Find the midpoint of the line segment that joins points P(-4,3) and Q(9,14)?

Answer:

The answer is\sqrt{13}

Step-by-step explanation:

Answer:

\(\frac{dx}{dt}=2-\frac{3}{40}x+\frac{y}{15}\)

\(\frac{dy}{dt}=\frac{3}{40}x-\frac{y}{5}\)

x(0)=20,y(0)=5

Step-by-step explanation:

We are given that

Tank A contains water=80 gallons

x(0)=20,y(0)=5

Tank B contains water=30 gallons

Rate=4 gallon/min

Concentration of salt  is pumped into tank=0.5 pound /gallon of water

Solution pumped from tank A to tank B at the rate=6 gallons/min

Solution pumped from tank B to tank A at the rate=2gallon/min

Solution from tank B is pumped out of the system at the rate=4 gallon/min

We have to find the DE at time t

For x

Rate in=\(0.5\times 4+y(t)/30\times 2\)

Rate in=\(2+y/15\)

Rate out=\(x/80\times 6\)

Rate out=3x/40\)

\(\frac{dx}{dt}=\)Rate in-Rate out

\(\frac{dx}{dt}=2+y/15-3x/40\)

\(\frac{dx}{dt}=2-\frac{3}{40}x+\frac{y}{15}\)

For y

Rate in=\(x/80\times 6\)

Rate in=3/40x

Rate out=\(y/30\times (4+2)\)

Rate out=y/5

\(\frac{dy}{dt}=\)Rate in-Rate out

\(\frac{dy}{dt}=\frac{3}{40}x-\frac{y}{5}\)

The associations that best describe the scatter plot is Option A and C

When below-average values also tend to occur together and above-average values of one variable tend to be accompanied by below-average values of the other, there is a positive association between the two variables. When the average values of two variables tend to be below average, two variables have a negative connection.

Note that a statistical term used to describe a straight-line relationship between two variables is a linear relationship (or linear association).

Additionally, a straight line connecting the spots indicates a linear association. As a result, the scatter plot indicates that as practice time increases,  giving off also rise.

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The association that describe the scatter plot is

A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of connection, if any, between the values of observed quantities or events (called variables).

The connection is positive if the variables tend to rise and fall together. When one variable tends to rise while the other falls, there is a negative connection.

The connection between the variables demonstrates a straight line in the positive direction. hence the option having linear and positive association is the correct choice

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The percentage error in the density of metal will be 3.4%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that the density of the metal in the handbook is 4.018 g/mL and the measured value of the density is 4.16 g/mL.

The percentage error will be calculated as:-

Percentage = [ ( 4.16 - 4.018 ) / 4.16 ] x 100

Percentage = 0.034x 100

Percentage = 3.4%

Hence, the percentage error will be 3.4% for the densities.

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The nearest kilometers to 999.09344471 km is 1000 km.

Given value is 999.09344471 Km.

We have to calculate the round off value to the nearest kilometers. we know that after the decimal if the value of tenth place is 5 or bigger than 5 then we add 1 to the tens place digit, this is the fundamental rule of rounding off.

Now on following this rule from the very right hand side up to the tenth place digit we come to the conclusion that only  the value after the decimal (934) is to be rounded off which is (900).

So 999.09344471 km is finally becomes 999.900 km after rounding of to nearest hundredth value.

Again rounding off 999.900 km to nearest km so it becomes 1000 km.

The nearest kilometers to 999.09344471 km is 1000 km.

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Answer:

\(8.182X10^8 $pounds\)

a=8.182 and b=8

Step-by-step explanation:

Weight of the Empire State Building =\(7.3X 10^8\) pounds.

Weight of the One World Trade Center building= 88,200,000 pounds.

=\(8.82 X 10^7\)

The addition of the two:

\(=7.3X 10^8+8.82 X 10^7\\$To make it easier to add, express both as powers of 8\\=7.3X 10^8+0.882 X 10^8\\=(7.3+0.882)X10^8\\=8.182X10^8 $ pounds\)

Comparing with the form: \(aX10^b\)

a=8.182 and b=8

Answer:

\(y = 3x - 5 \\ x = - y \\ substitute \: - y \: in \: the \: place \: of \: x \\ y = - 3y - 5 \\ y + 3y = 5 \\ 4y = 5 \\ y = \frac{5}{4} \)

Answer and Step-by-step explanation:

There is a two-dimensional numbers line in a coordinate plane, which has a horizontal line x-axis, and the vertical line is known as the y-axis. These lines intersect each other at zero points, and they are perpendicular. Zero points are known as the origin. The axes divide the plane into  quadrants.

A point in the coordinate plane is of the form of (x, y). This point is named as ordered pair; the first number is from the x coordinate, and the second number from the y coordinate.

To make a graph, we draw a dot, starting from the origin, at the coordinate that communicates to the ordered pair. The y coordinates describe how many steps to move up or down ( positive or negative), and x coordinates tell us to move right or left ( positive or negative).

The completeness property for points describes:

Exactly one point in the plane given  the number of ordered pair

And

Exactly one ordered pair of numbers at a given point in the plane.

A relation is ordered pairs; the x coordinates are known as domain, and the y coordinate is known as the range.

The domain contains the value that corresponds to the independent variable and the range equal to the dependent variable.

Answer:-52

Step-by-step explanation:

-4x-40-6=-3x+6

-4x-46=-3x+6

-52=x

Answer : 94

Step by Step :

47/0.5=94

Answer:

About 95% of individuals have IQ scores in the interval 100 ± 2 ( 15 ) = [ 70 , 130 ] .

Step-by-step explanation:

hope this helps

Answer:

C

Step-by-step explanation:

7.55 x 35 =

264.25

Hope this helped

For the given graph of quadratic function whose vertex is (4,2) , the domain  and the range in the interval notation is given by :

Domain = ( -∞ , ∞ )

Range = ( 2 , ∞ )

As given in the question,

For the given graph of quadratic function ,

Given graph represents the parabola.

Standard equation of the parabola with vertex ( h, k) is given by,

y = a ( x - h )² + k

Substitute the value ( h ,k ) = ( 4, 2 )

y = a ( x - 4 )² + 2

As it is a parabola in the first quadrant and faces in the upward direction,

Value of x tends to -∞ to ∞

Domain = ( -∞ , ∞ )

Minimum value of y coordinate is 2 and increases to ∞.

Range = ( 2, ∞ )

Therefore, for the given graph of quadratic function whose vertex is (4,2) , the domain  and the range in the interval notation is given by :

Domain = ( -∞ , ∞ )

Range = ( 2 , ∞ )

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Answer:

I would say

Step-by-step explanation:

303030 divided by 666 =455

666x455=303030

455-666=2110

so it would be 2110

Step-by-step explanation:

firstly suppose f(X) as y and later interchange it with x and solve it to get inverse function of x.

The inverse of the given function is \(f^{-1}(x)=\dfrac{x+4}{2}\).

Important information:

We need to find the inverse of the given function.

Substitute \(f(x)=y\).

\(y=2x-4\)

Interchange \(x\) and \(y\).

\(x=2y-4\)

Isolate \(y\).

\(x+4=2y\)

\(\dfrac{x+4}{2}=y\)

Substitute \(y=f^{-1}(x)\).

\(\dfrac{x+4}{2}=f^{-1}(x)\)

Thus, the inverse of the given function is \(f^{-1}(x)=\dfrac{x+4}{2}\).

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A cube is a three-dimensional shape with all sides of equal length, width, and height. If the length of the packaging box is 4xy, then all the sides of the cube have the same length 4xy.

What is the straightforward meaning of volume?

The volume of an object is the area occupied inside its three-dimensional boundaries. It is referred to as the object's capability on occasion.

To find the volume of a cube, we use the formula: volume = side x side x side = (side)^3

Therefore, the volume of the packaging box in terms of x and y is (4xy)^3 = (4xy)(4xy)(4xy) = (4xy)^3 = (4x)^3 * y^3 = 64x^3 * y^3

So the volume of the packaging box is 64x^3 * y^3 cubic units.

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Answer:

i got negative 108

Step-by-step explanation:

i got this because just put it in a porportion like x/y = x/?

then plug in the numbers it gives you. so it should look like this 5/-45 = 12/?

then multiply 12 and -45 and then divide by 5. you should get -108

pls mark branliest

Answer:

10.92

Step-by-step explanation:

136.5*(8/100)that is tax

Answer:10.92

Step-by-step explanation:

Step-by-step explanation:

18,200

-12,350

5,850 (A) 5,850

The volume of C.a .cylinder is twice the volume of a cone.

The formula fro the cylinder is πr²h and that of the cone is ⅓ the volume It should be noted that the volume of a cone can be equated to theone-third of the volume of a cylinder , this can be established when they are having same base radius and height.

The cylinder's volume  can be expressed as π r² h,  along with the surface area  which can be expressed as 2π r h + 2π r² and this can be used to get the values.

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The function is given to be:

The graph of the function is shown below:

The critical points are points where the function is defined and its derivative is zero or undefined.

The derivative is calculated to be:

The critical points are at f'(x) = 0:

Factoring:

Therefore, applying the zero factor principle:

or

Therefore, the critical numbers are given below with their descriptions:

Answer:

The correct answer is C = 16 兀

explanation:

In this problem, C represents the cost and r represents the rate. The formula for calculating the cost is C = 2 * r, where C is the cost in 兀 and r is the rate in 兀/unit.

When r is 8 兀/unit, the cost is C = 2 * 8 = 16 兀.

Answer:

C = 16 π

Step-by-step explanation:

If C = 2 π r, and r = 8:

C = 2 π (8)

Simplify (multiply 2x8):

C = 16 π

Answer:

C

Step-by-step explanation:

x + 2 < -5

x < - 5 - 2

x < - 7

Answer:

{x| x R, x<-7}

Step-by-step explanation:

=> x+2<-5

=> x<-5-2

=> x<-7

The domain of the function f(x) = -3x + 2 is (-∞, +∞), representing all real numbers, and the range is (-∞, 2], representing all real numbers less than or equal to 2.

The function f(x) = -3x + 2 is a linear function defined by a straight line. To determine the domain of this function, we need to identify the range of values for which the function is defined.

The domain of a linear function is typically all real numbers unless there are any restrictions. In this case, there is no explicit restriction mentioned, so we can assume that the function is defined for all real numbers.

Therefore, the domain of the function f(x) = -3x + 2 is (-∞, +∞), which represents all real numbers.

Now, let's analyze the range of the function. The range of a linear function can be determined by observing the slope of the line. In this case, the slope of the line is -3, which means that as x increases, the function values will decrease.

Since the slope is negative, the range of the function f(x) = -3x + 2 will be all real numbers less than or equal to the y-intercept, which is 2.

Therefore, the range of the function is (-∞, 2] since the function values cannot exceed 2.

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Answer:

The correct option - Figure A

Step-by-step explanation:

The exact question is as follows :

Given - Royce kept track of the inches of snowfall in his town over a 15-day period. Royce's data is given below.

1, 0, 0, 3, 5, 0, 0, 0, 2, 2, 1, 7, 2, 2, 3

To find - Which box plot shows this data set?

Solution -

Given the data is -

1, 0, 0, 3, 5, 0, 0, 0, 2, 2, 1, 7, 2, 2, 3

Firstly,

Arrange the data from smallest to largest

0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 5, 7

Now,

Find the median

Median is the middle value - i.e. (15 + 1)/2 = 8th value

So, we get Median = 2

Now,

Find the Quartile -

The first quartile is the median of the data points to the left of the median.

i.e. Median of 0, 0, 0, 0, 0, 1, 1

so, we get

Q1 = 0

The third quartile is the median of the data points to the right of the median.

i.e. Median of 2, 2, 2, 3, 3, 5, 7

so, we get

Q3 = 3

Now,

Compute the min and the max

Minimum value = 0

Maximum value - 7

So,

five number summary is -

0, 0, 2, 3, 7

And we draw the box as follows -

So,

The correct option - Figure A

Answer:

x = -1,375

y = -5

Step-by-step explanation:

{-8x + y = 6, / : (-1)

{-8x + 3y = -14;

Multiply the first equation by -1, so that we could eliminate 8x:

+ {8x - y = -6,

{-8x + 3y = -14;

----------------------

4y = - 20 / : 4

y = -5

Now, make x the subject from the first equation (you can do it from the 2nd one instead):

8x = -6 + y / : 8

x = -0,75 + 0,125y

x = -0,75 + 0,125 × (-5) = -0,75 - 0,625 = -1,375

Answer:

the answer is 12

Step-by-step explanation:

d=2r=2*6.2=12.4

Answer:

x = 9

Step-By-Step Explanation:

1. 3x + 5 + 6x + 4 = 90

2. 9x + 9 = 90

3. 9 + -9

4. 90 + -9

5. 9x = 81

6.  x= 9                              Substituting X:

                                        3 X 9 + 5 = 27 + 5 = 32

                                        6 X 9 + 4 = 54 + 4 = 58       58 + 32 = 90, so X = 9

Answer:

Step-by-step explanation:

The reason I say the answer above is wrong is because their answer equals up to a angle of 100 degrees however your angle is equaling up to 90 degrees. First off we know this angle is going to be 90 degrees right so we put it into the eqution:

=90

but we don't know what x is in order to solve the degrees that add up to 90, so since these equations add up to 90 we put them into the equation:

(3x + 5)+ (6x + 4) = 90

we then add all the numbers that have the same variables or are simply numbers in the equation

3x + 6x and 5 + 4 to get 9x + 9 = 90

we then subtract 9 from both sides (because what you do to one side you do to the other) to get 81

the equation now looks like this: 9x = 81 so now we divide 9 from both sides to get x = 9

Now how do we know if x is really 9 well we plug it into the equations (3x + 5) and (6x + 4) making them look like this (3(9) + 5) and (6(9) + 4)

and you get (3(9) + 5)= 32

                     (6(9) + 4)= 58

and when you add them together you get 90

32 + 58 = 90

Sorry it took so long to answer back. I hope this helps you

Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

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Based on the information provided, the inference that a significant number of students in the homeroom class plan to become soldiers is valid.

The teacher surveyed his homeroom class about their post-graduation plans. He found out that most of his students plan to become soldiers.

An inference is a conclusion that can be drawn from a given set of data. In this case, the inference that can be made is that a significant number of students in the homeroom class plan to become soldiers.Therefore, the inference is valid based on the data provided.

However, it is essential to keep in mind that the sample size in the homeroom class is relatively small and may not be representative of the entire population. If the teacher had surveyed a more extensive and diverse population, the results might have been different.

In conclusion, based on the information provided, the inference that a significant number of students in the homeroom class plan to become soldiers is valid. However, this may not apply to the entire population, and it is crucial to consider the sample size when drawing inferences.

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