Two car owners are in need of car repairs. Hazel will need to pay the mechanic $1 per minute for labor, plus $40 to cover the cost of new parts. Megan will need to pay $10 for parts and $4 per minute for labor. Depending on how long each repair takes, the two jobs might end up costing the same amount. How much time would that take?
Write a system of equations, graph them, and type the solution.

The domain and range of this linear function f(x) = 4x – 8 is: A. domain: {x | x is a real number}; range: {y | y > –8}.

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate. This ultimately implies that, a linear function is typically used for uniquely mapping an input variable to an output variable.

A domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain refers to the set of all possible input numerical values (numbers) to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.

In conclusion, the domain of this linear function consist of all real numbers while the range comprises the set of all real numbers on the y-axis that are greater than negative eight (-8).

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Answer:

its a

Step-by-step explanation:

The probability that the jury will make a wrong decision when it reaches a decision by majority rule is 0.033

To solve this, the number of jury that makes the wrong decision can be modeled as a binomial random with parameters n=7 and p=0.2. This jury as a whole will make wrong decision if 4, 5, 6, or 7 make the wrong decision.

We denote these events with A, B, C, D for 4, 5, 6, 7 respectively. The probability of this union is the sum of probabilities, so

P(Jury Error) = P(A)+P(B)+P(C)+P(D)

  = [tex]\left({{7} \atop {4}} \right.)(0.2)^{4} *0.8^{3} +(\left \({7} \atop {5}} \right)(0.2)^{5} *0.8^{2} +(\left{7} \atop {6}} \right.)(0.2)^{6} *0.8^{1} +(\left{7} \atop {7}} \right.)(0.2)^{7} *0.8^{0}[/tex]

   =0.033

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A graph of the relationship between Sam’s age and Matt’s age has been plotted in the graph shown in the image attached below.

An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.

In order to solve this word problem, we would assign variables to Sam and Matt's age, and then translate the word problem into algebraic equation as follows:

Translating the word problem into an algebraic equation, we have;

x = 5 + y

Re-arranging the algebraic equation, we have;

y = x - 5

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Answer:

10 times

Step-by-step explanation:

To figure this out, the first thing we will do is to find the LCM (Least Common Multiple). We will do this by making a list of the denominators that we have right now. Right now we have [tex]\frac{20}{4}[/tex] and [tex]\frac{3}{6}[/tex]. We will use 4 and 6 to make a list to find our multiple that is in both lists. (That comes up first)

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32...

Multiples of 6: 6, 12, 18, 24, 30, 36, 42...

Now, we just realized that we have 24 that are in common with both 4 and 6. Now we will multiply both the numerator and denominator by the same number to have the denominator equal 24.

[tex]\frac{20}{4} * \frac{6}{6}[/tex] = [tex]\frac{120}{24}[/tex] & [tex]\frac{3}{6} * \frac{4}{4}[/tex] = [tex]\frac{12}{24}[/tex]

Now that we have [tex]\frac{120}{24}[/tex] and [tex]\frac{12}{24}[/tex]. We will read the question again about how many [tex]\frac{3}{6}[/tex] equal to [tex]\frac{20}{4}[/tex]. Since we have our fractions, we will add [tex]\frac{12}{24}[/tex] multiple times until we get [tex]\frac{120}{24}[/tex].

[tex]\frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} = \frac{120}{24}[/tex]

Therefore, [tex]\frac{3}{6}[/tex] equals to [tex]\frac{20}{4}[/tex] 10 times.

The height of the triangular prism is calculated as: 12 cm.

The volume of a right-triangular prism = 1/2(base of triangular face)(height of triangular face)(length of the triangular prism).

Given the following:

Plug in all the values into the volume formula for the triangular prism:

750 = 1/2(5)(h)(25)

750 = (1 × 5 × h × 25)/2

750 = (125h)/2

Multiply both sides by 2

750 × 2 = (125h)/2 × 2 [multiplication property of equality]

1,500 = 125h

Divide both sides by 125

1,500/125 = 125h/125 [division property of equality]

12 = h

h = 12 cm

Thus, the height of the prism that has a base of the triangle measuring 5cm, a prism length of 25 cm., and a volume of 750 cubic cm is determined as 12 cm.

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Answer:

x = 7

Step-by-step explanation:

To get rid of the x^2, do the opposite of x^2: radicals, or square roots.

x^2 = 121

x = √121

Think about what number can multiply by itself to get 121...

7 • 7 or 7^2 = 121

So, in x^2 = 121, x = 7.

x^2 = 121

x = √121

7 = √121

7 = 7 ✔

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By the degfinition of a congruent triangle, the statement that was made that ∆JOL and ∆IOM are congruent triangles is false.

The two triangles are said to be congruent triangles based on the fact that all of their corresponding sides are the same and said to be equal. Then all of the corresponding sides of the angles would also have an equa; measure.

The definition that I have given above says that the congruent triangles are those that have the same shapes and also have the same sizes. The corresponding sides of the angles and the sides would also be the same.

In the diagram that we have here, we can see that IOM and JOL do not have the same size. Hence the congruent law is not correct. To be congruent it would have to be that the the corresponding sides are the same and there is the equality in the angles of the triangles.

Since this property is not in the shape we would have to conclyde that the statement is wrong. They are not congruent triangles.

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The equivalent expression for −12(8a − 7b) + 8(4x + 3y) is represented  as - 96a + 84b + 32x + 24y

Two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).

Therefore, the equivalent expression of  −12(8a − 7b) + 8(4x + 3y) can be solved as follows:

−12(8a − 7b) + 8(4x + 3y)

open the bracket

−12(8a − 7b) + 8(4x + 3y)

- 96a + 84b + 32x + 24y

Therefore, the equivalent expression of −12(8a − 7b) + 8(4x + 3y) is - 96a + 84b + 32x + 24y

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the answer is x= -48

solve for x by simplifying bith sides of the equation then isolating the variable so the answer is x= -48 your welcome!

The most appropriate choice for cost function and average cost function will be given by -

[tex]\lim_{x \to \infty} \bar{C}(X) = 6[/tex]

The number of flashdrive is very large, the average cost will come down to as low as $6.

What is cost function and average cost function?

Cost function C(x) is a function of x (quantity) which gives the cost of producing x units of the commodity.

Average cost function is the per unit cost of production and can be obtained by dividing the cost function by the quantity of the commodity.

Here,

C(x) = 17000 + 6x

[tex]\bar{C}(x) = \frac{17000 + 6x}{x}\\[/tex]

        [tex]= \frac{17000}{x}+ \frac{6x}{x}\\[/tex]

        =   [tex]\frac{17000}{x}+6[/tex]

[tex]\lim_{x \to \infty} \bar{C}(x)[/tex] = [tex]\lim_{x \to \infty} (\frac{17000}{x} + 6)[/tex]

                    = 0 + 6

                    = 6

This means as the number of flashdrive is very large, the average cost will come down to as low as $6

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Complete Question

The cost​ (in dollars) for manufacturing a particular flashdrive is 17000 + 6x ​, where x is the number of flashdrives produced. Recall from the previous chapter that the average cost per​ flashdrive, denoted by ​, is found by dividing​ c(x) by x. Find and interpret [tex]\lim_{x \to \infty} \bar{C}(X)[/tex]

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The expression 5^8/ 5^2 is equal to  5×5×5×5×5×5. Option C

An algebraic expression can be defined as a  are mathematical expression with a minimum of two terms containing variables, factors, constants and coefficients.

An exponential function is simply defined as a function in which its value is a constant that is raised to the power of a variable or number.

It is a relation or expression that takes the form y = aˣ  in mathematics, where x is a independent variable.

Given the expression as;

⇒ 5^8 / 5²

⇒ 5^8-2

⇒ 5^6

⇒ 5×5×5×5×5×5

Hence, the value is 5×5×5×5×5×5

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The complete question;

Which of the following expressions is equal 5^8/ 5^2 to?

A.5×5×5

B. 1/5×5×5×5

C. 5×5×5×5×5×5

D.3

Answer:

91/8

Step-by-step explanation:

[tex]2\frac{4}{5} *4\frac{1}{6}[/tex]

→ Convert to improper fraction

14/5 × 65/16

→ Simplify

7 × 13/8 = 91/8

The amount of petrol consumed in one hour will be 200 liters.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

In 45 minutes, an automobile uses 150 gallons of gasoline.

Consequently, the rate of gasoline consumption in liters per minute will be

= 150 / 45

= 10 / 3  Liters per minute

We are aware that an hour is made up of 60 minutes.

The amount of gasoline that will be used in an hour will then be

= (10 / 3) x 60

= 10 x 20

= 200 liters

Thus, 200 liters of gasoline will be burned in an hour.

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Answer:

there the vehicle uses 250 litres

Step-by-step explanation:

[tex]150 = 45[/tex]

[tex]x = 75[/tex]

[tex]x = 75 \div 45 \times 150[/tex]

[tex]x = 250litres[/tex]

The graph that correctly represent the experiment that was graphed with the function  t(m) = 0.2m + 6 is the first option with points

given data

t(m) = 0.2m + 6

information deduced from the graph

examining the graph shows that first graph have the intercept as 6

using the points to calculate slope we have

= (y2 - y1) / (x2 - x1 )

= (6 - 0) / (0 - -30)

= 6 / (0 + 30)

= 6 / 30

= 0.2

Since the points are same with the given information we can conclude that the first option has the graph of the given function

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The additional money Ms. May must invest at rate of 4% to get the 5% interest on entire income is $16,000.

For the given question,

The money invested by Ms. May at 7% rate of interest is $8,000.

Let 'x' be the money invested at the rate of 4%.

The interest for the total annual income is 5%.

Thus,

7%of 8,000 + 4% of x = 5%(8,000 + x)

8,000×0.07 + 0.04×x = 0.05(8,000 + x)

On solving,

560 + 0.04x = 400 + 0.05x

0.01x = 160

x = 16,000

Thus, the additional money Ms. May must invest at rate of 4% to get the 5% interest on entire income is $16,000.

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From calculations, we can see that the number of smaller boxes to completely fill the larger one are; 250 boxes

The volume of a cuboid is given by the formula;

Volume = Length * Width * Height

Looking at the given dimensions of the larger box in the cuboid image attached, we can calculate the volume as;

Volume = 50 * 30 * 20

Volume = 30000 cm³

The length , width and height of smaller box are 10 cm, 3 cm and 4 cm respectively. Thus, the volume of smaller box is;

volume = 10 * 3 * 4

volume = 120 cm³

Thus, the number of smaller boxes to completely fill the larger one are;

n = 30000/120

n = 250 boxes

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If each player loses 5 points for each second that he or she finishes after the first-place finisher.  the players in order from greatest to least number of points is: player 4, player 2, player 1, player 4.

Payer 1 :

Player 1 = 3(31) - 5(8)

Player 1 = 93 - 40

Player 1 = 53 points

Player 2 :

Player 2 = 3 (18)

Player 2 = 54 points

Player 3:

Player 3 = 3(24) - 5(3)

Player 3 = 72 - 15

Player 3 =  57 points

Player 4:

Player 4 = 3(27) - 5(6)

Player 4 = 81 -30

Player 4 = 51 points

Now list the players in order from greatest to least number of points.

Player 3 = 57 points

Player 2 = 54 points

Player 1 = 53 points

Player 4 = 51 points

Therefore the player based on ranking is: player 4, player 2, player 1, player 4.

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The equation of the line with the given slope and the y-intercept.

slope = 1/5; y-intercept = -5 is y = 1 / 5 x - 5

The equation of a line can be described as follows:

y = mx + b

where

Therefore,

slope of the line = 1 / 5

y-intercept = - 5

Hence, the equation of the line can be represented as follows:

y = 1 / 5 x - 5

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Lower bound of 2.6 is 2.5

An element of K that is greater than or equal to each element of S is referred to as an upper bound or majorant in mathematics, notably in order theory. To determine a rounded number's upper and lower bounds: Determine the place value of the claimed level of accuracy. By two, multiply this place value. Find the upper bound by adding this amount to the provided value, and the lower bound by deducting this amount from the given value.

Given Data

2.6 to the lower bound

Bound of 2.6 is 2.5 to 2.7

Lower bound of 2.6 is 2.

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The information that a slope of 0.416 represents in the scatterplot is the crime index will increase 416 for every 1000 increment in the population.

The information that an intercept of -669.96 represents in the scatterplot is the value of the crime index when the population is zero.

A graph is a pictorial representation of data. It is used by as many fields that uses data. Graphs helps to make information that the data represents easier to understand the relationship existing within the variables

The graph plots the crime index against the population. The slope is the represents how the crime index will behave with respect to the population. While the intercept is the point where the graph intercept the y axis which represents the crime index

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Answer: 48300

Step-by-step explanation:

23 % of 3.000.000 is [tex]\frac{3.000.000*23}{100} = 690.000[/tex]

So, 690.000 have college degree.

7 % of 690.000 is [tex]\frac{690.000* 7}{100} = 48.300[/tex]

So, 48.300 people have advanced degree.

Completing the checkbook register using the transactions done on the checking account at Really Awesome Bank shows that the ending balance was $298.12.

A checkbook register records transactions with a bank for a checking account.

The transactions of a checking account include withdrawals or payments, deposits, and bank charges if any.

Check   Date        Description          Payments         Deposit,       Balance

No.                                                   Withdrawal (-)     Credit (+)  

           August 1  Initial deposit                                  $200.00      $200.00

101       August 2 Groceries (Shaw’s)      $59.94                               140.06

           August 2 Parking fee                   $12                                    128.06

           August 4 Paycheck                                         465.00         593.06

102     August 6  Electricity                     $47.50                             545.56

103     August 6  Pants                            $70.56                             475.00

104     August 7  Bike, Helmet, Gloves $188.42                             286.58

         August 11  Paycheck                    $287.50                            574.08

        August 11   Savings account        $250.00                            324.08

        August 12  Luch (Red Robin)         $25.96                             298.12

August 2 – $59.94 ($57.91 x 1.035%)

August 4 – $465 ($15.50 x 30)  (15.50/hr for 30 hours)

August 6 – $70.56 (3 x $25.98 x 85% x 1.065)

August 7 – $188.42 ($165 + $35.12 + $10.99 x 85% x 1.05)

August 11 – $287.50 (15.50 x 25 - $100)

August 12 – $25.96 (24.61 x 1.055)

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Answer: 495

Step-by-step explanation:

The missing side length that is represented by x in the triangles that are similar is: B. 5.

According to the similarity theorem, the corresponding side lengths of two triangles that are similar have the same ratio and are therefore proportional to each other.

The two triangles are considered similar to each other, this means that their corresponding side lengths would be proportional to each other and would have the following equal ratio:

45/9 = 25/x

Cross multiply

(45)(x) = (9)(25)

45x = 225

Divide both sides by 45

45x/45 = 225/45

x = 5

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The angles are given below

What is an angle?

An angle is a symbol in Euclidean geometry created by two rays, called the flanks of the angle, that share a common termination, called the vertex of the angle. Angles created by two rays are placed in the plane having the rays. Angles are also generated when two planes overlap. These are termed as dihedral angles. An angle defined by two overlapping curves is the angle of both the rays falling tangent to the individual curves at their place of junction. Angle can also refer to the measurement of an angle or of a rotation. This measurement is the length of a circular arc divided by its radius.

(a) angle a = 112° (alternate angles)

angle b = angle a = 112° (vertically opposite angles)

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From the figure the shaded parts are two: the quadrant part and the sector part. The solution shows that:

area of the shaded part of the quadrant = area of the shaded part of the sector = ( pi * r^2) / 4 - bh/2

given data

ACD is a sector of a circle

From the figure we deduce that arc AC with line O is a quadrant of a circle. Hence the area of the shaded part of the quadrant is:

= area of a circle /4 - area of the right angle triangle

where area of a circle = pi r^2

area of triangle =  1/2 * base * height = bh/2

Area of the shaded part of the quadrant

= ( pi * r^2) / 4 - bh/2

base AO = radius of the circle = height CO

this forms an isosceles triangle and base angles of an isosceles triangle are equal. < A = < C = x

< A + < C + 90 = 180

x = 45 degrees

area of sector

= ∅/360 * pi*r^2  

= (45 / 360) * (pi*r^2)

= (pi * r^2) / 4

area of the shaded part of the sector = area of sector - area of the right angle triangle

= (pi * r^2) / 4 - bh/2

Comparing both sides that shows that the tow shaded parts are equal hence the shaded part of the quadrant is equal to the shaded part of the sector

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2 grams = 2000 milligrams

Conversion between different units of measurement of the same quantity is called as conversion of units.

The process of conversion depends on the specific situation and the precision and accuracy of measurement.

Conversions from one unit to another should be exact, without changing the precision of the first. This is sometimes called soft conversion. It does not involve changing of the physical configuration of the unit being calculated.

'g' is the same as grams and similarly 'mg' is the same as milligrams.

Thus, when asked to convert 2 g to mg, as in the given question,

first multiply the value in grams by the conversion factor '1000'.

So, 2 grams = 2 × 1000 = 2000 milligrams.

A gram is larger unit than a milligram.

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Answer:

This is not an arithmetic sequence because -15 + 7 = -8, not 8.