A pronto lube garage charges £25 to lube any vehicle. Other work adds about €6000 per month to the
revenue. It costs pronto lube £6 in materials to service cars. Monthly operating expenses are €23,500.
2.1). Write an expression for net profit for C cars.
2.2). If the number of cars serviced in a particular month is 3000, find the profit
2.3). If the number of car serviced in a particular month is 900, then the garage got a
profit. True / false.

Solving for x in the angle bisector which resulted to the proportion  x over 18 = 45 over 20 results to x = 40.5

In geometry, a line that divides an angle into two equal angles is referred to as an angle bisector.

By definition, a bisector is something that divides an object or a shape into two equal parts. A ray is said to be an angle bisector if it divides an angle into two equal portions of the same measure.

The division from angle bisectors gave rise to the proportion which is given by

x / 18 = 45 / 20

cross multiplying

x = 18 * 45 / 20

x = 40.5

hence x is solved to get 40.5

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The factors of given quadratic expression are (4a+3) and (a+6).

The factors are the polynomials which are multiplied to produce the original polynomial.

The given quadratic expression is 4a²+27a+18.

By splitting middle term method, we get

4a²+3a+24a+18

= a(4a+3)+6(4a+3)

= (4a+3)(a+6)

Therefore, the factors of given quadratic expression are (4a+3) and (a+6).

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Answer:

[tex]v=-18,14[/tex]

Step-by-step explanation:

[tex]2|v+2|-41=-9\\2|v+2|=32\\|v+2|=16\\\\v+2=16\\v=14\\\\v+2=-16\\v=-18[/tex]

The values of x are 5 or 13.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given is an equation, [tex]\sqrt{2x-1}[/tex] - x = -8

[tex]\sqrt{2x-1}[/tex] - x = -8

[tex]\sqrt{2x-1}[/tex] = -8+x

Squaring both sides,

2x-1 = x²+64-16x

x²-16x-2x+1+64 = 0

x²-18x+65 = 0

Factorizing the equation,

x²-18x+65 = 0

x²-13x-5x+65 = 0

x(x-13)-5(x-13) = 0

(x-5)(x-13) = 0

x = 5 or 13

Hence, the values of x are 5 or 13.

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The family's monthly payment for their new minivan is $6,664.52

To calculate the monthly payment, we first need to find the total amount that the family is financing by subtracting the down payment from the total cost of the minivan: $45,000 - $12,000 = $33,000.

Then, we can use the monthly payment factor to calculate the monthly payment. The formula to do this is:

Monthly Payment = Financed Amount * Monthly Payment Factor

So in this case:

Monthly Payment = $33,000 * 0.202764 = $6,664.52

Therefore, the family's monthly payment for their new minivan is $6,664.52

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Answer:

A

Explanation:

A line graph is a unique type of graph which is used in statistical application which represents the change in a quantity with respect to another quantity.

The price of different flavors of chocolates varies which can be represented, these variation is plotted in a two-dimensional XY plane.

If the relation include two measures can be presented by using a straight line in a graph called as linear graphs or a linear graph.

There are different types of the line graph, Simple Line Graph refers to Only one line is plotted on the graph, Multiple Line Graph where More than one line plotted on the same set of axes.

Compound Line Graph refers to the information can be divided into two or more types of data and this line graph is called a compound line graph which can be drawn to show the component.

Answer:

It's B, -2, v/5 4, and 3².

Answer:

1/8

Step-by-step explanation:

total probability = 1

total probability = probability of red + probability of green + probability of yellow

1 = 1/4 + 5/8 + yellow

we want to find a common denominator

in this case, we know 4 * 2 = 8, so we can multiply 1/4 by 2/2 = 1 to get

1/4 * 2/2 = 2/8

1 = 2/8 + 5/8 + yellow

1 = 7/8 + yellow

subtract 7/8 from both sides to isolate yellow

1 = 8/8

1 - 7/8 = 8/8 - 7/8 = 1/8 = yellow

The value of a is [tex]-\frac{12}{5}[/tex] if 2 is a zero of the polynomial [tex]$4 x^2-2 x+5 a$[/tex].

As per the given data, the polynomial is p(x) = [tex]$4 x^2-2 x+5 a$[/tex]

The polynomial is zero polynomial if x is 2

The places where a polynomial becomes zero overall are known as the zeros of the polynomial. The term "zero polynomial" refers to a polynomial with a value of zero (0).

Replace x with 2 we get

Therefore [tex]4(2)^2-2(2)+5 \mathrm{a}=0[/tex]

[tex]\Rightarrow[/tex] 4 (4) - 2 (2)+5 (a) = 0

[tex]& \Rightarrow[/tex] 16 - 4 + 5 (a) = 0

[tex]& \Rightarrow[/tex] 12 + 5 (a) = 0

Add -12 on both sides we get

12 + 5 (a) - 12 = 0 - 12

5 (a) = -12

Divided by 5 into both sides we get

a = [tex]-\frac{12}{5}[/tex]

Therefore the value of a is [tex]-\frac{12}{5}[/tex]

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Answer:

x = 4, y = 12

Step-by-step explanation:

xy = -16

y = x + 8

substitute y = x + 8 into xy = -16

x(x + 8) = -16

x^2 +8x + 16 = 0

x = 4

sub x = 4 into y = x + 8

y = 4 + 8

y = 12

The correct numbers to complete the statements given are 40, 400, and 4000.

This question requires you to complete a statement with a given number (40, 400 or 4000) to make the statement true by dividing the number by 40.1. To find the correct order the numbers must be place using division, let's find out the results of each of these divisions:

Based on the above, it can be concluded:

Based on this, the complete statements are:

Note: This question is incomplete; here is the complete question:

Use each of the numbers 4, 40, and 4000 once to make true statements.The value of ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯÷40.01 is close to 1

The value of ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯÷40.01 is much less than 1.

The value of ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯÷40.01 is much greater than 1.

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Answer:

y = 72 and x = 36

Step-by-step explanation:

So firstly, the outside angle is 108, right? And the total of all angles in a triangle is 180 degrees. So:
180 - 108 = 72
Then the other angle, angle x, is also 72 degrees. That's because they are supplementary angles.
Now that we know x = 72 degrees. To find the y angle, you add 72 and 72 together. Which is 144.
Then you do 180 - 144. Which is 36. So, x = 72 and y = 36

I hope it helped you!

The probabilities are given as follows:

a) No injuries: 0.4493 = 44.93%.

b) More than two injuries: 0.0474 = 4.74%.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following equation:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

The mean for this problem is of:

[tex]\mu = 0.8[/tex]

The probability of no injuries is of P(X = 0), hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-0.8}(0.8)^{0}}{(0)!} = 0.4493[/tex]

The probability of more than two injuries is of:

P(X > 2) = 1 - P(X <= 2)

In which:

P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2)

Hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-0.8}(0.8)^{0}}{(0)!} = 0.4493[/tex]

[tex]P(X = 1) = \frac{e^{-0.8}(0.8)^{1}}{(1)!} = 0.3595[/tex]

[tex]P(X = 2) = \frac{e^{-0.8}(0.8)^{2}}{(2)!} = 0.1438[/tex]

Then:

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The ratio for cos (cosine) of angle θ is: cos(θ) =  adjacent side of θ / hypotenuse

We know that in right triangle the cosine of an angle is nothing but the ratio of the side adjacent of  given angle to the hypotenuse.

In right tirnagle for an angle θ, the ratio for cosine of angle θ would be:

cos(θ) =  adjacent side of θ / hypotenuse

Consider following right triangle PQR with angle PQR = 90 degrees

Here, PR is the hypotenuse.

Assume that angle QPR measure α degrees and angle PRQ measures θ degrees.

By definition of cosine of angle θ,

cos(θ) =  adjacent side of θ / hypotenuse

cos(θ) =  QR / PR

And by definition of cosine of angle α,

cos(α) =  adjacent side of α / hypotenuse

cos(α) = PQ / PR

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Observational data collection might be best to study how voters might decide an upcoming ballot issue.

The majority of big data is observational data, such as bank transaction records, user viewing patterns on video streaming services, or social media posts. Observational data, however, can also be sparse data (based on just a few people).

In observational research, participants and phenomena are observed in their most natural environments. Instead of using structured environments like research labs or focus groups, this allows researchers to observe how their subjects make decisions and respond to situations in their everyday lives.

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Answer:

y = 90°

Step-by-step explanation:

The graph of the given equation y=2x+1 is attached below.

There are many tools we can use to find the information of the relation which was used to form the graph.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

For example, when the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.

If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.

The equation y=2x+1 gives the following information:

The slope is 2

The line intercepts is 1 on the y axis

First, we would put a point or a dot on (0,1) on the y axis. Then start making 2 points above and below my original point. IT would do this by using the slope 2/1.

By using my slope we know that (1,3) and (-1,-1).

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Answer:

2.50 × 19 = 47.5

Therefore, she would get $47.5 if she sold 19 cups.

When Ava purchased six packages of tulip bulbs and twelve bags of daffodil bulbs, the price per tulip bulb was $7 and the price each daffodil bulb was $13.

The algebraic equation y=mx+b is known as a linear equation. M serves as the y-intercept, and B serves as the slope. The previous clause has two variables, y and x, and is sometimes referred to as a "linear equation with two variables". Bivariate linear equations are those with two independent variables. The following are a few examples of system of equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation takes the form y=mx+b, with m denoting the slope and b denoting the y-intercept, it is referred to as being linear. The term "linear" refers to an equation having the form y=mx+b, where m stands for the slope and b for the y-intercept.

given

Let x be the price of a single tulip bag.

Y should equal the price of one bag of daffodil bulbs.

Grace = 14x + 12y = 254

ava = 6x + 12y = 198

- 8x = - 56

x = - 56/-8

x = 7.

Equation 1 becomes

6* 7 + 12y = 198

42 + 12y = 198 when x = 7 is substituted.

12y = 198 - 42

12y = 156

y = 156/12

y = 13

When Ava purchased six packages of tulip bulbs and twelve bags of daffodil bulbs, the price per tulip bulb was $7 and the price each daffodil bulb was $13.

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The graph of the system of equations y - 2x + 5 = 0 and y + 4x + 1 = 0 intersect at (0.667, - 3.667)

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, A system of equations y - 2x + 5 = 0 and y + 4x + 1 = 0.

Let's write the terms in the order x, y therefore,

y - 2x + 5 = 0

- 2x + y = - 5.

2x - y = 5.

And

y + 4x + 1 = 0.

4x + y = - 1.

The graph of the system of equations is attached in the image.

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The work done on the toy car is 164.4 J.

The formula for work is:

Work = force * distance

In this case, given that:

Force = 5.2 N

Distance = 32 m

So, the work is:

Work = force * distance

Work = 5.2 * 32

Work = 166.4 J

Hence, the work done is 164.4 J.

Force is described as the rate of change of momentum with respect to time, in which momentum is mass multiplied by velocity. Work is the product of displacement and the component of force in the direction of displacement. When work is done, then the kinetic energy of an object changes.

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a) The quadratic function is factored as follows: f(x) = 4(x - 0.5)(x + 2.5).

b) The x-intercepts of the quadratic function are given as follows: x = -2.5 and x = 0.5.

c) The end behavior of the quadratic function is given as follows: as x -> ± ∞, f(x) -> ∞.

d) The graph is constructed at the end of the answer, considering the x-intercepts, the y-intercept, the end behavior and the vertex.

The quadratic function for this problem is defined as follows:

f(x) = 4x² + 8x - 5.

Hence the coefficients are given as follows:

a = 4, b = 8, c = -5.

The discriminant is given as follows:

D = 8² - 4 x 4 x (-5)

D = 144.

Hence the x-intercepts are given as follows:

Considering the intercepts and the leading coefficient of a = 4, the function is factored as follows:

f(x) = 4(x - 0.5)(x + 2.5).

As the leading coefficient is positive, the parabola is concave up, meaning that the end behavior is that the function increases to infinity both at the left tail and at the right tail.

The y-intercept is given as follows:

f(0) = 4(0)² + 8(0) - 5

f(0) = -5.

The coordinates of the vertex are given as follows:

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Answer:

C is a function

Step-by-step explanation:

for a relation to be a function each value of x must map to exactly one unique value of y

A

2 → 5 and 2 → 2 ← not a function

B

- 1 → 6 and - 1 → 7 ← not a function

C

all values of x map to exactly one unique y ← function

D

3 → 1 and 3 → 2 ← not a function

the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale is 4√5

What is altitude Class 9?

The altitude of a triangle is the perpendicular line segment drawn from the vertex to the opposite side of the triangle.

In geometry, a line segment is bounded by two distinct points on a line. Or we can say a line segment is part of the line that connects two points. A line has no endpoints and extends infinitely in both the direction but a line segment has two fixed or definite endpoints.

Let's call it x

According to Euclidean theorem x^2 = 5×16

x^2= 80 and

x = 4√5

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On solving the provided question we can say that - here in equation we have [tex]y = 160+ 2 *t= > y = 160 + 2X 30 = > y= 160+ 60 = > y = 220 pounds[/tex]

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

[tex]y = 160+ 2 *t\\y = 160 + 2X 30\\y= 160+ 60\\y = 220 pounds[/tex]

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Answer:

Step-by-step explanation:

good

Given that,

Perimeter of kite -  38 cm

Let "x" be the one side of kite

Both of the top sides are equal

Therefore, other side = x

One side of a kite is 2 cm less than 2 times the length of another

Therefore,

One of bottom side = 2x - 2

Bottom sides are also equal

Thus, other bottom side = 2x - 5

We know that,

Perimeter = sum of all sides

38 = x + x + 2x - 2 + 2x - 2

38 = 6x - 4

6x = 38 + 4

6x = 42

x = [tex]\frac{42}{6}[/tex]

x = 7

Thus length of each side of kite is:

x = 7

2x - 2 = 2(7) - 2 = 14 - 2 = 12

Thus length of each side of kite is 7 cm , 7 cm , 12cm , 12cm

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Therefore ,we can conclude from answering the offered question that the region of the circle, triangle, and square is where the darkest area is. A=210-123 = 87 square units

A triangle is a polygon since it has three sides plus three vertices. It is one of the basic geometric forms. An illustration of a triangle with the sides A, B, and C is Triangle ABC. A distinct plane or triangle in Geometrical are discovered when the three aspects are not collinear. Three sides & three corners define a triangle as a polygon. The triangle's corners are defined as the locations where three sides converge. 180 degrees is the result of multiplying three triangle angles.

Here,

The total of the circle, triangle, and square's surface areas.

The region of the darkish area is comprised of the areas of the Circle, Triangle, and Square.

=>A = 210 – 123 = 87 square units

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6=3

6÷3

2 is the required answer for this question

The ratio of days in May and days in a year is 31 to 365 or 31:365

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

We need to find the days in May and days in a year as a ratio

Therefore, Days in may = 31

Days in a year = 365

Thus, the expected ratio = 31/365

Or

31:365

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a) The probability that a student will study and will pass is 0.765.

b) The probability that a student will pass is 0.715.

What is probability?

Simply put, probability is the likelihood that something will occur. When how an event will turn out is not known, one can discuss the likelihood of several outcomes.

Define some events -

A: A  student studies.

B: A student will pass.

Given that P(A)=0.85 and

P(B|A)=1-P([tex]\bar{B}[/tex]|A)

=1-0.10

=0.90

a) P(a student will study and will Pass)= P(A∩B)

= P(A)·P(B|A)

= 0.85×0.90

= 0.765

b) Given that P( student will either study or pass), the probability is -

=P(A∪B)= 0.8 then P(a student will pass)

=P(B)

It is known that P(A∪B)= P(A)+P(B)-P(A∩B)

Then P(B)=P(A∪B) -P(A) +P(A∩B)

=0.8-0.85 + 0.765

=0.715

Therefore, the probabilities are 0.765 and 0.715.

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