-5q=8=r
what is the dependent variable and what is the independent variable.

The required value of integration of given function is 82.

To evaluate the integral  we need to find the anti-derivative of F(x) and then evaluate it at the limits of integration.

Since F(x) = 8 for x < 8 and F(x) = x for x ≥ 8, we can split the integral into two parts, one from 0 to 8 and another from 8 to 10

According to question:

[tex]$$\begin{aligned}& \int_0^{ 10} \mathrm{~F}(\mathrm{x}) \mathrm{dx} \\& =\int_0^8 F(x) d x+\int_8^{10} F(x) d x\end{aligned}\\$$[/tex]

The anti-derivative of

[tex]F(x)=8$ is $F(x)=8 x$, so:$$[/tex]

[tex]$$\begin{aligned}& \int_8^{10} F(x) d x \\& =\left.\left(x^2 / 2\right)\right|_8 ^{10} \\& =\left(10^ 2 / 2\right)-\left(8^2 / 2\right) \\& =50-32 \\& =18\end{aligned}$$[/tex]

Putting it all together

[tex]$\int_0^10 \mathrm{~F}(\mathrm{x}) \mathrm{dx}=64+18=82$[/tex]

So, the value of the integral [tex]$\int_0^{10} F(x) d x$[/tex] is 82.

To know more about Integral visit:

brainly.com/question/18125359

#SPJ4

Complete question:

The equation of line is given by y = 3x - 1 and the slope is m = 3

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Substituting the values in the equation , we get

y = 3x - 1   be equation (1)

And , equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

So , the slope of the line is m = 3

The y intercept of the line b = -1

Hence , the equation of line is y = 3x - 1 and the graph is plotted

To learn more about equation of line click :

https://brainly.com/question/14200719

#SPJ1

By using Heron's formula, it can be calculated that the material used for the entire kite is 48 square inches.

Heron's formula is used for finding the area of a triangle in terms of the lengths of its sides.

Area = √s(s - a)(s - b)(s - c) where:

s = half the perimeter = (a + b + c)/2

a,b,c = sides of the triangle

A kite is made up of two isosceles triangles, ΔKIT and ΔKET.

Area ΔKIT=  17 square inches

KI = 6 in

ET = 8 in

KT = 10 in

Start by calculating the perimeter of ΔKET:

perimeter = KE + ET + TK

                = 8 + 8 + 10

                = 26 in

The area of ΔKET can be obtained using Heron's formula:

Area = √s(s - a)(s - b)(s - c)

        = √ 13 (13 - KE) (13 - ET) (13 - TK)

        = √ 13 (13 - 8) (13 - 8) (13 - 10)

        = √ 13 · 5 · 5 · 3

        = √ 975

        = 31.22 square inches

Since the quadrilateral KITE is composed of ΔKIT and ΔKET, then its area is equal to the total area of the triangles:

Area KITE = Area ΔKIT + Area ΔKET

                 = 17 + 31.22

                 = 48.22

                 ≈ 48 square inches

Thus, the material used for the entire kite is 48 square inches.

To learn more about Heron's formula, click here: https://brainly.com/question/10713495

#SPJ4

The solution to this system of equations is x = -6, y = 9, and z = 5.

To solve this system of equations using row operations or elementary matrices, we can first start by subtracting 4x from both sides of the first equation. This leaves us with 3x - 3x = -6. Since the x terms cancel out, this equation is now true for any value of x. We can then use this equation to substitute -6 for the x terms in the other two equations. In the second equation, we have 5y - 2y - 6 = -16. We can then subtract 5y from both sides of the equation to get -2y - 6 = -16. Dividing both sides by -2 gives us y = 9. The third equation is now 3y - 3z - 4z - 4z = -6. We can then subtract 3y from both sides of the equation to get -3z - 4z = -15. We can then divide both sides of the equation by -3 to get z = 5. Therefore, the solution to this  system of equations  is x = -6, y = 9, and z = 5.

Learn more about  system of equations here:

https://brainly.com/question/90105

#SPJ4

The correct statements regarding the algebraic expression are given as follows:

In 2a, 2 is a coefficient, as it multiplies the letter that composes the expression.

(2a + 5) is a sum of two terms.

In (2a + 5), 5 is the constant.

4 and 1 are like terms, as they have the same variable part of x^0 = 1.

2a + 5 is a factor, not just 2a.

More can be learned about algebraic expressions at https://brainly.com/question/723406

#SPJ1

The original points for the parent function of f(x) = -2|1/4(x-1)| +3 is (0, 0)

From the question, we have the following parameters that can be used in our computation:

f(x) = -2|1/4(x-1)| + 3

The above function is an absoluute value function

The parent function of an absolute value function is represented as

y = |x|

When x = 0. we haeve

y = 0

This means that (0, 0) is the point on the parent function

Read more about transformation at

https://brainly.com/question/27224272

#SPJ1

Lucy divides 1.8 into 6 groups of 0.3.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

Based on the information, Lucy solves 1.8 ÷ 0.3. This will be:

= 1.8 / 0.3

= 6

In conclusion, Lucy divides 1.8 into 6 groups of 0.3.

Learn more about expressions on:

brainly.com/question/723406

#SPJ1

Lucy solves 1.8 ÷ 0.3 using the diagram shown.

Use the drop-down menus to explain her reasoning.

Lucy divides ______

into _______

groups ______

of

The function u(x, y) = x^(1/3) * y^(2/3) is a multivariable function.

We have the function u(x,y) = x1/3y2/3. The function u(x, y) = x^(1/3) * y^(2/3) is a multivariable function, where x and y are variables and x^(1/3) and y^(2/3) are exponents. It describes the relationship between the inputs x and y and the output u. To solve for u, you would need to substitute specific values for x and y and evaluate the expression.

However, it is not possible to solve this function in the traditional sense because it is not a linear equation with a single solution. Instead, it is a surface in a three-dimensional space, where x and y are the two axes and u is the height. The value of u at any given point on the surface can be found by evaluating the function with the corresponding x and y values.

Therefore, The function u(x, y) = x^(1/3) * y^(2/3) is a multivariable function

To learn more about functions,

Visit; brainly.com/question/12431044

#SPJ4

6 people be lined up to get on the bus in 480 ways

A permutation is an act of arranging objects or numbers in order. Combinations are the way of selecting objects or numbers from a group of objects or collections, in such a way that the order of the objects does not matter.

For this, the easiest way is doing the complement. Calculate how many the 2 people are together and subtract from the total, so:

We can consider 2 people a block that will permutation, so, instead of 6 people we have 5 [a block of 2 people and 4 more):

5! = 5.4.3.2.1 = 120

The 2 people from the block will permutation as well:

2! = 2.1 = 2

Total: 5!.2! = 120.2 = 240.

For the case they are not following each other:

720 - 240 = 480

learn more about permutation and combination at: https://brainly.com/question/11732255

#SPJ1

The second and third image will be congruent to the pre-image. The solution has been obtained by applying the concept of transformations.

What is transformation?

Any action that moves a polygon or other two-dimensional object on a plane or coordinate system is referred to as a transformation.

Pre-image or "inverse image" refers to the two-dimensional shape that exists before any change. The transformed shape is represented by the image.

1. This is not congruent because both the coordinates are dilated and after dilation the size of the image is not the same as of original figure.

2. This is congruent because there is only translation which means it is same as the original figure but the position is different.

3. This is congruent because only translation has taken place which means it is same as the original figure but the position is different.

4. This is not congruent because one coordinate i.e. x has been dilated and after dilation the size of the image is not the same as of original figure.

Hence, second and third are congruent to the pre-image.

Learn more about transformation from the given link

https://brainly.com/question/17311824

#SPJ1

Answer: 240

Step-by-step explanation:

Answer: 240

Step-by-step explanation:

60 percent *400

= (60/100)*400

= (60*400)/100

= 24000/100 = 240

Now we have: 60 percent of 400 = 240

Question: What is 60 percent of 400?

We need to determine 60% of 400 now and the procedure explaining it as such

Step 1: In the given case Output Value is 400.

Step 2: Let us consider the unknown value as x.

Step 3: Consider the output value of 400 = 100%.

Step 4: In the Same way, x = 60%.

Step 5: On dividing the pair of simple equations we got the equation as under

400 = 100% (1).

x = 60% (2).

(400%)/(x%) = 100/60

Step 6: Reciprocal of both the sides results in the following equation

x%/400% = 60/100

Step 7: Simplifying the above obtained equation further will tell what is 60% of 400

x = 240%

Therefore, 60% of 400 is 240

Answer:

The coefficient a = -1, b = 4, c = -1 and d = 0. To solve for the coefficients, substitute the values from the table into the equation y = ax³ + bx² + cx+d. When x = 0 and y = 0, we get 0 = -1a + 4b + c + d, so d = 0. When x = 1 and y = -2, we get -2 = -1a + 4b + c, so c = -1. When x = 2 and y = -26, we get -26 = -1a + 4b, so b = 4. Finally, when x = 3 and y = -54, we get -54 = -1a, so a = -1.

Step-by-step explanation:

The mean is a statistics tool used to find the approximate "middle" in a set of data.

Statistic is a branch of mathematics that deal with the collection analyzes interpretation and presentation of data it is used to summarize analyze and compare data in order to draw conclusion and make decisions statistical method are used in a wide variety of field including economics finance business engineering medicine psychology social science and many others.

It is calculated by adding the values of the data set and dividing the sum by the number of items in the data set. The mean is also known as the average, and it can be used to compare sets of data and to measure the central tendency of a data set.

To know more about statistic click-
https://brainly.com/question/15525560
#SPJ1

To determine whether the sequence converges or diverges, we can use the Squeeze Theorem.

We can see that

4/ n+5n^2 < = An <= 4+3n^2/ n+5n^2

As n tends to infinity,  4/ n+5n^2  tends to 0 and 4+3n^2/ n+5n^2 tends to  4/5n^2 which also tends to 0.

So by the Squeeze Theorem, we can say that An tends to 0 as n tends to infinity. Hence the limit of the sequence is Lim n-> An = 0

We can also see that the numerator of An is a constant and the denominator is a polynomial with degree 2. Since the denominator's degree is greater than the numerator, the limit will be zero as n -> infinity.

Therefore, the sequence converges to 0.

To learn more about Squeeze Theorem,

brainly.com/question/30077508

#SPJ4

Approximately 84% of scores fall between the mean and z = -1 for normally distributed scores.

In a normal distribution, approximately 68% of the scores fall within one standard deviation of the mean, both above and below. Z-scores are used to describe the location of a score relative to the mean, in terms of standard deviations.

A z-score of -1 indicates that a score is 1 standard deviation below the mean. So, if we consider all the scores that are 1 standard deviation below the mean or closer to the mean, then we would have a total of 68% of the scores, which includes the mean.

And, if we consider only the scores that are between the mean and 1 standard deviation below the mean, then we would have 84% of the scores. Hence, approximately 84% of scores would fall between the mean and z = -1 for normally distributed scores.

To know more about Z-scores click on the link below:

https://brainly.com/question/15016913#

#SPJ11

The ratio of the orbital radii of the planets is  4:1.

The ratio of their periods is 8:1.

What is orbital radius and periods in circular motion?

Planetary bodies circle the Sun according to Kepler's three laws. They explain how planets orbit the Sun in elliptical fashion, how they traverse the same amount of space in a given length of time regardless of where they are in their orbit, and how their orbital periods are related to the size of their orbits (its semi-major axis).

An object's orbital radius is the typical distance it travels around a bigger object. An illustration would be that the Sun and Earth are typically 150 million kilometres apart. The orbital radius is also this.

Let the mass of the planet be m and the mass of the star be M.

r = radius of ordit

v = speed

We know that

gravitational attraction = centripital force

GMm/[tex]r^{2}[/tex] = m[tex]v^{2}[/tex]/r

Hence

v  ∝ 1/

a) Here v₁/v₂ = v/2v =  

squaring both sides

1/4 = r2/r1

Thus r1/r2 = 4/1

Hence ratio of orbital radii is 4:1.

b) As per keplers law of planetary motion,

T^2 ∝ [tex]r^{3}[/tex]

Thus ratio of time periods is 8:1.

To know more about radius refer:

brainly.com/question/929044

#SPJ4

A country's population in 1995 was 23 million. In 2001 it was 25 million, the population in 2013 using the exponential growth formula in 2013 will be around 30 million.

For this problem, we have the final population P, the starting population A, and the time passed t.

We still need to determine the value of the growth factor k.

This can be done using the information for the years 1995 and 2001.

In this case, A will be 23 million (the population in 1995), P will be 25 million (the population in 2001), and t will be 6 years (the number of years between 1995 and2001):

[tex]P=Ae^{kt}[/tex]

[tex]25=23e^{k 6}[/tex]

[tex]e^{6k} =\frac{25}{23}[/tex]

[tex]k = \frac{ln(25) - ln(23)}{6}[/tex]

k = 0.013897

Now, let's use this information to determine P in 2013.

A will still be 23 million, but t will be 18 years.

[tex]P= 23e^{0.013897*18} \\P= 23e^{0.250146} \\P=23 * 1.28421\\P=29.5368\\[/tex]

Therefore, the population in 2013 using the exponential growth formula in 2013 will be around 30 million.

Learn more about Population;

https://brainly.com/question/14108108

#SPJ4

Answer:

Adriana recorded a temperature of 38°C.

Step-by-step explanation:

It is because negative temperatures in Celsius is cold.

#LearnYourBasics!

The warmest temperature was recorded by Adriana. Because it's the highest temperature shown.

The concept of temperature is used to quantify how hot and cold an object is. You can use a thermometer to measure the temperature. The most common scales are the Celsius scale with the unit symbol °C, the Fahrenheit scale (°F) and the Kelvin scale (K).

Fahrenheit is primarily used in the United States. According to this ice-enclosed thermometer, the temperature is around 0 degrees Celsius, or 32 degrees Fahrenheit. The temperature would be about 274 if this thermometer read the Kelvin scale used by scientists.

To know more about Temperature:

https://brainly.com/question/12799702

The value of x in the system of equations is: x = 11.2.

The value of x can be found by solving the system of equations.

One method is to substitute the value of x from one equation into the other equation, solve for y, then use the value of y to find x.

Starting with the second equation: 5x + 2y = 48

Solve for y: y = (48 - 5x) / 2

Now substitute this expression for y into the first equation:

-5x - 12((48 - 5x) / 2) = -8

-5x - 6(48 - 5x) = -8

-5x - 288 + 30x = -8

25x - 288 = - 8

25x = -8 + 288

25x = 280

x = 280/25

x = 11.2

Finally, solving for x:

x = 11.2

Learn more about the system of equations on:

https://brainly.com/question/25976025

#SPJ1

Answer:

-11.8

Step-by-step explanation:

To find the value of x in this system of equations, we can use substitution or elimination method.

Using substitution:

Solve for one of the variables in one of the equations and substitute it into the other equation. We can start by solving for y in the second equation:

[tex]\sf:\implies{5x + 2y = 48}[/tex]

[tex]\sf:\implies{2y = -5x + 48}[/tex]

[tex]\sf:\implies{y = (-5/2)x + 24}[/tex]

Now, substitute this expression for y into the first equation:

[tex]\sf:\implies{-5x - 12y = -8}[/tex]

[tex]\sf:\implies{-5x - 12((-5/2)x + 24) = -8}[/tex]

[tex]\sf:\implies{-5x + 30x + 288 = -8}[/tex]

[tex]\sf:\implies{25x = -296}[/tex]

[tex]\sf:\implies{x = -11.84}[/tex]

The value of x rounded to the nearest tenth is -11.8.

Amount of loaves of bread to be placed on each platter= 12 /7

The Total loaves of bread equal to 12

The Total number of platters to 7

find the amount of loaves of bread to be placed on each platter ?

In order to find the amount of loaves of bread to be placed on each platter, we will divide total loaves of bread by total number of platters.

Thus, amount of bread in each platter can be given by:

amount of loaves of bread to be placed on each platter= Total loaves of bread  / Total number of platters

Amount of loaves of bread to be placed on each platter= 12 /7

Therefore option D is correct.

To know more about Fraction visit brainly.com/question/10354322

#SPJ4

By applying standard equation of a circle concept, it can be concluded that the equation that defines the circle is  (x + 4)² + (y - 3)² = 50.

Circle is a collection of points on a plane line that are all the same distance (the radius) from a given point (the center).

Standard equation of a circle can be written as:

(x - h)² + (y - k)² = r²   , where:

(h,k) = center of the circle

r = radius

We know that the radius of the circle has endpoints (-4,3) and (1,-2), which means that one of these points is the center of the circle.

Since we know that its center is in the second quadrant, we can conclude that (-4,3) is the center.

Now we can substitute these values into the equation:

   (x - h)² + (y - k)² = r²

(1 - (-4))² + (-2 - 3)² = r²

              5² + (-5)² = r²

                25 + 25 = r²

                        50 = r²

As we know the r, now we can have the standard equation of the circle:

   (x - h)² + (y - k)² = r²

(x - (-4))² + (y - 3)² = 50

 (x + 4)² + (y - 3)² = 50

Thus the equation that defines the circle is  (x + 4)² + (y - 3)² = 50.

To learn more about the standard equation of a circle, click here: https://brainly.com/question/4334736

#SPJ4

Bar notation is used to show the decimal is repeating.

So,

"We use bar notation to show that a decimal is terminating" is an incorrect statement.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Bar notation is used in decimal numbers to show that the number is repeating.

Example:

1/3 = 0.33333333

This can be written as,

1/3 = 0.[tex]\over3[/tex]

Thus,

Bar notation is used to show the decimal is repeating.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

If the account earns 6.5% simple interest per year , Diego will give his granddaughter a sum of $1130

To calculate the simple interest earned on an initial amount of $500 at 6.5% for 18 years, you can use the formula:

$I = Prt$, where

$I$ = interest earned

$P$ = initial amount ($500)

$r$ = interest rate (6.5%)

$t$ = time in years (18)

So, $I = 500 * 6.5 * 18 / 100 = 630$.

Thus, on the granddaughter's 18th birthday, Diego will give her $500 + 630 = $1130.

learn more about simple interest: https://brainly.com/question/25793394

#SPJ1

The student can only work a whole number of hours, the student should work 8 hours at the doctor's office each week. The student should then tutor for 12 hours each week in order to earn at least $375.

Let x represent the number of hours the student works at the doctor's office each week, and let y represent the number of hours the student tutors each week. The system of inequalities that represents the given constraints can be written as:

x + y ≤ 20

15x + 25y ≥ 375

To maximize the number of hours the student works at the doctor's office while still earning at least $375, we must solve this system of inequalities. To do this, we can subtract 15x from both sides of the second inequality to isolate y:

25y ≥ 375 - 15x

We can then divide both sides of this equation by 25 to solve for y:

y ≥ (375 - 15x) / 25

We can then substitute this expression for y in the first inequality to solve for x:

x + (375 - 15x) / 25 ≤ 20

We can then rearrange and solve this equation for x:

15x + 375 ≤ 500

15x ≤ 125

x ≤ 8.33.

Since the student can only work a whole number of hours, the student should work 8 hours at the doctor's office each week. The student should then tutor for 12 hours each week in order to earn at least $375.

Learn more about student tutors here :

https://brainly.com/question/29073158

#SPJ4

If time to complete a constructions project is normally distributed  , then the probability the project will be finished in 62 weeks or less is 0.6915 or 69.15% .

The required probability can be calculated using the Z-score.

The Z-score is defined as a measure of how many standard deviations a value is from mean.

The mean = 60 and standard deviation = 4 of the normal distribution, the Z-score can be calculated as follows:

⇒ Z = (x - mean) / standard deviation = (62 - 60) / 4 = 0.5

Using a standard normal table, the p value for z = 0.5  is approximately 0.6915.

Therefore, the probability that the project will be finished in 62 weeks or less is approximately 0.6915.

The given question is incomplete , the complete question is

The time to complete a constructions project is normally distributed with a mean of 60 weeks and a standard deviation of 4 weeks. What is the probability the project will be finished in 62 weeks or less ?

Learn more about Probability here

https://brainly.com/question/28996721

#SPJ4

The right solution is option C, which is Y'(1, -4) and Z'(-2, -1).

A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same. A triangle is a three-sided polygon with three edges and three vertices in geometry. The total of a triangle's interior angles equals 180 degrees, which is its most essential feature. This is known as the angle sum property of a triangle.

Here,

To translate a triangle, you need to add the same value to each x-coordinate and each y-coordinate. In this case, the translation moves each point 2 units to the left and 3 units down, so the new coordinates of Y and Z would be:

Y'(3 - 2, -1 - 3) = Y'(1, -4)

Z'(0 - 2, 2 - 3) = Z'(-2, -1)

The correct answer is Y'(1, -4) and Z'(-2, -1) that is option C.

To know more about triangle,

https://brainly.com/question/22469440

#SPJ1

The proportional relationship that models the situation is given as follows:

y = 2x/3.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

The variables for this problem are given as follows:

Hence the constant is given as follows:

k = 2/3.

Then the relationship is given as follows:

y = 2x/3.

The problem is incomplete, hence the proportional relationship is given so it can be used to obtain the desired amounts.

More can be learned about proportional relationships at https://brainly.com/question/7723640

#SPJ1

The total amount of deposits shown is, $713.29.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

The graph of a passbook is shown in figure.

Now, By figure,

The total amount of deposits is,

⇒ $310.58 + $402.71

⇒ $713.29.

Thus, The total amount of deposits shown is, $713.29.

Learn more about the addition visit:

https://brainly.com/question/25421984

#SPJ1

Answer:86 yards

Step-by-step explanation:

We have the diameter, so the solution simply is:

D= 2 r= 2 x 43= 86 yards

P.S. I'm sorry if this isn't clear enough, but that's how i could explain.

The relation is not a function, enter NONE in the Domain is possible x values from the graph i.e (-infinity,-2) U [2,infinity)

Range is all possible functional values i.e (-infinity,4] U (7,infinity)

A) vertical line test :

the vertical line through the point x = -2 cuts the graph at two points

the points on the graph are (-2,-1) and (-2,5)

that is x=-2 assigned to two values -1,5.

recollect that a relation represents a function when each element of x-coordinate associated with unique element of y-coordinate

therefore, this relation is not a function.

Domain is none and codomain is also none.

B) any vertical line through graph cuts the line at only one point.

that is each element of x coordinate associated with the unique element of y-coordinate. so, it represents a function.

Domain is possible x values from the graph i.e (-infinity,-2) U [2,infinity)

Range is all possible functional values i.e (-infinity,4] U (7,infinity)

Learn more about the domain and range here :

https://brainly.com/question/28135761

#SPJ4