second equation to find the number of sodas sold:

s = 3h = 3(43) = 129

Therefore, 129 sodas were sold.

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The equation y = -5x - 1 is steeper than the equation y = -2x - 7.

In mathematics, the relative slope or rate of change of two lines or curves is referred to as "steeper." If one line or curve's slope or rate of change is larger than another, it is said to be steeper than the other.

To compare the steepness of two linear equations, we can look at their slopes, which represent the rate of change of the dependent variable (y) with respect to the independent variable (x). The slope of a line is given by the coefficient of x in the equation y = mx + b, where m is the slope.

Let's compare the slopes of the two equations:

y = -5x - 1: The coefficient of x is -5, so the slope is -5.

y = -2x - 7: The coefficient of x is -2, so the slope is -2.

Since the slope of the first equation (-5) is greater in magnitude than the slope of the second equation (-2), we can conclude that the first equation is steeper than the second equation.

Alternatively, we can look at the absolute values of the slopes. The absolute value of the slope of the first equation is 5, which is greater than the absolute value of the slope of the second equation, which is 2. This confirms that the first equation is steeper than the second equation.

Therefore, the equation y = -5x - 1 is steeper than the equation y = -2x - 7.

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Answer:

The answer is: K = 14.

Answer:

200 km

Step-by-step explanation:

Let's use the formula:

distance = rate × time

Let the original average speed of the car be r km/h, and let the distance between the two cities be d km.

According to the problem, the car takes 2 hours to cover the distance, so we have:

d = r × 2

If the car's average speed decreased by 20 km/h, its new average speed would be (r - 20) km/h. If it took 30 minutes (0.5 hours) longer to cover the same distance at the slower speed, we have:

d = (r - 20) × 2.5

Now we have two equations for d:

d = r × 2

d = (r - 20) × 2.5

We can solve for r in the first equation:

r = d / 2

Substituting into the second equation:

d = (d/2 - 20) × 2.5

Simplifying:

d = 1.25d - 50

0.25d = 50

d = 200

Therefore, the distance between the two cities is 200 km.

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Answer:

Hi! In order to determine how much money Aiden will have in his account after 8 months, let's figure out how much he deposits each month.

He started with $250. After one month, he had $586; after two months, he had $922; after three months, he had $1,258. Each month, there is a gain of $336.

Therefore, after four months, Aiden will have $1,594. After five months, he will have $1,930. After six months, he will have $2,266. After seven months, he will have $2,602. Finally, after eight months, he will have $2,938.

Hope this helps!

The probability of rolling a 7 with a pair of dice is 1/6. This is because there are six possible combinations that add up to 7.

Each of these combinations has an equal probability of occurring, so the probability of rolling a 7 is 1/6. (1+6, 2+5, 3+4, 4+3, 5+2, 6+1).

To explain further, when two dice are rolled, there are 36 possible outcomes, each with an equal probability of occurring. Of the 36 outcomes, 6 of them will result in the total number of dots appearing on top being 7. Since 6 out of 36 outcomes result in a 7, the probability of rolling a 7 is 6/36 or 1/6. This means that if two dice are rolled 36 times, there is a 1 in 6 chance that the total number of dots appearing on top will be 7 at least once.

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By calculating the distance we know that the PR measures 198.94 ft to the nearest foot.

Distance is the sum of an object's movements, regardless of direction.

The distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively.

The distance can refer to a physical length in physics or to an estimate based on other factors in common usage.

So, the triangles PRE and POC appear to be comparable triangles in the diagram.

Let PR = x.

Utilizing the similarity theorem:

PR/RE = PR+RO/OC

x/135 = (x+140)/230

Now, cross multiply as follows:

230x = 135(x+ 140)

230x = 135x + 18,900

230x - 135x = 18,900

95x = 18900

x =18900/95

x = 198.94

Therefore, by calculating the distance we know that the PR measures 198.94 ft to the nearest foot.

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Correct question:

To indirectly measure the distance across a river, Nolan stands on one side of the river and uses sight lines to a landmark on the opposite bank. Nolan draws the diagram below to show the lengths and angles that he measured. Find PRPR, the distance across the river. Round your answer to the nearest foot.

To calculate z table online we put Raw Score, Population Mean, Standard Deviation, σ   then calculator give us answer.

A z-table, also called a standard normal table or unit normal table, is a table of standardized values ​​used to determine the probability that a given statistic is below, above, or below the standard normal distribution. A z-score of 0 indicates that the given point is the same as the mean. Therefore, on the graph of the standard normal distribution, z = 0 is the midpoint of the curve. A positive Z value indicates that the point is to the right of the mean, and a negative Z value indicates that the point is to the left of the mean. There are several different types of Z-tables. The values ​​in the table below represent a range from z=0 to a specific z-score.

Z Means table (0 to Z)  

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Answer:

Variable p represents "the puppy is tired", and variable q represents "the puppy will sleep".

The statement in symbolic form is: p → q, where the symbol → means "implies" or "if...then".

The mathematical phrase "e to the ipi" is composed of the imaginary unit i (the square root of -1 raised to the power of pi), which is symbolized by "pi," and the mathematical constant "e" (Euler's number).

The expression "e to the ipi" may be expressed as follows:

[tex]e^{(i*pi)}[/tex]

The following formula is known as Euler's formula:

[tex]e^{(ipi)}[/tex] = cos(pi) + isin(pi)

where "cos" and "sin" are the sine and cosine functions, respectively.

We may reduce this formula to using the cosine and sine trigonometric identities.

[tex]e^{(i*pi)}[/tex] = -1

"e to the ipi" hence equals a negative one. This startling and outstanding finding ties together various crucial mathematical ideas, including calculus, complex numbers, and trigonometry.

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Answer:

[tex](x - 3)^2 + (y + 2)^2 = 41[/tex]

Step-by-step explanation:

The general shape of the equation is:

(x-a)² + (y-b)² = r²

Where (a,b) is the center and r is the radius.

(a,b) = (3,-2) is given.

To find the radius r, or even simpler, r², calculate the distance between (-3,2) and (8,2) using pythagoras.

r² = (8-3)² + (2--2)² = 41

Note that the complete proof that ∠A ≅ ∠D is given as follows:

Note that the Alternate Interior Angles Theorem states that when two parallel lines are crossed by a transversal, the alternate interior angles are congruent.

The Basic Proportionality Theorem states that in a triangle, a line parallel to one side divides the other sides proportionally.

The Vertical Angles Theorem states that vertical angles are congruent.

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The estimated product is  6000

What is estimation?

To make calculations simpler and more realistic, estimation of a number refers to a plausible assumption of the actual value.

Estimation is the process of approximating a quantity with the necessary accuracy.

The result is quickly and roughly determined by rounding off the numbers used in the calculation.

To estimate the product, we first round off the multiplier and the multiplicand to the nearest tens, hundreds, or thousands and then multiply the rounded numbers.

598 ≈ 600

9≈ 10

600*10

= 6000

The estimated product is  6000

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Pythagorean theorem tells us how the side lengths of right triangles are related.

The Pythagorean theorem, also known as the Pythagorean identity, states that the sum of the squares of the lengths of the two sides forming the right angle is equal to the square of the length of the hypotenuse in any right triangle (the side opposite the right angle). In other words, the Pythagorean theorem can be used to calculate the length of the hypotenuse given the lengths of the two sides of a right triangle.

This relationship can be written as the equation:

[tex]a^2 + b^2 = c^2[/tex]

where a and b are the lengths of the legs, and c is the length of the hypotenuse. The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery.

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The value of 122 pounds using conversion factor of 0.453592 kilograms is equal to 55.3382 kilograms .

Converting factor used to convert pounds to kilograms is equal to :

1 pounds = 0.453592 kilograms  ___( 1 )

Now multiply both the side of equation ( 1 ) by 122 to get the value of 122 pounds we have,

⇒ ( 122 multiply by 1 ) pounds = ( 122 multiply by 0.453592 ) kilograms

⇒ 122 pounds = 55.338224 kilograms

⇒ 122 pounds = 55.3382 kilograms

Therefore, the value after converting pounds to kilograms for 122 pounds is equal to 55.3382 kilograms .

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Answer:

x = 3 units

Step-by-step explanation:

These two triangles are similar figures, which means the ratio of the lengths of their corresponding sides are equal:

[tex]\frac{Side AB}{Side AC} = \frac{Side DE}{Side CE}[/tex]

= [tex]\frac{24}{2x} = \frac{56}{3x + 5}[/tex]

Cross-multiplication is applied:

= [tex](24)(3x + 5) = (56)(2x)[/tex]

Parenthesis are expanded by using the Distributive Law:

= [tex]72x + 120 = 112x[/tex]

Bring all the like terms together and then isolate x:

= [tex]120 = 112x - 72x[/tex]

= [tex]120 = 40x[/tex]

= x = [tex]\frac{120}{40}[/tex]

∴ x = 3 units

The length of JI is equal to 6 cm (i.e., JI = 6 cm) since J is the midpoint of line segment KI.

In geometry, a line segment is a part of a line that has two endpoints. It is a straight path that connects two points, and it is the shortest distance between those two points. A line segment is named by its two endpoints, and the symbol “‾‾” is placed over the two endpoints to denote that it is a line segment.

Line segments can be measured, and their lengths can be calculated by using the distance formula, which is based on the Pythagorean theorem. The distance formula states that the distance between two points (x1, y1) and (x2, y2) in a two-dimensional plane is given by:

[tex]d = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)}[/tex]

Line segments are important in many areas of geometry and mathematics. They are used to define shapes and figures, to measure distances, and to calculate areas and volumes. In trigonometry, line segments are used to define angles, and they are also used to calculate the length of sides in right triangles.

Line segments can be compared and classified based on their lengths. A line segment that has the same length as another line segment is said to be congruent to it. Line segments can also be classified as equal (having the same length), longer or shorter than others, and parallel or intersecting.

By definition, the midpoint of a line segment divides the line segment into two equal parts. Since J is the midpoint of KI, it means that KJ is equal in length to JI, and therefore JI is also 6 cm.

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a). The expression which correctly represents the length of the rectangular area is; 4x - 5.

b). The product of the length and width of the rectangle is; (4x - 5) 3x = 12x² - 15x.

Recall; for rectangles;

Area = length × width

Therefore, Length= Area / Width

Length = 12x² - 15x / 3x

Length = 4x - 5

Therefore, the expression which represents the length is; 4x - 5.

b) By multiplying the length and width of the rectangular area; we have;

Area = (4x - 5) 3x

= 12x² - 15x

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The equation for the height of the trapezoid is 402.8 = (1/2)h(14.6 + 35.4)

The formula for the area of a trapezoid is:

A = (1/2)h(b1 + b2)

where A is the area, h is the height, b1 and b2 are the lengths of the two bases.

We can use this formula to write an equation to determine the height of the trapezoid

When the known values are substituted, we have

402.8 = (1/2)h(14.6 + 35.4)

Hence, the equation is 402.8 = (1/2)h(14.6 + 35.4)

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Coterminal angles can have different angle measures.

Therefore the answer is True.

Coterminal angles are angles that have the same initial and terminal sides, but may differ in their angle measures. To find a coterminal angle, you can add or subtract a multiple of 360 degrees or 2π radians to the original angle.

For example, an angle of 45 degrees is coterminal with an angle of 405 degrees (45 + 360), as well as an angle of -315 degrees (45 - 360). Similarly, an angle of π/4 radians is coterminal with an angle of 9π/4 radians (π/4 + 2π), as well as an angle of -7π/4 radians (π/4 - 2π). Coterminal angles are useful in trigonometry and calculus when working with periodic functions, as they allow for simplification and generalization of calculations.

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--The question is incomplete, answering to the question below--

"Coterminal angles can have different angle measures. T or F."

The area of the path is 256 square feet.

What is the area of rectangle?

The area of a rectangle is given by the formula:

Area = length x width

where "length" and "width" are the dimensions of the rectangle. To find the area of a rectangle, simply multiply the length by the width.

To find the area of the path surrounding the rectangular garden, we need to subtract the area of the garden from the area of the larger rectangle that includes the path. The larger rectangle measures 25 feet by 43 feet.

Area of the larger rectangle = 25 ft * 43 ft = 1075 sq ft

Area of the garden = 21 ft * 39 ft = 819 sq ft

So, the area of the path surrounding the garden is:

Area of the larger rectangle - Area of the garden = 1075 sq ft - 819 sq ft = 256 sq ft

Hence, the area of the path is 256 square feet.

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The angle of depression from point R to point S is ∠1.

The angle of elevation from point S to point R is ∠2.

∠2 is the angle of elevation from S to R.

∠1 is the angle of depression from point R to point S.

What is an angle of elevation?

The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.

There is an angle of elevation from point R to S. Thus point R is lie above S.

The angle of depression from point R to point S is ∠1.

The angle of elevation from point S to point R is ∠2.

∠2 is the angle of elevation from S to R.

∠1 is the angle of depression from point R to point S.

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The 1 meter is 3.28084 feet.

Since 1983, the meter has been internationally defined as the length of the path traveled by light in a vacuum in 1/299,792,

58 seconds. This definition can be applied easily and precisely with modern techniques, and the speed of light is considered a universal constant, making it an ideal  basis for a standard of length.

foot, plural of feet, measured by a number of  ancient, medieval and modern linear measurements (usually 25–3

cm) based on the length of a human foot, used exclusively in English-speaking countries, where it usually consists of 12 inches. , or a third of a yard.

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Car B will catch up with Car A at 4:45pm, after travelling for 2 5/8 hours (3 hours minus 1 hour minus 3/8 of an hour).

Car A leaves the Grand Canyon at noon and travels at 80 mph. At 3 pm, it stops for an hour. Car B leaves the Grand Canyon at 2 pm and travels at 90 mph without stopping.To calculate when Car B will catch up with Car A, we need to find the time difference between their departure times and the difference in their speeds.Car A leaves one hour before Car B, so we can subtract 1 hour from the total travel time. The difference in their speeds is 10 mph, which is equivalent to 1/8 of an hour for every hour of travel. Therefore, we can subtract 1/8 of an hour from the total travel time for every hour of travel.We can use these two deductions to calculate the total travel time: 3 hours - 1 hour - 3/8 of an hour = 2 5/8 hours. Therefore, Car B will catch up with Car A at 4:45pm.

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Since quadrilateral MATH has opposite sides congruent and parallel, it is a parallelogram.

In a parallelogram, opposite sides are parallel and congruent, but the opposite angles are also congruent.

Therefore, we can say that angle M is congruent to angle H, and angle A is congruent to angle T.

Option A states that MT is congruent to AH, which is not always true for a parallelogram.

Option B states that MT is perpendicular to AH, which is also not always true for a parallelogram.

Option C states that angle MHT is congruent to angle ATH. Since angle M is congruent to angle H and angle A is congruent to angle T, we can say that angle MHT is congruent to angle ATH. This is always true for a parallelogram, as opposite angles are congruent.

Option D states that angle MAT is congruent to angle MHT. This is not always true for a parallelogram. While angle MHT is congruent to angle ATH (as explained in Option C), there is no reason to assume that angle MAT is congruent to angle MHT.

Therefore, the correct answer is: C. Angle MHT is congruent to Angle ATH.

The method to convert milimeter to meters will be through multiplication of [tex] {10}^{-3} [/tex] with the quantity in milimeter.

The abbreviation mm is representative of milimeters. Now, we know that milimeters is 1/1000 meters and hence is smaller unit in comparison to meters.

Based on the above mentioned fact, we can multiply the same number (smaller unit) with negative exponent. It will be carried out like this -

Quantity in meters = quantity in milimeter ×

[tex] {10}^{-3} [/tex], where [tex] {10}^{-3} [/tex] has negative exponent. Let us say we have 10⁹ milimeters and need to convert in into meters.

So, quantity in meter = 10⁹ × [tex] {10}^{-3} [/tex],

Performing multiplication which will be done through subtraction of powers

Quantity in meters = 10⁶ meters

Hence, mm to meters will be multiplication with [tex] {10}^{-3} [/tex].

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Answer:

D

Step-by-step explanation:

draw a right triangle, with the segment being the hypotenuse. Use Pythagorean theorem to calculate.

to use pythagorean Theorem

Step-by-step explanation:

The Pythagorean Theorem is a formula that allows you to calculate the distance between two points in a coordinate plane. It states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides. In the case of two points on a coordinate grid, the distance between them is the length of the hypotenuse of the right triangle formed by the horizontal and vertical distances between the two points.

Answer:

x = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Solve for x

[tex]\frac{2}3}(3-6x)=-3(8x-4)[/tex]

Distribute [tex]\frac{2}{3}[/tex] and -3.

[tex]2-4x=-24x+12[/tex]

Simplify

[tex]-4x+2=-24x+12[/tex]

Subtract 2 on both sides

[tex]-4x=-24x+10[/tex]

Subtract -24x on both sides

[tex]20x=10[/tex]

Divide by 20

[tex]x=\frac{1}{2}[/tex] or 0.5