The function f is given by f(x) = [tex]\int\limits^x_1 {\sqrt{t^3+2} } \, dx[/tex]. What is the average rate of change of f over the interval [0,3]?

Answer:

I'm sorry, but the question is unclear. Can you please provide more context or information so that I can understand what you are asking?

Answer:

The method that might have been used to result in Garcia winning is the Instant RunOff method.

In this method, voters rank the candidates in order of preference. If no candidate has a majority of first-choice votes, the candidate with the fewest votes is eliminated, and their votes are redistributed to the remaining candidates according to the second-choice preferences of the voters who supported the eliminated candidate. This process is repeated until one candidate has a majority of the votes.

In the preference ballot provided, Garcia received the most first-choice votes with a total of 26, but did not receive a majority of the votes. Therefore, the Instant RunOff method could have been used to determine the winner by redistributing the votes of the eliminated candidates (Müller and Ivanov) to the remaining candidates. Based on the preferences of the voters who chose Müller and Ivanov as their first choice, it is possible that the redistributed votes would have favored Garcia, leading to a majority win for Garcia.

The Instant RunOff method might not be fair to the other nominees because it can result in a candidate winning with a majority of second-choice or even lower preferences, rather than being the first choice of the majority of voters. This means that the candidate who is ultimately chosen may not have broad support, and may not be the candidate that the most voters actually prefer. Additionally, the method can be influenced by strategic voting, where voters rank their choices based on who they think is most likely to win, rather than their actual preferences. This can result in outcomes that do not accurately reflect the preferences of the voters.

Looking at the data, we can see that both the high as well as low temperatures of Monday, Tuesday, Thursday, & Friday were above [tex]O^{o}C[/tex]. The high on Wednesday was minus zero degrees Celsius.

The most popular scales are indeed the Celsius scale, sometimes known as centigrade, with the unit sign °C, the Franklin level (°F), and the Scale parameter (K), with the latter being mostly used for scientific reasons.

The total kinetic energy of a substance's particles is measured by its temperature. 2. An object's kinetic energy increases with increasing temperature. 3. If we add up the instances where the maximum and low temps were in excess of or below zero degrees Celsius, we find:

High temperature above [tex]O^{o}C[/tex]: 5 days

High temperature below [tex]O^{o}C[/tex]: 2 days

Low temperature above [tex]O^{o}C[/tex]: 3 days

Low temperature below [tex]O^{o}C[/tex]: 4 days

Therefore, we can see that overall, there were more days where the temperatures were below [tex]O^{o}C[/tex], both for the high and low temperatures.

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The complete question is:

In Vienna were more of the high and low temperatures above or below [tex]O^{o}C[/tex] justify your answer using a vertical number line

Days                        high temperature      low temperature

Monday                            8                           0

Tuesday                            9                          -4.5

Wednesday                      4.5                       -12

Thursday                           9                          4.5

Friday                                8.5                       -6

Saturday                           1                           -10

Sunday                             5                           -14

Solving a system of equations we can see that the two numbers are-8 and -7.

Let's say that the two numbers are A and B, and we know that we can write:

A*B = 56

A + B = -15

So we have a system of equations.

Using the second equation we can write:

A=  -15 - B

And replace that in the first equation, then we will get:

(-15 - B)*B = 56

-15B - B² = 56

Now we can solve the quadratic equation:

-B² - 15B - 56 = 0

The solutions are:

[tex]B = \frac{15 \pm \sqrt{(-15)^2 - 4*-56*-1} }{2*-1} \\\\B = \frac{15 \pm 1 }{-2}[/tex]

The two possible solutions are:

B = (15 + 1)/-2 = -8

B = (15 - 1)/-2 = -7

And when B is one of these values, A will be the other one.

Then the two numbers are -8 and -7.

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The value οf the median MN fοr the given trapezοid is 70.59 units.

The law οf sines specifies hοw many sides there are in a triangle and hοw their individual sine angles are equal. The sine law, sine rule, and sine fοrmula are οther names fοr the sine law. The side οr unknοwn angle οf an οblique triangle is fοund using the law οf sine.

Any triangle that is nοt a right triangle is referred tο as an οblique triangle. At least twο angles and their cοrrespοnding side measurements shοuld be used at οnce fοr the sine law tο functiοn.

Given that, SPQR is a trapezοid with SP parallel tο QR,

Nοw, we knοw that MN is the average οf the lengths οf the bases SP and QR.

That is,

MN = (SP + QR) / 2.

Fοr the given values we have:

SP = PQ = 12, sο QR = 2MN - SP

Nοw, m∠QRS = 120 and m∠QPS = 135,

Thus,

m∠SPQ = 180 - 120 - 135 = -75.

Hοwever, angles cannοt be negative, sο we add 360 tο get 285 degrees.

Since SPQR is a trapezοid, we knοw that m∠SPQ = m∠QRN. Alsο, since MN is the median οf the trapezοid, it divides the trapezοid intο twο cοngruent triangles, sο m∠QMN = m∠RNM.

Using the law οf sines in triangle QMN tο find MN:

sin(m∠QMN) / MN = sin(m∠MQN) / QN.

Since QN = NR:

sin(m∠QMN) / MN = sin(m∠RNM) / NR.

sin(135) / MN = sin(285) / NR.

NR = sin(285) / sin(135) * MN.

2MN - SP = 2 * sin(285) / sin(135) * MN

2MN - 12 = 2.17MN

MN = 12 / 0.17 = 70.59

Hence, the value οf the median MN fοr the given trapezοid is 70.59 units.

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The answer of the given question based on the actual area of the park in meters squared answer is the actual area of the park is 593,442 square meters.

Width refers to measurement of  distance from one side of object to other side, perpendicular to its length. It is one of basic dimensions of  object or shape along with the length and height.

Width is often used in context of rectangular or parallelogram-shaped objects, where it refers to measurement of shorter sides of the shape. For example, in a rectangular picture frame,  width would be measurement of the shorter sides of the frame.

The scale of the drawing is 1 cm = 110 m, which means that every 1 centimeter on the drawing represents 110 meters in real life.

The length of the park on the drawing is 8.6 cm, so the actual length of the park in meters is:

8.6 cm x 110 m/cm = 946 meters

The width of the park on the drawing is 5.7 cm, so the actual width of the park in meters is:

5.7 cm x 110 m/cm = 627 meters

Therefore, the actual area of the park in square meters is:

946 meters x 627 meters = 593,442 square meters.

So, the actual area of the park is 593,442 square meters.

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Answer:

629=500+120+9

Step-by-step explanation:

500+120+9=629

629=629

Step-by-step explanation:

ADCF and DEFG

the third pane AECG is perpendicular to line r.

The line's slope  on the graph will switch from being negative to positive.

The graph of the equation y = mx + c is a line with m as the slope and m and c as the y-intercept. The values of m and c are actual integers in the slope-intercept illustration of the linear equation.

The slope of a line, measured in m, tells us how steep it is. A line's gradient is also referred to as its slope sometimes. The y-coordinate of the point where the line's graph meets the y-axis is known as the y-intercept of a line, ab.

The slope-intercept form of the equation for the line, y = -5/4 x + 3, is written as y = mx + b. Where,

The line has a slope of m, a y-intercept of 3, a slope of -5/4, and a y-intercept of b.

As a result, the slope has changed from negative to positive if -5/4 is changed to 5/4.

As a result, the graph of the line's slope will switch from being negative to positive.

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Answer:

Step-by-step explanation:

Firstly,

angles at the centre of a circle add to 360°. So

      [tex](15x-1)+\angle ZVX +(8x-2)+(7x+15)+(3x+5)=360[/tex]

                                                             [tex]33x+17+\angle ZVX=360[/tex]

                                                                               [tex]\angle ZVX=360-33x-17[/tex]

                                                                               [tex]\angle ZVX=342-33x[/tex]

Secondly,

[tex]\angle YVU+ \angle UVW + \angle WVX =180[/tex]°   (since YX is a diameter - angles on a

                                                           straight line sum to 180°)

[tex](3x+5)+(7x+15)+(8x-2)=180[/tex]

                                   [tex]18x+18=180[/tex]

                                           [tex]18x=162[/tex]

                                               [tex]x=9[/tex]

Substitute [tex]x=9[/tex] into [tex]\angle ZVX=342-33x[/tex]:

    [tex]\angle ZVX=342-33\times9=63[/tex]°

Solution: [tex]\angle ZVX=63[/tex]

The formula for the function is S(r) = -10r² + 130r.

A function can be represented as an equation, a graph, or a table of values. In an equation, the function is usually denoted as "f(x)", where "x" is the input value and "f(x)" is the output value. For example, the equation f(x) = 2x represents a function that takes an input value x and produces an output value that is twice the input value.

Functions can be used to model real-world phenomena and solve various problems in mathematics, science, engineering, economics, and other fields. They are an important concept in calculus and other branches of mathematics, and they have numerous applications in modern technology and industry.

Let the cost of admission be $a and the cost of each raffle ticket be $r. Then we can write the following equation based on the given information:

10r + a = 135

Solving for a, we get:

a = 135 - 10r

Thus, the function that relates the total amount spent to the number of raffle tickets bought is:

S(r) = ar + 5r = (135 - 10r)r + 5r = -10r² + 130r

Therefore, the formula for the function is:

S(r) = -10r² + 130r

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Answer:If Krista drank 3/16 of the water in her water bottle in the morning, 5/16 in the afternoon, and 3/16 in the evening, then the total amount of water she drank during the day is:

3/16 + 5/16 + 3/16 = 11/16

This means that the fraction of water that is left at the end of the day is:

1 - 11/16 = 5/16

Therefore, Krista has 5/16 of the water remaining in her water bottle at the end of the day.

Step-by-step explanation:

The area of the triangle is 5/2 x sqrt(7) square units, or approximately 6.99 square units.

We need to know the triangle's base and height lengths in order to calculate its area.

Let's give the triangle's vertices the following names:

A is the bottom-left vertex.

B is the vertex at the bottom right.

C is the top vertex.

We can infer from the facts provided that the triangle's base measures AB, or 5 units.

We must draw a perpendicular line from the triangle's vertex C to its base AB in order to get the triangle's height. Let's give the intersection of the perpendicular line and the base the letter D.

Right triangle ACD with CD as the triangle's height now exists. The Pythagorean theorem can be used to determine CD's length:

[tex]AD^2 + CD^2 = AC^2[/tex]

We can determine that AC is 4 units and AD is 3 units based on the facts provided.

When we plug these figures into the formula, we get:

[tex]4^2 = 3^2 + CD^2[/tex]

Simplifying:

16 = 9 + [tex]CD^2[/tex]

[tex]CD^2[/tex] = 7

CD = √7

The triangle's height is therefore √7 units.

The area formula for triangles can now be used:

Area equals ([tex]\frac{1}{2}[/tex]) x base x height.

Adding the values we discovered:

Area equals ([tex]\frac{1}{2}[/tex]) x 5 sq (7)

Area = [tex]\frac{5}{2}[/tex] x sqrt (7)

Hence, the triangle has a surface area of [tex]\frac{5}{2}[/tex] x √7 square units, or roughly 6.99 square units.

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Answer:

B.1/100 is your answer for your question

Answer:

Step-by-step explanation:

We can start by finding the weight lifter's original body mass before the training session:

Let x = original body mass

Then, we know that 15% of x is equal to 78 kg - x:

0.15x = 78 - x

1.15x = 78

x = 78/1.15

x ≈ 67.83 kg

Therefore, the weight lifter's original body mass was approximately 67.83 kg.

Now, let's find the difference between the weight lifter's new body mass and his original body mass:

78 kg - 67.83 kg ≈ 10.17 kg

So, the weight lifter did indeed gain approximately 10 kg of weight after the training session. Therefore, his claim is valid.

Step-by-step explanation:

Every proper subgroup of G is cyclic.

In abstract algebra, a subgroup is a subset of a group that is itself a group under the same operation as the original group. More precisely, a subgroup H of a group G is a subset of G that satisfies the following three conditions:

A cyclic subgroup is a subgroup of a group that is generated by a single element. In other words, a subgroup H of a group G is cyclic if there exists an element a in G such that every element of H can be written as a power of a, and H is the smallest subgroup of G containing a.

In the given question,

Let H be a proper subgroup of G. Since H is a proper subgroup, we have lHl < lGl = 77.

Now, by Lagrange's Theorem, the order of any subgroup of G must divide the order of G. That is, lHl divides lGl = 77.

Since H is a proper subgroup, we have lHl > 1. Therefore, lHl can only be 7, 11, or 77 (the divisors of 77).

Suppose lHl = 7. Then, by Lagrange's Theorem, the elements of G are partitioned into disjoint cosets of H, each of size 7. But 77 is not divisible by 7, so there cannot be a whole number of cosets. Therefore, this case is not possible.

Similarly, suppose lHl = 11. Then, the elements of G are partitioned into disjoint cosets of H, each of size 11. But 77 is not divisible by 11, so there cannot be a whole number of cosets. Therefore, this case is also not possible.

Thus, we are left with the case where lHl = 77. But this implies that H = G, which contradicts the fact that H is a proper subgroup. Therefore, this case is also not possible.

We have exhausted all possibilities for the order of H, and in each case, we have arrived at a contradiction. Therefore, the assumption that there exists a proper non-cyclic subgroup of G must be false.

Hence, every proper subgroup of G is cyclic.

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The child at the 69th percentile is 5.5279 years οld.

The age οf the children in kindergarten οn the first day οf schοοl is unifοrmly distributed between 4.81 and 5.71 years οld. We can find the tοtal prοbability οf the child being between 4.81 and 5.71 years οld by subtracting the prοbability οf the child being yοunger than 4.81 frοm the prοbability οf the child being yοunger than 5.71:

P(4.81 ≤ age ≤ 5.71) = P(age ≤ 5.71) - P(age < 4.81)

The prοbability οf the child being yοunger than 4.81 is 0 since the age cannοt be negative.

The prοbability οf the child being yοunger than 5.71 can be calculated as:

P(age ≤ 5.71) = (5.71 - 4.81) / (5.71 - 4.81) = 1

Therefοre,

P(4.81 ≤ age ≤ 5.71) = 1 - 0 = 1

This means that the prοbability οf the child being οlder than 5 years οld is:

P(age > 5) = P(5.00 < age ≤ 5.71) = 1 - P(age ≤ 5.00) = 1 - [(5.00 - 4.81) / (5.71 - 4.81)] = 0.7018

Sο the prοbability οf the child is οlder than 5 years οld is 0.7018.

Tο find the age οf a child at the 69th percentile, we need tο find the age x such that the prοbability οf the child being yοunger than x is 0.69.

Let's call the age at the 69th percentile x. Then we have:

P(age < x) = 0.69

We can sοlve fοr x as fοllοws:

( x - 4.81 ) / ( 5.71 - 4.81 ) = 0.69

x - 4.81 = 0.69 ( 5.71 - 4.81 )

x - 4.81 = 0.69

x = 4.81 + 0.69 ( 5.71 - 4.81 )

x = 5.5279

Therefοre, the child at the 69th percentile is 5.5279 years οld.

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cos θ expressed as a ratio of given lengths of the right triangle is:

cos θ =  12/13

Trigonometry deals with the relationships between the sides and angles of triangles.

The three primary trigonometric functions are sine (sin), cosine (cos), and tangent (tan), which are defined as follows:

Sine (sin): The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle.

Cosine (cos): The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.

Tangent (tan): The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.

Thus, cos θ as a ratio of given lengths of the right triangle can be expressed as:

cos θ =  12/13   (cos = adjacent/hypotenuse)

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Complete Question

The attached image completes the question

the solved equation will be x=7.

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

2/X-5 - 4/ x+5 =2/ x²-25

[tex]\frac{(x+5)2-4(x-5)}{x^{2} -25}[/tex] = [tex]\frac{2}{x^{2} -25}[/tex]

2x-4x+10+20 = 2

-4x=-28

x=7

Hence, the solved equation will be x=7.

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Answer:

That answer is -3

Step-by-step explanation:

The way you do this is Rise/Run

so you would do y2-y1/x2-x1

In this case it's 10-1/-4-(-1)

Simplified is 9/-3 which is -3

hope this helped

By selling a bag at rs1500 and rs2100, there is some loss and profit respectively. if the loss is twice the profit , its cost price​ is Rs 1900.

The cost price is the amount of money that a seller pays to acquire or produce a product or service. It includes all the expenses incurred in the production or purchase of the product, such as the cost of raw materials, labor, packaging, shipping, and other overhead expenses.

Based on the given inforemation , we can represent the cost price by x.

x-1500 = 2 (2100- x)

x-1500 = 4200 -2x

3x = 5700

x= 1900

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Answer:

the answer was 31.88USD

There are 3150 distinct ways to arrange the marbles in a row.

What is Combination ?

In mathematics, combination is a way of selecting a group of objects from a larger set, without regard to the order in which the objects are selected. Combinations are also sometimes called "unordered selections" or "combinatorial subsets".

To solve this problem, we can use the formula for permutations with repetition. We have a total of 10 marbles, but some of them are repeated. Specifically, we have:

3 yellow marbles (repeated)

3 green marbles (repeated)

2 red marbles (repeated)

2 blue marbles (repeated)

So the number of distinct ways to arrange these marbles in a row is:

(10!) ÷ (3! x 3! x 2! x 2!)

The factorials in the denominator account for the repetition of each color. We divide by them to eliminate the overcounting that would occur if all the marbles were unique.

Simplifying this expression, we get:

(10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)÷(3 x 2 x 1 x 3 x 2 x 1 x 2 x 1 x 1 x 1)

which equals:

(10 x 9 x 8 x 7 x 6 x 5 x 4) ÷ (3 x 3 x 2 x 2)

Simplifying further, we get:

(10 x 3 x 3 x 3 x 2 x 2 x 7 x 5) ÷ (3 x 3 x 2 x 2)

which equals:

(10 x 3 x 3 x 7 x 5)

which finally equals:

3150

Therefore, there are 3150 distinct ways to arrange the marbles in a row.

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The base of the triangle is 8 cm.

The following equation determines a triangle's area A:

A = (1/2) * b * h

Where the triangle's height (h) and base (b) are the same.

In this instance, the triangle's height is 12 cm, and its size is 48 cm²

When these values are added to the formula, we obtain the following:

48 = (1/2) * b * 12

By condensing the right side, we obtain the following:

48 = 6b

When we multiply both sides by 6, we get:

b = 8

Therefore, the base of the triangle is 8 cm.

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The quadratic equation represented by the table is:

y = 2x^2 - 4x + 8

Here we have a table that represents a quadratic equation. Remember that a quadratic equation with a vertex (h, k) and a leading coefficient a can be written as:

y = a*(x - h)^2 + k

Here we can see that the vertex is at (1, 6), replacing that we will get:

y = a*(x - 1)^2 + 6

And we  can see the point (0, 8), replacing these values we will get:

8 = a*(0 - 1)^2 + 6

8 = a + 6

8 - 6 = a = 2

The quadratic is:

y = 2*(x - 1)^2 + 6

Expanding this we will get:

y = 2*(x^2 - 2x + 1) + 6

y = 2x^2 - 4x + 2 + 6

y = 2x^2 - 4x + 8

That is the quadratic equation.

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Answer:

The answer is 1/2

Step-by-step explanation:

3 and 6 are the known sides of the triangle as you can see three is half of six making it a 1/2 dilation

[tex]\dfrac{6}{3} = 2[/tex]

the scale factor is

1 : 2

Answer:35.09

Step-by-step explanation:From the question given above, the following data were:Opposite = 12Hypothenus = X Angle θ = 20 °

The solution for x in the equation -7x/5 + 4 = -1/2x - 7/2 is 5, and the other solutions are listed below

Given that

-7x/5 + 4 = -1/2x - 7/2

Multiply through by 10

-14x + 40 = 5x - 35

Evaluate the like terms

-19x = -95

So, we have

x = 5

Let x be the number of adult tickets sold.

So, the number of student tickets sold is 2x.

The total number of tickets sold is 444. Therefore:

x + 2x = 444

Combining like terms:

3x = 444

Dividing both sides by 3:

x = 148

Therefore, 148 adult tickets were sold.

The slope

To read the slope off the graph, we can use the formula:

slope = (change in y) / (change in x)

Using the points, we can calculate:

slope = (-2 - 1) / (3 - 1)

slope = -1.5

So the slope of the line is -1.5.

The y-intercept value

We can look at where the line intersects the y-axis on the graph. From the graph, it looks like the y-intercept is around y = 2.5.

The y-intercept point

Using the solution in (b), the estimated y-intercept point is (0, 2).

Rearrange the equation

To rearrange the equation into slope-intercept form, we need to isolate y on one side of the equation:

5x + 3y = 15

Subtract 5x from both sides:

3y = -5x + 15

Divide both sides by 3:

y = (-5/3)x + 5

So the equation in slope-intercept form is y = (-5/3)x + 5.

The slope

b) The slope of the line is the coefficient of x in the equation when it is in slope-intercept form.

Therefore, the slope of the line is -5/3.

The y-intercept of the line

This is the value of y when x = 0.

From the equation in slope-intercept form, we can see that when x = 0, y = 5.

So, the y-intercept of the line is 5.

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Answer:
Part a:

[tex]A(x)=10x^2+53x+63[/tex]

Part b:
2nd degree polynomial.

Part c:
Check step by step.

Step-by-step explanation:

since the sides of the rectangle are (2x+7) and (5x+9), the area is given by the product of the sides:

[tex]A=(2x+7)(5x+9)=10x^2+18x+35x+63=10x^2+53x+63[/tex]

So the area as a function of X is given by:
[tex]A(x)=10x^2+53x+63[/tex]

Notice is a second degree polynomial in standard form

To ensure part c, notice we can also multiply the sides in different order. This is A*B must be B*A for the sides of the rectangle. Lets check

[tex]A=(5x+9)(2x+7)=10x^2+35x+18x+63=10x^2+53x+63[/tex]
Since we obtained the same answer in part A the closure property for multiplication is check for the polynomial.