Find the derivative of the function.
F(x) =
x2 integral et7dt
x

There are 8 half dollars and 9 quarters inside the cup.

We can set up a system of equations to represent the number of half dollars (h) and quarters (q) in the cup and the total value of the coins.

Let h be the number of half dollars and q be the number of quarters.

The first equation represents the total number of coins in the cup:

The second equation represents the total value of the coins:

To solve for h and q, we can use either the substitution or elimination method.

By substitution, we can solve for one variable in terms of the other in one of the equations and substitute it into the other equation.

So, q = 17 - h

then substitute it into the second equation:

0.5h + 0.25(17 - h) = 5.50

By solving for h, we get h = 8, then we can substitute it back into the first equation to get q = 9

So, there are 8 half dollars and 9 quarters inside the cup.

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rate of change for this linear equation, y = 5x - 1 is +5

the initial value of the linear equation, y = 5x + 2 is +2.

A linear equation is an algebraic equation of the form y = mx+c, where m is the slope and c is the y-intercept, and only a constant and a first-order (linear) component are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables." If a linear equation contains two variables, it is referred to as a linear equation in two variables, and so on.

Non-linear equations are those that do not produce a straight line. It has a changeable slope value and resembles a graphed curve.

Given that,

y = 5x - 1 is a linear equation.

As we know, when linear equation is in the form of y = mx + c, here m is the slope or the rate of change, and c is the Y-axis intercept, or value of y when x is zero, or initial value.

Therefore, for the given equation, rate of change is 5 and initial value is -1.

Given that,

y = 5x + 2

is a linear equation.

As we know, when linear equation is in the form of y = mx + c, here m is the slope or the rate of change, and c is the Y-axis intercept, or value of y when x is zero, or initial value.

Therefore, for the given equation, rate of change is 5 and initial value is + 2.

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The correct statement regarding the probabilities from the table is given as follows:

C The golf ball is 2 times as likely to be orange as it is to be pink.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of balls for this problem is given as follows:

4 + 11 + 8 + 18 = 41.

Hence the probability of selecting each ball is obtained as follows:

Hence statement C is correct, as:

2 x 4/41 = 8/41.

(which is the probability of orange, obtained multiplying the probability of pink by two).

The number of pink balls is of 4.

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g(6) must be greater than 21 which is 22 only.

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable.

Since g'(x) > 0 for all x and we know that g(x) is an increasing function.

Additionally, since g"(x) > 0 for all x, we know that g(x) is a concave-up function.

Since g(x) is increasing, we know that g(6) > g(5) = 18.

Now, we can use the fact that g(x) is concave-up to find a lower bound on g(6).

By the definition of concave-up, we know that the slope of the tangent line to g(x) is increasing.

This means that the slope of the line connecting (3,g(3)) to (5,g(5)) is less than the slope of the line connecting (5,g(5)) to (6,g(6)).

Using this information, we can find a lower bound on g(6):

g(5)- g(3) / (5-3) < g(6)- g(5)/ (6-5)

18- 12/2 < g(6)- 18

3 < g(6) - 18

g(6) > 21

Therefore, g(6) must be greater than 21.

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Answer:

30 degrees

Step-by-step explanation:

Answer:

3, 2

Step-by-step explanation:

In order for the equation to be equal to zero, the following must be true:

x-3 = 0   or,

x-2 = 0

Therefore the 2 solutions are x=3, x=2

The odds against exactly 5 cars passing over the bridge in that time are given as follows:

5.25:1.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

An odd, conversely, is calculated as the division of the number of desired outcomes by the number of non-desired outcomes.

The probability(in favor) that 5 cars will pass over a small bridge in a 4-minute period is 0.16, hence the odds are given as follows:

0.16 : (1 - 0.16) = 0.16 : 0.84.

To obtain the odds against, we must exchange the desired and the non-desired outcomes, meaning that the odds against is then given as follows:

0:84 : 0.16.

As the quotient of 84 by 16 is of 5.25, the simplified odd is given as follows:

5.25 : 1.

Meaning that it is 5.25 times more likely that exactly 5 cars do not pass over the bridge over that time rather that they do pass.

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Answer:

To determine the number of miles Coroline runs per minute, we need to first convert the distance she runs to a fraction of a mile and the time it takes her to run that distance to a fraction of an hour.

3 1/2 miles is equivalent to 3 + 1/2 = 3 + 1/(2*1) = 7/2 miles.

22 1/4 minutes is equivalent to 22 + 1/4 = 22 + 1/(4*1) = 23/4 minutes.

To convert the time to hours, we can divide the number of minutes by the number of minutes per hour. There are 60 minutes per hour, so we have:

23/4 minutes / (60 minutes/hour) = (23/4) / (60/4) = 23/60 hours

To determine the number of miles Coroline runs per minute, we can divide the distance she runs by the time it takes her to run that distance:

(7/2 miles) / (23/60 hours) = (7/2) / (23/60) = (760) / (223) = 420/46

Simplifying, we have:

420/46 = 9 1/23

Therefore, Coroline runs approximately 9 1/23 miles per minute.

Step-by-step explanation:

Answer:

she runs 0.078 miles  per minute.

Step-by-step explanation:

Answer:

Option b.  -2x + 3y - 6 = 0

Step-by-step explanation:

Let's look for a linear equation of the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).

Calculate the slope first.  Slope is the Rise/Run of any two points on a straight line.   Using the given points, (0,2) and (3,4) we find:

  Rise = 4 - 2 = 2

  Run = 3 - 0 = 3

Slope, m, Rise/Run = (2/3)

The equation becomes y = (2/3)x + b

To find b, enter either of the two given points.  

y = (2/3)x + b

2 = (2/3)(0) + b  :  for point (0,2)

b = 2

The equation becomes:  y = (2/3)x + 2

Reformat this to match the format of the answer options.  

y = (2/3)x + 2    

3y = 2x + 6      [Multiplied by 3]

3y - 2x - 6 = 0

-2x + 3y - 6 = 0     [rearrange]

This matches option b.

Answer:

Step-by-step explanation:

3(23-2b) + 3b = 48

1. Use the distributive property and distribute the 3 before the parenthesis

             3(23-2b)   (make sure you read the (-) as part of the 2b so it's -2b

              69 - 6b

2. 69 - 6b +3b = 48   (combine like terms...the bs: -6b + 3b)

    69 -3b=48

3. 69 - 3b = 48         (subtract 69 from both sides)

   -69           -69

4. -3b = -21      (divide both sides by negative three...we want the b to be +

   /-3    /-3

Answer: b = 7

So, C is your answer

Answer:

√259 or 16.09

Step-by-step explanation:

Hello!

I'll be labeling the vertices so that it is easier to understand the sides.

These are both right triangles, and we can find the measures of right triangles (given two other sides) by using the Pythagorean theorem:

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

In Triangle BCD, we have the measures of the hypotenuse and a leg. We can use that to find the missing side: CB

Since DB is the hypotenuse, it would be side c, and we can say that CD can be side a.

CB in simplest radical form is 5√21.

We can now solve for x, because now in triangle ABC, we have the measures of two sides: hypotenuse AC and leg CB.

AB in simplest radical form is √259, which is approximately 16.09.

The solution for x is √259 or 16.09.

The distance in miles represented by a length on the map of 7 inches is 0.28

The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.

Given;

The scale of a map says that 2 inches represents 50 miles.

2 inches = 50 miles

1 Mile = 2/50 inches

Hence, 7 Mile = 7 * 2/50 inches

7 Mile = 14/50 inches

7 Mile = 0.28 inches

Therefore, the scale factor of 7miles in the map will be 0.28inches

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Lia gave away 3/5 of the trail mix, which is equal to 2 2/5 pounds.

Lia bought 4 3/5 pounds of trail mix. She gave 3/5 of it to her iter.Since Lia bought 4 3/5 pounds of trail mix, we can express this as 4 + 3/5 pounds, or 9/5 pounds.

To find out how much trail mix Lia gave away, we can multiply 9/5 by 3/5.

3. 3/5 multiplied by 9/5 is equal to 27/25.

To simplify this fraction, we can divide both the numerator and denominator by 3.

27/25 can be simplified to 9/5 or 2 2/5 pounds.

Therefore, Lia gave away 2 2/5 pounds of the trail mix.

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The correct answer is option A. For P= -1/2 0 1/2 1/2 0 -1/2 0 0 1 D= 0 4 0 0 0 4 -1 0 0. The matrix can be diagonalized using the eigenvectors.

To diagonalize the matrix, the eigenvectors must be found first. The eigenvectors can be found by solving the characteristic equation and finding the eigenvalues. The eigenvalues of the matrix are 2 and -1. The eigenvectors associated with each eigenvalue are determined by solving the eigenvalue equation.

The eigenvectors for the matrix are [1, -2], [1, 2], [1, 0], and [0, 1]. After the eigenvectors are found, the matrix can be diagonalized by constructing the transformation matrix P. The transformation matrix P is composed of the normalized eigenvectors. The transformation matrix P is: P=[-1/2, 0, 1/2, 1/2, 0, -1/2, 0, 0, 1], and the diagonal matrix D is composed of the eigenvalues.

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In the coordinate geometry the translation represents one type of transformation to change the location without changing the shape, size.

As given in the question,

In the coordinate geometry,

Therefore, in the coordinate geometry the translation represents one type of transformation to change the location of the geometrical figure.

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Answer in explanation:

although there's an addition sign, you subtract the two because a

(+) + (-) = (-) subtract

[This is a general rule, writing down the "rules" for reference is a good way to help if your having trouble]

subtract to find your answer (you keep the sign of 1.8 because it's the larger number.)

1.3 + (-1.8) =

-0.5

-0.5 is your answer

Hope this is clear!

If Lin is solving the inequality [tex]15-x < 14[/tex] and she know the solution is x = 1 , then the solution of  inequality is [tex]x > 1[/tex] .

The inequality that Line is solving is [tex]15-x < 14[/tex] ,

the solution of the equation [tex]15-x = 14[/tex] is given as x = 1 ;

we have to find the value of x for which the given inequality expression is true ,

Case(i) , let us take [tex]x > 1[/tex] ,

So , putting x = 2 , in the inequality ,

we get ; [tex]15-2 < 14[/tex]

= 13 < 14 , that is TRUE .

Case(ii) , let us take [tex]x < 1[/tex] ,

So , putting x  = 0 in the inequality ,

we get ; [tex]15-0 < 14[/tex]

= 15 < 14 , that is FALSE .

Therefore , the solution of the inequality is x > 1 .

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y=­−12(x+4)(x−1) A quadratic function that satisfies the requirement and passes through the points (4, 2) and has the equation +2 (1,2) .

A mathematical formula known as an equation combines two assertions using the equal sign (=) to denote equivalence. The terms 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14, for example. Mathematical equations are used to express the relationship between two phrases on either side of a letter. In most cases, the symbol serves as the sole variable. a good example is 2x - 4 = 2.

given

a )a vertex at (­−2,−­5) :

y=[tex](x+2)^{2}[/tex]−5

y=­−[tex](x+2)^{2}[/tex]−5

y=3[tex](x+2)^{2}[/tex]−5

b) a y-­intercept of (0,−­6) :

y=[tex]x^{2}[/tex]−6

y=[tex]x^{2}[/tex]+13x−6

y=2[tex]x^{2}[/tex]−6

c)  the points (−­4,2) and (1,2):

y=(x+4)(x−1)+2

y=2(x+4)(x−1)+2

y=­−12(x+4)(x−1)+2

y=­−12(x+4)(x−1) A quadratic function that satisfies the requirement and passes through the points (4, 2) and has the equation +2 (1,2).

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The number of boxes to complete the partial quotient model is found to be as 19 cars .

On dividing 95 from 5 we will get 19 as the quotient.

95 / 5 = 19

The quotient is the number that is produced when two integers are divided. It is the outcome of the division process , when we divide a number from another the result is known as quotient.

In arithmetic division, four primary terms are used which are  divisor, dividend, quotient, and remainder. In this post, each phrase will be defined and shown using examples.

Dividend = Divisor + Quotient + Remainder

If the divisor is not able to completely divide the dividend then it leaves a remainder.

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The domain is all values of x that makes the expression defined.

Set-Builder Notation: {x| x ≤ 3 }

Interval Notation: (-∞,3]

Given the function in the question;

y = 5√(6−2x)​

To find the domain, set the radicand greater than or equal zero and solve for x.

6 - 2x ≥ 0

Subtract 6 from both sides

6 - 6- 2x ≥ 0 - 6

-2x ≥ -6

Divide both sides by -2

-2x/-2 ≤ -6/-2

x ≤ -6/-2

x ≤ 3

Therefore, the domain is;

Set-Builder Notation: {x| x ≤ 3 }

Interval Notation: (-∞,3]

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The average speed of Sam's race car is equal to 20 kilometers per hour.

In this question we find the case of a race car being displaced in a race whose length (s) is 10.6 kilometers, a distance traveled in a time (t) of 31 minutes and 46 seconds (1906 seconds). The average speed (v), in kilometers per hour, is described by the following formula that assumes an hypothetical constant speed:

v = s / t

Where:

First, convert time into hours:

t = (31 min) · (1 hour / 60 min) + (46 s) · (1 hour / 3600 s)

t = 0.529 h

Second, calculate the average speed:

v = (10.6 km) / (0.529 h)

v = 20.038 km / h

v = 20 km / h

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The complete problem equation will be c = k*m + b

The cost equation for renting a car from the ABC Car Rental Company in terms of the number of miles driven, m, and the cost, c, would likely take the form of:

c = k*m + b where k is the rate of cost per mile and b is the fixed cost for renting the car independent of the miles driven.

It is important to note that this is a general equation and the specific cost equation of the ABC Car Rental Company is not provided. Also, this equation assumes that the cost of renting a car is linear to the miles driven, which may not be the case in practice. Other factors such as the type of car and duration of the rental period could also be included in the cost equation.

Therefore, the problem equation will be c = k*m + b

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The surface area that can be painted with one complete rotation of the roller is 226.19 inches².

Surface area is defined as the total amount of area that covers the surface or outside of a three-dimensional figure.

A paint roller is in the shape of a cylinder. To determine the surface area that can be painted with one complete rotation of the roller, solve for the surface area of a cylinder without the circular bases.

SA = 2πrh

where SA = surface area

r = radius of the base = 3 inches

h = height of the cylinder = width = 12 inches

Plug in the values and solve for the surface area.

SA = 2πrh

SA = 2π(3 inches)(12 inches)

SA = 226.19 inches²

Hence, the surface area that can be painted with one complete rotation of the roller is 226.19 inches².

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Answer:

Step-by-step explanation:

factoring

e =

(a+1)(a-1-3(a+1))
= (a+1)(a-1-3a-3)

= (a+1)(-2a-4)

= -2(a+1)(a+2)

The processing capability for the size of the Santa rounded to three decimal places is 1.07.

CP (Process Capability) is a statistical measure that compares the performance of a process to the specifications of that process. It can be calculated using the formula:

CP = (USL - LSL) / (6 * standard deviation)

Where:

USL = Upper Specification Limit (3.5 + 0.9) = 4.4 cm

LSL = Lower Specification Limit (3.5 - 0.9) = 2.6 cm

Standard deviation = 0.28 cm

Substituting these values into the formula:

CP = (4.4 - 2.6) / (6 * 0.28) = 1.8 / 1.68 = 1.07

So, CP rounded to three decimal places is 1.07

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The parent function of a line (usually of the form y = ax + b) is y = x.

The most basic form of a function is a parent function. Its essential shape is not changed in any manner. In mathematics, some graphs are frequently seen. Because of this, the graphs of quadratic functions, square roots, absolute values, cubics, and cube roots are among the original, widespread functions that are referred to as parent graphs.

For instance, you should still be able to identify the parabola that has undergone various transformations when you view a u-shaped graph that has been inverted and stretched vertically.

Linear functions have x as the term with the highest degree and a general form of y = a + bx. All linear functions have a straight line as a graph. The parent function of linear functions is y = x, and it passes through the origin. The domain and range of all linear functions are all real numbers.

These functions represent relationships between two objects that are linearly proportional to each other.

Therefore, the parent function of a line (usually of the form y = ax + b) is y = x.

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The area of a polygon with the given vertices is calculated by adding the areas of the individual triangles that make up the polygon.

A polygon is a closed figure in a plane consisting of a set of straight line segments connected end-to-end. The sides of a polygon are all of equal length, and the angles between them are all of equal measure. Polygons are one of the most fundamental shapes in geometry. They include triangles, squares, rectangles, hexagons, and many more.

The area of triangle WXZ is calculated as (1/2) × |XW × ZY|,

where XW is the vector from W to X and ZY is the vector from Z to Y.

In this example,

XW = (3, -2) and ZY = (-2, -4).

Therefore, the area of triangle

WXZ is (1/2) ×|(3, -2) × (-2, -4)| = (1/2) × 14 = 7.

The area of triangle XYA is calculated similarly,

where XY = (2, 3) and YA = (-2, -4).

Therefore, the area of triangle

XYA is (1/2) ×|(2, 3) ×(-2, -4)| = (1/2)× (-14) = -7.

The area of the polygon is calculated by adding the areas of the individual triangles, which in this example is 7 + (-7) = 0. Therefore, the area of the polygon with the given vertices is 0.

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Submarine must descend 17 feet in the 5th minute.

What is the average of the data?

Only numerical variables, whether continuous or discrete, can be used to calculate the mean. It is calculated by merely dividing the total number of values in a data set by the sum of all the values in the data set. A frequency table of data or raw data can both be used for the calculation.

Let the distance descended by submarine in 5th minute = x feet

Average distance descended by the submarine

= (Total distance distended/ Duration or time)

= (6 + 8 + 14 + 15 + x) / 5

= (43 + x) / 5

Statement given in the question → "Submarine must descend at an average rate of at least 12 feet per minute"

So the inequality for the statement will be,

(43 + x) / 5 ≥ 12

43 + x ≥ 60

x ≥ 17

Therefore, submarine must descend 17 feet in the 5th minute.

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