Tommy and Ruth are cycling to meet each other. Tommy cycles twice as fast as Ruth and they both set off at the same time. At which coordinate will they meet?

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:

Answer: The domain of a function is the set of all input values (x-values) for which the function produces a valid output value (y-value).

For the function y = 3^√x, the input value x can't be negative because the value under the square root should be non-negative and 3^√x is defined for all x in the domain of real numbers. This means that the domain of the function y = 3^√x is (-∞,∞).

Step-by-step explanation:

The domain of the function is  [0, ∞).

A function has an input and an output.

A function can be one-to-one or onto-one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The function y = 3^√x has a base of 3, which means that the output of the function is always a positive number.

For the function to be defined, the input x must also be a positive number or zero, as the square root of a negative number is not a real number.

Therefore,

The domain of the function is all non-negative real numbers, or [0, ∞).

In interval notation, the domain can be written as [0, ∞).

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The value of y in the equation that we have here is given as , y = x + (10 + y)i

To solve for y, we can start by isolating y on one side of the equation. We can do this by adding yi to both sides:

x+10i+yi = y-yi+yi

This simplifies to:

x+10i+yi = y

We can then rearrange the equation to get:

y = x+10i+yi

So, y = x + (10 + y)i

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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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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

(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

Answer:

Step-by-step explanation:

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

                  =log(2^(-1))^16

                  =-16log(2)=-4.81647

The confidence interval is (0.0104, 0.0496) (can include those endpoints too)

You can find the standard mean error and then use that to find the confidence interval limits.

The 99% confidence interval for the proportion of all employees at the company who own an electric car is given by

Lower limit = 0.0104

Upper limit = 0.0496

The confidence interval is (0.0104, 0.0496) (can include those endpoints too)

To find the confidence interval for proportions

Let the sample size be n

Let the interested quantities in the sample be present x times

Let the confidence level be of p%.

Then the level of significance is given by

The standard mean error is calculated by:

Then the confidence interval limits can be found by

Using the above formula for finding the confidence interval

We have n = 500, x = 15 and

Finding the standard mean error:

From the z tables, we get z = 2.5758

Thus, the confidence interval is obtained by

Lower limit = 0.0104

Upper limit = 0.0496

Thus,

The 99% confidence interval for the proportion of all employees at the company who own an electric car is given by

Lower limit = 0.0104

Upper limit = 0.0496

Therefore, The confidence interval is (0.0104, 0.0496) (can include those endpoints too)

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Answer: C. Inside the school cafeteria.

Step-by-step explanation:

Answer:

don’t care 9

Step-by-step explanation:lol

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:

-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

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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Answer: B

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

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:

  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 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:

Step-by-step explanation:

350 + x people = 1500

x = 1500 - 350

x = 1150 / 12.50

x = 92 people

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 value of the variable, x is 7

Algebraic expressions are defined as expressions that are composed of terms, coefficients, variables, constants and factors.

These mathematical operations are also made up of arithmetic operations. These operations includes;

From the information given, we have;

-5(2x+14)=-2(x+63)

expand the bracket

-10x -70 = -2x - 126

Now, collect like terms

-10x + 2x = -126 + 70

Add or subtract the terms

-8x = -56

Make 'x'' the subject

x = 7

Hence, the value is 7

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A situation which could be represented by the equation 18x = 19 + 12x include the following: J. Krystal can make $18 per hour by tutoring. Jondo can make $12 per hour by tutoring. Jondo already has $19. How many hours, x, would Krystal and Jondo need to tutor for them to have the same amount of money?

In Mathematics, an algebraic expression simply refers to a mathematical equation that can be used for showing the relationship which exist between two (2) or more variables, numerical quantities, as well as in conjunction with different mathematical operations.

Assuming the variable x represents the number of hours spent tutoring, an algebraic expression which relates the number of hours which these two tutors must spent during tutorial to earn the same amount of money is given by:

18x = 19 + 12x

18x - 12x = 19

6x = 19

x = 19/6 hours.

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Complete Question:

Which situation can be represented by this equation?

18x = 19 + 12x

F Krystal reads 12 pages per hour. Jondo reads 18 pages per hour.

How many hours, x, would it take for Krystal and Jondo to read

the same number of pages?

G Krystal paid a deposit of $19 plus $18 per hour to rent a dining

room at a restaurant. Jondo paid $12 per hour to rent a dining

room at a restaurant. How many hours, x, would it take for

Krystal and Jondo to pay the same amount of money?

H Krystal installs 12 tiles per hour. Jondo installs 19 tiles per hour

and started with 18 tiles already installed. How many hours, x,

would it take for Krystal and Jondo to install the same number

of tiles?

J. Krystal can make $18 per hour by tutoring. Jondo can make $12 per hour by tutoring. Jondo already has $19. How many hours, x, would Krystal and Jondo need to tutor for them to have the same amount of money?

This calculation yields a volume of a cube equal to 1728 cube inches. In order to calculate the volume, the length must be multiplied by itself three times.

Volume =[tex]a^{3}[/tex], where an is the length of the cube's sides or edges, is how you can calculate the volume of a cube.

A.) 12 × 3 cubic inches

B.) Volume of a cube equals length × breadth × height, which is                    12× 12 × 12 = 123 = 144 × 12 = 1728 cube inches. V=[tex]a^{3}[/tex]=123=1728 [tex]cm^{3}[/tex]is the result, giving the cube's volume.

1,728 times twelve cubed. The term "x cubed," or cubing a number, is identical to: x cubed equals x 3. A real number with a cube equal to 12 is the cube root of 12. It is about equal to 2.289 to take the cube root of 12. Volume per volume, or % v/v, is the way volume concentrations in solutions are stated. This is employed when a solution contains liquid versions of both compounds.

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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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Using dimensional analysis we have converted 44 yards/sec = 90 miles/hour.

Dimensional analysis is the study of how dimensions and units of measurement affect the relationship between physical quantities.

Dimensional analysis is crucial because it maintains the consistency of the units, which facilitates accurate mathematical computation.

As we use conversion factors to obtain the same units, dimensional analysis is also known as the Factor Label Method or Unit Factor Method.

We know that 1 yards/sec = 2.04545 miles/hour

Here given that 44yds/s = ? miles/hour

Lets solve

1 yards/sec = 2.04545 miles/hour

44 yards/sec = 44 × 2.04545 miles/hour

44 yards/sec = 89.9998 miles/hour

44 yards/sec = 90 miles/hour

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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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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 equation of the cross-section of the reflector which is in the form of a parabola is y² = -10x

A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.

Given that, The cross-section of the reflector in a flashlight is a parabola, the light bulb is located at the focus of the cross-section, 2.5 cm in front of the vertex.

We know that, the equation of the parabola turned to the left i.e. to the negative side of the coordinate system is:

y² = -2px  

where p is the parameter of the parabola

The relationship between the parameter and the focus is.

p = 2 f  

p = 2×2.5 = 5 cm  

Since, the equation of the parabola is:

y² = -2p

Therefore, put p = 5

y² = - 2×5x = -10x

y² = -10x

Hence, the equation is y² = -10x

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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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