Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Will and his good buddy Owen are both mechanics at a shop that does oil changes. They are in a friendly competition to see who can complete the most oil changes in one day. Will has already finished 4 oil changes today, and can complete more at a rate of 2 oil changes per hour. Owen just came on shift, and can finish 3 oil changes every hour. Sometime during the day, the friends will be tied, with the same number of oil changes completed. How many oil changes will Will and Owen each have done? How long will that take?

Option (a) is correct option.

The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality.

Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality. When two or more parameters are proportional to one another either directly or indirectly, their relationship is stated as a = kb or a = k/b, where k denotes the direction of the relationship between the two variables.The proportionality constant is thus k.

Constant of proportionality in given case is nothing but slope of given graph.

Slope is given by tangent of the angle made by line with positive x-axis.

p =slope of line

p = [tex]\frac{y-axis}{x-axis}[/tex]

p=[tex]\frac{140}{2}[/tex] = 70

So option (a) is correct.

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The value of P(A and B)  is 1/5.

What is Sample Space?

The set of all potential outcomes or results of an experiment or random trial is referred to as the sample space in probability theory. The sample points, or potential ordered outcomes, are listed as elements in the set notation used to represent a sample space.

Here, we have

Given

Sample Space = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A = {1, 2, 3, 4}

B={1, 3, 5, 7, 9}

We have to find P(A and B).

First, we will find A and B i.e A∩B

A∩B = {1,3}

Now, we will find P(A and B).

P(A and B) = n(A∩B)/n(S)

P(A and B) = 2/10

P(A and B)  = 1/5

Hence, the value of P(A and B)  is 1/5.

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The factory produces 72 bottles of juice per minute.

What is the rate?

A rate is a special ratio in which the two terms are in different units. If a 12-ounce can of corn costs $69, the rate is $69 for 12 ounces. This is not a proportion of two comparable units, such as shirts. This is a proportion of two dissimilar units: cents and ounces.

To find the factory's production rate in bottles per minute, we need to divide the number of bottles produced by the time it took to produce them. In this case, the factory produced 360 bottles in 5 minutes, so the production rate is:

360 bottles / 5 minutes = 72 bottles/minute

This means that the factory produces 72 bottles of juice per minute.

Hence, the factory produces 72 bottles of juice per minute.

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Answer:

Biotic factors of a marine ecosystem typically include algae, plankton, bacteria, seaweed, corals, fish, sharks, seals, whales, penguins and jellyfish.

Step-by-step explanation:

i hope this answer helped

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Answer: 240

Step-by-step explanation: you take 10 times 12 and you get 140

Answer:

$240

Step-by-step explanation:

If ten friends went out and each was $24 it’s 10x24 which is equal to $240

Answer:

8.0

Step-by-step explanation:

There are 1000 milliliters in one liter, so a two-liter bottle contains 1000 * 2 = 2000 milliliters of milk. Since one cup contains approximately 250 milliliters, a two-liter bottle contains 2000 / 250 = 8 cups of milk. Rounding this value to the nearest tenth, we find that there are approximately 8.0 one-cup servings of milk in a two-liter bottle.

Answer:

5f + 4s

Step-by-step explanation:

Third option

Using the parameters associated with the parabola and the formula for the equation using the focus and the focal diameter, The required equation is

[tex]x = \frac{-1}{62} (y+5)^{2}+ \frac{9}{2}[/tex] .

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.

All points in a plane that are equally spaced out from a given point and a given line make up a parabola. The line is known as the directrix, and the point is known as the parabola's focus. The parabola's axis of symmetry is the subject of attention.

focus = (-11,5)

focal diameter =20

Required equation of parabola,

[tex]x = \frac{-1}{62} (y+5)^{2}+ \frac{9}{2}[/tex]

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The 90% confidence interval's margin of error is 0.0183, and its success probability is 0.546.

The term "margin of error" refers to the probability or "chances of error" when selecting or computing a sample in a survey.

Jamie works as an analyst for a provider of educational technologies. She gathered information on the outcomes of a particular kind of query. 1,092 of the 2,000 replies she examined were accurate.

Here,

Number of samples, N=2000

Probability of responding correctly,

=1092/2000

=0.546

Z-score at 90% confidence level,

=1.645

Margin of Error ME,

=z*√(p*(1-p)/N)

=1.645*√(0.546*(1-0.546)/2000)

=1.645*√(0.546*0.454)/2000

=1.645*√(0.248/2000)

=1.645*√0.000124

=1.645*0.011

=0.0180

With a success rate of 0.546 percent, the margin of error for the 90% confidence interval is 0.0183.

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As it passes through the point (2,6), it will convert to the function f(x) = (x + 2) -3 at (0,3).

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. A "vertical line test" can be used when examining a graph to determine whether a relation is a function. The relation is not a function if any point on the graph may be used to build a vertical line that crosses the relation twice.

Here,

g(x) = f(x + 2) – 3

This represents a shift of two units to the left and three units down:

x moves from two to two units left (-2) to become 0  

y moves from six to three units down (-3) to become 3.

At (0,3), It will translate to the function f(x) = ( x + 2) -3 as it goes through the point (2,6).

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The answer to this Question based on speed is 1m/s

What is speed?

Speed can be defined as the rate at which an object moves from one point to another. It is usually measured in units of distance per unit of time, such as kilometers per hour (km/h) or miles per hour (mph). Speed is a scalar quantity, meaning it has magnitude but no direction. Speed can also be thought of as the rate of change of position. When an object is in motion, its speed is constantly changing due to the force of gravity, air resistance, and other external factors. The speed of an object can be affected by its weight, shape, and size. An object's speed can also be affected by other factors such as the friction of the surface it is moving on and the wind or air resistance. Speed is an important concept in physics, engineering, and many other fields.

we are given that velocity as a function of time along a single direction

we write v(t) = -2t+5

hence speed = mod(velocity)

speed at t = 2 sec = mod (velocity at t = 2 sec)

speed = mod(-2(2)+5)

speed = mod(-4+5)

speed = 1 m/s

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Answer:

x=2.5, 5/2

y=1.5, 3/2

Step-by-step explanation:

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

2x+10x-28=2

12x=30

x=2.5

y=-5(2.5)+14

y=-12.5+14

y=1.5

Answer:

ANS:- 2439

Step-by-step explanation:

2439/3 = 813

2439/9 = 271

Circumference of the circle is 37.68 feet

A circle's diameter is multiplied by to determine its circumference (pi). You can also determine the circumference by multiplying 2radius by pi (=3.14).

R is specified as 6 feet, with a diameter of 12 feet (2 x 6).

Circumference: 12 feet times 3.14 inches, or 37.68 feet

If r is equal to 6 cm, the circumference is given by c = 2 (6) = 12 cm. If you'd rather have a number, the solution is 37.7 cm, rounded to the closest tenth.

D is the diameter, which is equal to 2 times r in the circumference formula ( r is the radius).

The distance between the center of the sphere and any plane passing through it is known as the circumference. 

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The distance Alex jumped and the distance Eric jumped compared with the state records indicates that the magnitude of Eric's score was closer to their grades state  record

The magnitude of a value is the value itself, indicating the distance of the number from zero.

Alex is an eight grader

Eric is a seventh grader

The distance Alex jumped = 39.75  feet

The distance Eric jumped = 37 feet 11 inches

The eight grade record = 42.25 feet

The seventh grade record = 39 feet 3 inches

Each athlete distance  jumped is compared with  the record for the grade at which they jumped

The deviation of the distance  jumped from the record scores are;

Alex's difference between distance jumped  and the record = 39.75 - 42.25 =  -2.5

The difference between the distance Eric jumped and the record =  37 feet + 11 inches - (39 feet + 3 inches)  =  -(1 feet + 4 inches)

-(1 feet + 4 inches) = -1.[tex]\overline 3[/tex] inches

The magnitude of the difference between the distance Eric jumped and the state record is smaller, therefore, Eric was closer to the state record

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Answer: I can confirm that Eric is closer!

Step-by-step explanation:

Answer: 35%

Step-by-step explanation:

A. The system of inequality is plotted and the graph is attached

B. (1, 3) is not a solution because it does not satisfy the two equations

C. the three points that are solutions are

Substituting the given point into the two system of equation if it satisfies the equation then it is a solution

For (1, 3)

3x + y ≥  - 1

3 * 1 + 3 ≥ - 1

6 ≥ - 1 correct

2y - 4 > 3x

2 * 3 - 4 > 3 * 1

2 > 3 - wrong hence not a solution

For  (-1, 3)

3x + y ≥  - 1

3 * -1 + 3 ≥ - 1

0 > -1 correct

2y - 4 > 3x

2 * 3 - 4 > 3 * -1

2 > -3 correct this is a solution

(-1, 4) and (1, 4) other solutions are deduced form the attached graph where two the two shaded points intersect

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Answer:

She bought 3 large frames and 8 small frames.

Step-by-step explanation:

X= Large frames = $19

Y= Small frames  = $ 9

Total Frames Cost = $129

Total Frames = 11

Then, costs formula:

1) 19X + 9Y = 129

2) X + Y = 11

So here you have a equation system and we will solve it by substituion method:

2) Y = 11-X

replace Y in 1)

1) 19X + 9(11-X) = 129

19X +99 -9X = 129

10X = 129-99

10X = 30

X = 30/10

X = 3

Then

Y = 11-3

Y = 8

Answer:

y =5x

Step-by-step explanation:

y = 5x

Because the slope is 5 and the y-intercept is 0.

From the equation, the value of m is 4

The given parameter is

0.m1+ 0.m2 + 0.m3 = 11/14

Simplify this to have

m1 / 99 + m2 / 99 + m3 / 99 = 11/14

Simplify the equation further

( m1 + m2 + m3 ) / 99 = 11/14

⇒( m1 + m2 + m3 ) = 126

By multiplication we have

( 10 * m + 1 ) + ( 10 * m + 2 ) + ( 10 * m + ) = 126

Simplify to get

30 * m + 6 = 126

30 * m = 120

m = 4

Therefore the value of m is 4

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Translated question:

Please help, given that 0.m1 +0.m2 +0.m3 = 14/11, Find the value of m

The height of the balloon is 21.33

According the the question the relation between height and surface area of balloon is

H=pA

where ,

H is height

p is proportionality constant

A is surface area

Surface area = 81

Height = 12

By Replacing the given values we get,

12=p x 81

p=12/81

Using it in given conditions,

H=(12/81)x144

H=21.33

So the height of the balloon in the given condition is 21.33

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Graph (D) represented the inequality solution of 5+x<3(2x+4).

The set of ordered pairs is the graph of a function f in mathematics, where These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.

To develop a graph is to make a diagram that depicts the relationship between two or more objects.

Make a sequence of bars on graph paper as an example of a graph.

So, we have the inequality:

5 + 8x < 3 (2x+4)

Now, we need to plot this on the graph:

(Refer to the graph attached below)

We can easily tell that this is identical to graph sin option (D).


Therefore, graph (D) represented the inequality solution of 5+x<3(2x+4).

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Answer:

write the equation in slope intercept form. Write the numbers in the equation as simplified proper fraction improper fraction or integer

The equation of the parallel line t is y = -4x  - 9.

The equation of line s is given as

y = -4x - 5/3

Also, from the question, the point on line t is given as Point = (-3, 3)

The equation of a line can be represented as

y = m x + c-------(1)

Where m represents the slope

c is the constant value

By comparing the equations, we have the following

m = -4

This means that the slope of y = -4x - 5/3 is -4

The slopes of parallel lines are equal

This means that the slope of the line t is -4

The equation of the parallel line is then calculated as:

y = m(x - x₁) +y₁

Where m = -4

(x₁, y₁) = (-3, 3)

Now, we should substitute the known values in the above equation(1)

y = -4(x + 3) + 3

By Evaluating we get

y = -4x - 12 + 3

y = -4x  - 9

Hence, the parallel line has an equation of y = -4x  - 9.

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Answer:

C

Step-by-step explanation:

A line perpendicular to the y-axis is a horizontal line

  Horizontal lines have  slope = 0

       answer C    y = 3   slope = 0

Answer:

  0.1220

Step-by-step explanation:

You want the probability that greater than 90 out of 149 software users will not call tech support, given that the probability a given user will not call is 56%. You want the value using the normal approximation to the binomial distribution.

For a sample size of n, and probability p of "success", the normal approximation to the binomial distribution can be used if ...

  min(pn, (1-p)n) > 5

Here, that is ...

  min(0.56·149, 0.44·149) > 5

  65.6 > 5 . . . . . . . . true, the normal approximation is appropriate

Then the parameters of the normal distribution are ...

  µ = pn = 0.56·149 = 83.44

  σ = √((1-p)µ) = √(0.44·83.44) ≈ 6.0592

The probability that X = N will occur can be considered to be ...

  P(N -0.5 < X < N +0.5)

Then the probability that X > N will be modeled using the normal distribution as ...

  P(X > N +0.5)

For this problem, we want ...

  P(X > 90.5) . . . . using the normal distribution with µ = 83.44, σ = 6.0592

The attached calculator shows that value to be ...

  P(>90) ≈ 0.1220 . . . . . . rounded to 4 decimal places

__

Additional comment

A probability calculator says the actual binomial distribution result for this problem is 0.1217.

To find the sum of vectors u and v, we can add their components separately:

(u + v)x = (7cos 310° + 2cos 115°)

(u + v)y = (7sin 310° + 2sin 115°)

Using a calculator to evaluate these expressions, we get:

(u + v)x = -2.16

(u + v)y = 8.48

The magnitude of the sum vector u + v can be found using the Pythagorean theorem:

|u + v| = √((u + v)x^2 + (u + v)y^2)

= √(-2.16^2 + 8.48^2)

= √(72.3584)

= 8.51

The direction of the sum vector u + v can be found using the inverse tangent function:

θ = tan^(-1)((u + v)y / (u + v)x)

= tan^(-1)(8.48 / -2.16)

= tan^(-1)(-3.928571428571429)

= 143.13°

Rounding the magnitude to the nearest tenth and the direction to the nearest degree, we get:

u + v = 8.5 (cos 143°, sin 143°)

Therefore, the sum of vectors u and v is equal to 8.5 (cos 143°, sin 143°).

Answer:

To write √73 in exponential form, we can use the fact that the square root of a number is the same as that number to the power of 1/2. Thus, we can write √73 as 73^(1/2).

Here's how we can show this using algebraic steps:

First, we can write the square root as a fractional exponent:

√73 = 73^(1/2)

Next, we can rewrite the fractional exponent using the rule that says that a^(m/n) = (a^m)^(1/n):

√73 = (73^1)^(1/2)

Finally, we can simplify the expression by evaluating the power of 1:

√73 = (73)^(1/2) = 73^(1/2)

Therefore, √73 can be written in exponential form as 73^(1/2).

Reflection of point 1 over X axis is (-4, -2)

Reflection of point 2 over Y axis is (2, 3)

Reflection of point 3 over x = 1 is (2, 1)

Reflection of point 4 over y = x is  (2, -1)

What is Reflection of a point?

A reflection point occurs when a figure is constructed around a single point known as the point of reflection or center of the figure. For every point in the figure, another point is found directly opposite to it on the other side.

According to the given question:

1. Reflection of point 1 over X axis (x, -y) ⇔ (x, y)

 ∴ Reflection of (-4, 2) over X axis is (-4, -2)

2. Reflection of point 2 over Y axis (x, y) ⇔ (-x, y)

 ∴ Reflection of (-2, 3) over Y axis is (2, 3)

3. Reflection of point 3 over x = 1

 ∴ Reflection of (-2, 1) over x = 1 axis is (2, 1)

4. Reflection of point 4 over y = x is  (x, y) ⇔ (y, x)

 ∴ Reflection of (-1, 2) over X axis is (2, -1)

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