Here are the weights (in pounds) of a sample of 13 male eleventh graders.
148, 140, 159, 141, 151, 156, 173, 167, 160, 159, 146, 174, 170
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Find the median weight of these students.


pounds?

The equation x / y = 4 is an example of direct variation formula. (Correct choice: A)

Herein we find four types of equations, of which we must determine what choice represents a direct variation formula, whose definition is shown below:

y ∝ x

y = k · x

Where k is the constant of proportionality.

This form is equivalent to the following expressions:

y / x = k, x / y = 1 / k

Then, by direct inspection, we see that equation x / y = 4 represents a direct variation formula.

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Answer:

Step-by-step explanation:

350 + x people = 1500

x = 1500 - 350

x = 1150 / 12.50

x = 92 people

The solution to the equation x^2-5x+7=0 are x=5/2+3/2i and x=5/2-3/2i

A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about math equations.

There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.

According to the given question, we see

by solving the inequality we get

x=5/2+3/2i and x=5/2-3/2i

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Answer: B

Step-by-step explanation: 85.10 is total. 46 per minutes.  $85/$/Min.46. The $ cancels and you get minutes.

Answer:

Step-by-step explanation:

log(0.5)^16=log(1/2)^16

                  =log(2^(-1))^16

                  =-16log(2)=-4.81647

The exponential function will be y=  -2(3)^x.

What are exponential functions?

An exponential function is a Mathematical function in the form f (x) = a^x, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

Now,

Given points for exponential function are (2, –50), (4, –1250).

and exponential function is y=ab^x

To find a and b put points in the function

-50=ab^2 -->1

-1250=ab^4 --->2

From equation 1

a=-50/b^2

Put value of a into 2

-1250=-50/b^2*b^4

b^2=25

b=5

For b=5, a=-50/5^2=-2

Hence, a=-2

Therefore,

               The exponential function will be y= -2*5^x.

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End Balance: $3,839.25 + $2,579.20 - $2,190.05 = $5,735.15, so the reconciled balance of $5,735.15.

This theory is used to compare the bank statements to the check register in order to properly reconcile the two balances.

The theory used in this question is the bank reconciliation theory.

Step 1: Begin by looking at the two balances - the check register balance and the bank statement balance.

In this case, the check register balance is $3,839.25 and the bank statement balance is $3,450.10.

Step 2: Add up all of the deposits that are not reported on the bank statement. In this case, the deposits are $2,000, $135.67, $254.77, and $188.76.

Step 3: Subtract all of the checks that are not reported on the bank statement. In this case, the checks are $567.89, $23.83, $598.33, and $1,000.

Step 4: Add the deposits and subtract the checks from the check register balance.

In this case, the check register balance ($3,839.25) plus the deposits ($2,579.20) minus the checks ($2,190.05) gives a reconciled balance of $5,735.15.

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(X+2)^2 +(Y+7)^2 =36

Since the centre of the circle is (-2;-7), we equate the variable to its coordinate:

X=-2

Y=-7

now we bring the coordinate over to the left side which changes its sign.

X+2=0

Y+7=0

That explains the :

(X+2)^2 +(Y+7)^2

Now for the R.

its given that the radius is 6 and since the standard form for the equation of a circle requires r^2.

we simply square 6.

6^2=36.

Answer: (x+2)^2+(y+7)^2=36

Step-by-step explanation:

To write an equation for a circle when you know

the radius is R

the center is at (A, B), remember that the standard form of the equation of the circle is:

Just plug those values into this equation:

(x-A)^2+(y-B)^2=R^2

You will end up with this equation

(x+2)^2+(y+7)^2=36

The number of seconds that the ball attains its height round to the nearest hundredth will be 4.06 seconds.

For the maximum value of the function if f''(x) < 0 and for the minimum value of the function if f''(x) > 0.

The maximum and minimum value of the function is at f'(x) = 0.

The function is given below.

h(t) = -16t² + 130t + 2

Differentiate the function with respect to t. Then we have

h'(t) = -32t + 130

h'(t) = 0

- 32t + 130 = 0

t = 130 / 32

t = 4.0625 seconds

The number of seconds that the ball attains its height round to the nearest hundredth will be 4.06 seconds.

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Answer:

Step-by-step explanation:

The triangle has length of the side h is equal to 97.1 inches approximately to the nearest tenth, using the sine rule.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

For the triangle ΔGHI, by sine rule;

g/sinG = h/sinH = i/sinI

We first derive the angle G as follows:

151° + 7° + G = 180° {sum of interior angles of a triangle}

G = 180° - 158

G = 22°

Hence by sine rule;

75/sin22° = h/sin151°

h = (75 × sin151°)/sin22° {cross multiplication}

h = 97.1

Therefore, by application of the sine rule we have the length of the side h = 97.1 inches approximately to the nearest tenth

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Answer:

Ruth is 36 years old

Step-by-step explanation:

let Colin's age be x , then

Dave's age is x + 4

Ruth's age is 3(x + 4) = 3x + 12

sum their ages and equate to 56

x + x + 4 + 3x + 12 = 56

5x + 16 = 56 ( subtract 16 from both sides )

5x = 40 ( divide both sides by 5 )

x = 8

Then

Ruth's age = 3x + 12 = 3(8) + 12 = 24 + 12 = 36

The age of Ruth is 36 years while Dave is 12 years old and Colin is 8 years old.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Using variables to represent the ages of Colin and Dave:

C = Colin's age

D = Dave's age

From the given statement,

D = C + 4 (Dave is 4 years older than Colin)

We know that Ruth's age is three times Dave's age:

R = 3D (Ruth is three times as old as Dave)

Now, the sum of their ages is 56:

C + D + R = 56

Substituting the expressions for D and R in terms of C, we get:

C + (C + 4) + 3(C + 4) = 56

Simplifying and solving for C:

5C + 16 = 56

5C = 40

C = 8

So Colin is 8 years old. Using the expression for Dave's age in terms of C, we get:

D = C + 4 = 8 + 4 = 12

So, Dave is 12 years old.

Ruth's age in terms of D:

R = 3D = 3(12) = 36

Therefore, Ruth is 36 years old.

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P(A|B) read as the probability of the event A given the event B is equal to 0.5000 rounded up to four decimal place.

Conditional probability is known as the possibility of an event or outcome happening, based on the existence of a previous event or outcome. The conditional probability P(A|B) occur only in the case of dependent events. It gives the conditional probability of A given that B has occurred.

P(A|B) = P(A∩B) / P(B)

P(A∩B) = Probability of happening of both A and B

When a die is rolled, the sample space = {1, 2, 3, 4, 5, 6}.

A is the event the blue die shows a number greater than 2, So;

A = {3, 4, 5, 6}

B is the event the red die shows a number less than 5. So;

B = {1, 2, 3, 4}.

Then A∩B = {3, 4}

P(A∩B) = 2/6 = 1/3

P(B) = 4/6 = 2/3

P(A|B) = 1/3 ÷ 2/3

P(A|B) = 1/3 × 3/2 {changing division to multiplication}

P(A|B) = 1/2

Therefore, the conditional probability of the event A given the event B denoted by P(A|B) is equal to 1/2 or 0.5000 to four decimal place.

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The slope - intercept form of the equations of each of the given lines is:

The slope - intercept form is:
y = mx + b

Where

m = slope

b = y - intercept

Basically, given the equations of each line, you are to move y such that it goes to the left of the equation and remains there alone, while the other figures stay on the right side.

Equation 1:

x − y = −3

x + 3 = y

y = x + 3

Equation 2:

2x + y = −6

y = - 6 - 2 x

y = - 2x - 6

Equation 3 :

4x + y = −7

y = - 4x -  7

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Answer:

K

Step-by-step explanation:

K represents negative 1 ⅓.

to find the opposite of a number you must look to see if its negative. if its negative then its opposite would be a positive. If its a positive then its opposite would be a negative. Opposites are always the number in opposite signs like 7 and -7.

I found K to be 1⅓ because there are 2 spaces in between numbers so it would be ¹ ⅓ ⅔ 1. so I went to the number 1 and went one space back/where K because I know it would be 1 ⅓

Therefore , the solution to the given problem of derivative comes out to be 2cos(mx+ny) for both the cases of partial derivative.

The definition of a derivative is the simultaneous change that occurs at a certain place. Implicit & explicit functions are typically distinguished from one another. Explicit functions are those where the value of the known individual entity "x" directly determines the value of the known dependent variable "y."

Here,

Given : f(x,y)= sin^(2) (mx+ny)"

Partial derivative with respect to x

=> dx/dy = 2sin (mx+ ny) *m

=> d²x/dy = 2cos(mx+ny)

Partial derivative with respect to y

=>  dx/dy = 2sin (mx+ ny) *n

=> d²x/dy = 2cos(mx+ny)

Therefore , the solution to the given problem of derivative comes out to be 2cos(mx+ny) for both the cases of partial derivative.

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Answer:

  2, 4, 6

Step-by-step explanation:

You want three consecutive even integers such that the sum of twice the first and three times the second is 4 more than twice the third.

Let x represent the middle integer. Then the first is (x-2) and the third is (x+2). The given relation is ...

  2(x -2) + 3x = 2(x +2) +4

Simplifying the equation gives ...

  2x -4 +3x = 2x +4 +4

  5x -4 = 2x +8 . . . . . . . collect terms

  3x = 12 . . . . . . . . . . . add 4-2x

  x = 4 . . . . . . the middle integer

The integers are 2, 4, 6.

__

Additional comment

It often simplifies the equation if the variable is used to represent the middle of the consecutive integers in problems like this. In this particular problem, there is not a great advantage.

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The correct option is E. the roots of the auxiliary equation are √6 and -√6.

Differential equations are defined as the equations in which consist of one or more terms which consist of the a dependent variable and it's derivatives with respect to the independent variable.

Given differential equation,

[tex]\frac{d^{2} y}{dx^{2} }[/tex] - 6y = 0

This can be also written as,

y'' - 6y = 0, where y'' indicates the second derivative of y.

Auxiliary equation is the polynomial equation which is found by replacing the right member of a standard differential equation by zero.

To find the roots of auxiliary equation can be found by,

Let m = y', then m² = y''

m² - 6 = 0

m² = 6

m = ± √6

So the roots are √6 and -√6.

Hence the roots of the auxiliary equation of the given differential equation are √6 and -√6.

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The set of 4 integers are is given by the equation A = { 1 , 2 , 3 , 4 }

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the set of 4 integers be represented as set A

Now , the equation will be

Let the first number be 1

The absolute value of 1 is | 1 | = 1

Let the second number be 2

The absolute value of 2 is | 2 | = 2

Let the third number be 3

The absolute value of 3 is | 3 | = 3

Let the fourth number be 4

The absolute value of 4 is | 4 | = 4

And , | 1 | < | 2 | < | 3 | < | 4 |

Hence , the set of integers are { 1 , 2 , 3 , 4 }

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Therefore , the solution of the given problem of triangle comes out to be ∠P = 30° , PQ = 4√3  and  PN = 2.

An triangle is a polygon since it has four or more parts. It is a simple geometric shape. A square having angles A, B, and C is referred to as a triangle ABC. When the sides are not collinear, Euclidean geometry generates a single plane and square. If a triangle has three sides and three corners, it is a polygon. The corners of a triangle are where its three sides meet. The sum of the angles in a triangle is 180 degrees.

Here,

Given :  A right triangle,

=> ∠P + 60° + 90° = 180°

=>  ∠P = 180° - 150°

=> ∠P = 30°

For PQ

=> Tan 60°  =  √3

=> PQ /4 = √3

=> PQ = 4√3

For PN ,

=> Sin 60°  = √3/2

=>  4√3  / PN =  √3/2

=> PN = 2

Therefore , the solution of the given problem of triangle comes out to be

∠P = 30° , PQ = 4√3  and  PN = 2.

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The total length of the race track that Antonio remote controlled car runs on is 70 m.

An equation is an expression that shows how numbers and variables relate with each other.

Equations can either be linear, quadratic and so on depending on the degree of the polynomial

Let x represent the length of the racetrack.

Antonio car stops 10m past the starting line. After he fixes a wheel, the car goes 2/5 the racetrack’s total distance. It can be represented by the equation:

(2/5)x + 10 = 38

(2/5)x = 28

x = (28 * 5)/2

x = 70

The length of the race track is 70 m.

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The coordinates of the linear equation for (m, s) are; (0, 4), (2, 3), (-2, 5), (8, 0)

This is a one to one mapping and example of a function

We are given the equation as;

2m + 4s = 16

Thus;

When m = 0, we have;

2(0) + 4s = 16

4s = 16

divide both sides by 4 to get;

s = 4

When s = 3;

2m + 4(3) = 16

2m + 12 = 16

2m = 16 - 12

Divide both sides by 2 to get;

m = 4/2

m = 2

When m = -2

we have;

2(-2) + 4s = 16

-4 + 4s = 16

4s = 20

divide both sides by 4 to get;

s = 5

When s = 0, we have;

2m + 4(0) = 16

2m + 0 = 16

2m = 16

Divide both sides by 2 to get;

m = 16/2

m = 8

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Answer: The answer provided is based on the following calculation:

To make a 75% syrup, Ella should add enough water to the sugar to create a solution that is 25% sugar and 75% water.

To calculate how much water to add, you can use the formula: (desired % of sugar) / (100 - desired % of sugar) * (amount of sugar).

In this case, it would be: (0.75) / (100 - 0.75) * (0.5 lb) = 0.67 lb of water.

To calculate the total amount of syrup, you add the amount of sugar and the amount of water: 0.5 lb + 0.67 lb = 1.17 lb.

So Ella should add 0.67 lb of water to make a 75% syrup and will have a total of 1.17 lb syrup.

Step-by-step explanation:

Answer:

for the 75% syrup: 0.167lbs

For the 1.5% syrup: 32.83 lbs

Answer: If the model kit for the Dornier Do17 airplane has a wingspan of 10 inches and the scale of the kit is 1 inch to 72 inches. This means that for every inch on the model, the equivalent measurement on the actual Dornier Do17 airplane is 72 inches.

We know that the wingspan of the model is 10 inches and we want to find the actual wingspan of the airplane so we'll use the scale factor of 1:72

To find the actual wingspan, we'll multiply the wingspan of the model by the scale factor.

10 inches * 72 inches/1 inch = 720 inches

Therefore, the actual wingspan of the Dornier Do17 airplane is 720 inches or 60 feet.

Step-by-step explanation:

The standard form is used to show horizontal lines and vertical lines, while the slope intercept form shows the slope and y intercept of the linear equation.

An equation is an expression relating two or more numbers and variables.

The standard form of a linear equation is:

Ax + By = C

where A, B and C are constants

The slope - intercept form of a linear equation is:

y = mx + b

Where m is the rate of change(slope) and b is the y intercept.

The standard form is used to show horizontal lines (A=0) and vertical lines (B=0), while the slope intercept form shows the slope and y intercept.

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The equation in slope intercept form is y=-9x-8

Slope is defined the rate of change of y with respect to x.  the slope is also denoted by increase in y over increase in x.

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis).

The equation of the slope intercept form is in the form y= mx +c

The given equation  y= -9x +9

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The probability of each outcome is given as follows:

1/12.

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

For this problem, we have that the total number of outcomes is of twelve, as:

Hence:

6 x 2 = 12.

(applying the Fundamental Counting Theorem).

Meaning that the probability of each outcome is given as follows:

1/12.

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Answer:

-4/√5

Step-by-step explanation:

when f(x) = 0.

we can set the function equal to 0 and solve for x:

√5x + 4 = 0

√5x = -4

x = -4/√5

So the zero of the function is x = -4/√5