25 Points

The total cost to rent and drive a car for one day is listed below for two car rental agencies.

Blue Car Rental charges $27.60 to rent a car plus $0.18 per mile driven.
Red Car Rental charges $40.40 to rent a car plus $0.14 per mile driven.
• Write a variable expression that shows the total cost to rent and drive a car for one day at Blue Car Rental. Write a variable expression that shows the total cost to rent and drive a car for one day at Red Car Rental. Define the variable.

• Calculate the total cost at each agency to rent a car for one day and drive it 280 miles. Show all your work.

• Write and solve an inequality that shows how many miles must be driven before the total daily cost at Red Car Rental is less than the total daily cost at Blue Car Rental. Show all your work.

• If Mr. Kao rents a car for one day and drives it 400 miles, which company has a lower total cost?

The cost of a racket and a  ball  is equal to $3.21 and  $4 as per the given data .

As given in the question,

Let us consider cost of a racket is equal to $x

Let us consider cost of a ball is equal to $y.

Equation formed using the given data we have,

3x + 3y = $21.63  ____(1)

3x + 10y = $49.63 ____(2)

Subtract equation (2) from (1) to eliminate x

3x + 10y = $49.63

3x + 3y = $21.63

0x + 7y = $28.00

⇒7y = 28.00

⇒ y = 28 / 7

⇒ y = $4

Substitute the value of y in (1) we get,

3x + 3(4) = 21.63

⇒3x = 21.63 -12

⇒3x = 9.63

⇒ x = $3.21

Therefore, from the given relation the cost of a racket and a ball is equal to $3.21 and $4.00.

The complete question is:

The cost of 3rackets and 3 balls cost $21.63.

The cost of 3rackets and 10 balls is $49.63.

Work out the cost of

a) a ball.

b) a racket

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SCl2 has a Bent molecular geometry and a tetrahedral shape in nature. SCl2 consists of a single Sulfur atom surrounded by two Chlorine atoms. In its most stable state, Sulfur acts as the central atom and forms two covalent bonds with the Chlorine atoms. It also possesses two lone pairs.

The three-dimensional configuration of the atoms that make up a molecule is known as molecular geometry. In addition to bond lengths, bond angles, torsional angles, and any other geometrical factors that affect each atom's location, it also contains the molecule's overall structure. The arrangement of atoms in a molecule in three dimensions is known as molecular geometry, commonly referred to as the molecular structure. A compound's polarity, reactivity, phase of matter, color, magnetism, and biological activity can all be determined by knowing its molecular structure.

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Answer:

55°

Step-by-step explanation:

Assuming the angle is at 180°

180° - 125° = 55°

The simplified form of  (m + 3n + 8)(m + 3n - 8) is  m^2 + 3n^2 + 6mn - 64.

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given,  (x+2)(x+3) = x^2+5x+6.

∴ (m + 3n + 8)(m + 3n - 8).

= m^2 + 3mn - 8m + 3mn + 3n^2 - 24n + 8m + 24n - 64.

= m^2 + 3n^2 + 6mn - 64.

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x = 1+i or x = 1-i are the complex roots of the graph

Below are the steps for determining the complex roots of a graph or curve:

1. Draw a vertical line passing through the vertex of the parabola or curve

2. The value of x where the line intersects the x-axis gives the real part of the root

3.  Draw a horizontal line of height twice the height of the vertex from the x-axis

4. Draw a vertical line from this point of intersection to intersect the x-axis

5. The distance of this point from the real part of the root gives you the imaginary part of the root

(Check the attached image for the labeling)

From the image attached:

Real part of the root: a = 1

Imaginary part of the root: b = 1

Remember: complex root is of the form x = a±bi

Therefore, the complex roots of the graph are x = 1+i or x = 1-i

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Answer:

x= –2

Step-by-step explanation:

y = 2

just substitute for y

2 = x + 4

2 – 4 = x

–2 = x

or x = –2

check

y=-2+4

y=2

so our answer is correct.

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There are 62 number of ways in which classes to these students can be assigned. It can be solved by using the fomula of combination.

What is the formula of combination?

Following is the fomula of combination:

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Here, n is the total objects available and r is the number of object need to choose from n objects.

Let six friends are A, B, C, D, E, and manoj.

Consider all 6 friends are in chemistry class. Hence, number of ways in which it can be is,

[tex]^6C_6[/tex]

Consider 5 friends are in chemistry class. Hence, number of ways in which it can be is,

[tex]^6C_5[/tex]

Consider 4 friends are in chemistry class. Hence, number of ways in which it can be is,

[tex]^6C_4[/tex]

Consider 3 friends are in chemistry class. Hence, number of ways in which it can be is,

[tex]^6C_3[/tex]

Consider 2 friends are in chemistry class. Hence, number of ways in which it can be is,

[tex]^6C_2[/tex]

Consider 1 friend is in chemistry class. Hence, number of ways in which it can be is,

[tex]^6C_1[/tex]

Consider no friend is in chemistry class all are in biology class. Hence, number of ways in which it can be is,

[tex]^6C_0[/tex]

Hence, total number of ways in which classes can be assigned to 6 students is,

[tex]^6C_6+^6C_5+^6C_4+^6C_3+^6C_2+^6C_1+^6C_0=64[/tex]

Now, the number of ways in which mnoj is alon. There are two ways. Either he will be in the chemistry class or he will be in the physics class.

Hence, subtract 2 from 64 to get the answer.

[tex]64-2=62[/tex]

Hence, there are 62 number of ways in which classes to these students can be assigned.

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Answer:

250.32 dollars

Step-by-step explanation:

The given loan amount is equal to 8,700 dollars and the number of years is 3 years and the a p r is equal to 2.31 percentage. The formula for monthly payment is a is equal to p into or divided by 12 into 1 plus or divided by 12 points the whole power and whole divided by 1 plus r divided by 12 points.The whole power n minus 1 in this formula, p is the lown amount and r is the well interest rate and n is the number of payments here. We have the number of years is 3, so the number of payments will be 36 points. Then, by this formula we have the monthly payment: a is equal to 8700 into 0.0231, divided by 12 into 0.0231 divided by 12 plus 1. The whole power 36 whole divided by 0.0231, divided by 12 plus 1, the whole power 36 minus 1, and it will be equal to 250.32 dollars. Therefore, the monthly payment is equal to 250.32 dollars.

Answer:

1 cm = 20 km

Step-by-step explanation:

Starting with what we know:

2/5 cm = 8 km

Need to change the left side to a 1. So multiply both sides by 5/2

5/2 × 2/5 = 8 × 5/2

1 cm = 40/2 km

1 cm = 20 km

Answer: Tyler has 22 cards

Step-by-step explanation:

To begin, we know that Morgan has 12 less than 5x Tyler's cards, so...

12+98=110

Now that we had 110, we then read that it is the PRODUCT of 5 and the number that Tyler has, so we will show that algebraically.

110=5x

Now, divide 110 by 5 to find X.

110/5=22

Tyler has 22 cards.

Answer:

y = (-2/3)x + (19/3)

Step-by-step explanation:

3x - 2y = 5

-2y + 3x = 5

      -3x        -3x

-------------------------

-2y = -3x + 5

-2      -2    -2

---------------------

       3            5

y = -------x - -------

       2            2

                            -2

Perpendicular:  -------- x

                             3

                     -2

(2, 5);  m =  --------

x₁ y₁               3

y - y₁ = m(x - x₁)

y - 5 = (-2/3)(x - 2)

y - 5 = (-2/3)x + (4/3)

   +5                 +5

--------------------------------

y = (-2/3)x + (19/3)

I hope this helps!

The density of the rock with a mass of 39.78 g and volume 12.45 cm³ is 3.2 g/cm³.

Density is simply the mass of a unit volume of a material substance.

It is expressed mathematically as;

p = m / v

Where m is mass and v is volume

Given the data in the question;

Plug the given values into the above formula and solve for p.

p = m / v

p = 39.78g / 12.45 cm³

p = 3.2 g/cm³

Therefore, the density of the rock is approximately 3.2 g/cm³.

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Answer:0.56

Step-by-step explanation:

First multiply $3.92 from 1 pound

Next dived the answer by 7 which will give you 0.56

Investigating an outlier that a data analyst has found is the best course of action.

To find the solution to a problem or provide an answer to a question, a data analyst gathers, purifies, and analyzes data sets.

They work in a variety of fields, including as government, business, finance, law enforcement, and science.

Depending on the question you're attempting to answer, data analysis might take on various shapes.

More information on different data analysis types is available here.

In a nutshell, descriptive analysis explains what happened, diagnostic analysis explains why it occurred, predictive analytics offers future projections, and prescriptive analysis generates actionable recommendations for what to do.

Hence, Investigating an outlier that a data analyst has found is the best course of action.

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Answer:

(10,6) and (-5, -3)

Step-by-step explanation:

The slope of the line is given by rise/run between (0,0) and (5,3)
Rise = y2 - y1 = 3 - 0 = 3

Run = x2 - x1 = 5 - 0 = 5

Slope m 3/5

Slope intercept form of a line is

y = mx + b

where m is the slope and b is the y-intercept

Since the line passes through (0,0) the y-intercept is 0

So we get

[tex]y = \dfrac{3}{5}x + 0 \\\\or\\\\y = \dfrac{3}{5}x[/tex]

This means for any x value, the corresponding y value should be 3/5th of that x value

Only the first and third choices have this requirement fulfilled

The shadow of the ball moving over the ground at 150 feet per second after 1 second.

How can I determine the shadow of the ball's speed?

Assuming the ball drops the distance indicated by this sentence:

S = 16t²

Additionally, the height (h) of the ball's shadow one second later is provided by

h = 30 - S

The term for the shadow of the ball would then be as follows:

OX/30 = (20 + XQ)/30 = XQ/h

30XQ = 20h + hXQ

20h = 30XQ - hXQ

20h = (30 - h)XQ

XQ = 20h/(30 - h)

Substituting the value of h, we have:

XQ = 20(30 - S)/(30 - 30 - S)

Substituting the value of S, we have:

XQ = 20(30 - 16t²)/(30 - 30 - 16t²)

XQ = 20(30 - 16t²)/16t²

XQ = (600 - 320t²)/16t²

XQ = 600/16t² - 320t²/16t²

XQ = 600/16t² - 20

Differentiating with respect to t, we have:

d(XQ)/dt = 600/16t² - 20

d(XQ)/dt = 600 (-64t/(16t²)²)

d(XQ)/dt = 600 (-64t/256t⁴)

d(XQ)/dt = 600 (-0.5/2t³)

d(XQ)/dt = -300/2t³

Then,

At t = 1, we have:

Speed = 300/2(1)

Speed = 150 ft/s.

That is,

After one second the ball's shadow was travelling over the ground at a speed of 150 feet per second.

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Answer:

5 hours

Step-by-step explanation:

To figure this out we will do the total she earned yesterday divided by the hours she worked. So, 84/7=12. So know we know how much she earns in an hour, $12. So if she is earn $60 today then we should do 60/12 to figure out how many hours she worked. 60/12=5. So she worked 5 hours.

I hope this helps!!!

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The required function of the line would be y = 2x + 1.

A coordinate plane is a two-dimensional plane formed by the intersection of two number lines. One of these number lines is a horizontal number line called the x-axis and the other number line is a vertical number line called the y-axis.

The slope-intercept form is one rule to represent linear function rules. f(x)=mx + b is sometimes used. In any scenario, m and b describe the line's overall features. The slope is denoted by m, while the y-intercept is denoted by b.

According to the given figure,

We clearly see that the coordinates of the y-intercept would be (0, 1).

The value of the x-coordinate is 1 when y-coordinate is 3.

Here the line passes through points (0, 1) and (1, 3).

Let the required linear function would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x₂ -x]

x₁ = 0, y₁ = 1

x₂ = 1, y₂ = 3

⇒ y - y₂ = (y₂ - y₁)/(x₂ -x₁ )[x -x₂]

⇒ y - 3 = (3 - 1)/(1 - 0 )[x -1]

⇒ y - 3 = (2)[x -1]

⇒ y - 3 = 2x - 2

⇒ y = 2x - 2 + 3

⇒ y = 2x + 1

Therefore, the required function of the line would be y = 2x + 1 .

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A good rule of thumb for sizing a struct in c/c assuming that the struct is optimally set up is count all the bytes of the data in the struct.

Rule:

In math rule refers a numerical pattern is a sequence of numbers that has been created based on a formula or rule called a pattern rule

Given,

Here we need to find a good rule of thumb for sizing a struct in c/c assuming that the struct is optimally set up.

According to the rule of thumb, the count all the bytes of the data in the struct.

and then we need to find the nearest power of 2, 4 or 8 based on the largest Data Type in your struct.

So, if the total number of bytes is larger than that power, then the struct will be the next power in size.

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Answer:

33

Step-by-step explanation:

-4(-6) + 9

24 + 9

33

The sample proportion of persons with credit card debts of further than $2,000 has a distribution that is roughly normal;

μ = 0.27 and σ = 0.022.

According to a research conducted in one town, the percentage of persons living there had credit card debt of at least $2,000:

p = 27% = 0.27.

An adult sample from the entire city was gathered: n = 400 adults.

The following two requirements should be used to determine the whether sample is adequate before obtaining a sampling distribution of the probability value p:

       400 x 0.27  = 108

       108 ≥ 10

And,

      400(1 - 0.27)  ≥ 10

      292  ≥ 10

We know that the as being p is nearly normally distributed the by suing  "Central limit theorem."

Mean of a sample proportion

μ = P = 0.27

The standard deviation's sample proportion P:

σ = √(p(1 - p)/n

σ = √(0.27(1 - 0.27)/400

σ = 0.022

Since the sample proportion of persons with credit card debts of further than $2,000 has a distribution that is roughly normal;

μ = 0.27 and σ = 0.022.

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Answer:

y = 5 + 3/5x

Step-by-step explanation:

We need to isolate y to get it in slope-intercept form. Let's subtract 12x from both sides, which gives us [tex]-20y=-100-12x[/tex]. Then, we can negate both sides, and then divide by 20, which results in [tex]y = (100+12x)/20[/tex], which we can further simplify to [tex]y=5 + 3/5x[/tex], which gives us our answer.

In linear equation, the solution of equations is ( -2 , 1)

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                             Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

y = 2x + 5

y = 1/2x + 2

the solution of equations is ( -2 , 1)

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The function which describes the arithmetic sequence is f(x) = −0.6x + 8.6.

The correct answer option is option D

Given the sequence:

8, 7.4, 6.8, 6.2, 5.6, …

Check all the options

Where,

x = number of term

A. f(x) = 0.6x + 8

When x = 1

f(x) = 0.6x + 8

= 0.6(1) + 8

= 0.6 + 8

= 8.6

B. f(x) = 0.6x + 8.6

When x = 1

= 0.6(1) + 8.6

= 0.6 + 8.6

= 9.2

C. f(x) = −0.6x + 8

When x = 1

= -0.6(1) + 8

= 0.6 + 8

= 8.6

D. f(x) = −0.6x + 8.6

When x = 1

= -0.6(1) + 8.6

= -0.6 + 8.6

= 8

Hence, f(x) = −0.6x + 8.6 is the function which describes the sequence.

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It has been suggested that 4% of all cars on the freeway are going 70 mph. If 4 cars are examined, the probability that at least 1 is going 70 miles per hour is 0.151.

A probability is a numerical representation of the likelihood or possibility that a particular event will occur. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Here, it is said that 4% of all vehicles on the roadway are going more than 70 mph.

P(speed excess of 70 mph) = 0.04. Radar is used to determine the speeds of four random cars. Then, n = 4. Then, X = the number of cars going over 70 mph.

Then, the probability that at least one car is going over 70 mph

= P(x = 1, 2, 3, 4)

= 1 - P(x = 0)

= [tex]1 - 4_{C}_{0} (0.04)^{0} (1 - 0.04)^{4-0}[/tex]

= 1 - 0.849

= 0.151

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The family of all least polynomials with roots at - 4, - 3, 0, 2 is represented by the polynomial y = a · (x + 4) · (x + 3) · x · (x - 2), where a is the lead coefficient.

Herein we must determine the family of all least polynomials whose roots must be the real numbers - 4, -3, 0, 2. Polynomials are algebraic expressions, whose factor form is described below:

y = a · Π (x - rₙ), for n = {1, 2, 3, 4, ..., m - 1, m}

Where:

In accordance with all these assumptions and definition, the function is defined below:

y = a · (x + 4) · (x + 3) · x · (x - 2)

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The height of the object after 1.00 seconds launched is 24 feet.

Quadratic function is a function where the maximum power of x variable is 2. Simply you can write quadratic function as:

y = ax^2 + bx + c

y is height in feet and x is time in second.

Known 2 conditions from the question:

From second condition (0 feet in 0 second), we can substitute 0 both in y and y:

y = ax^2 + bx + c

0 = a(0)^2 + b(0) + c

0 = 0 + 0 + c

0 = c

And this, we know that the constant (c) of the function is 0.

Just substitute c with 0 in previous function.

y = ax^2 + bx + c

y = ax^2 + bx + 0

y = ax^2 + bx

From first condition (25 feet in 1.25 seconds), we can substitute x with 1.25 and y with 25:

y = ax^2 + bx

25 = a(1.25)^2 + b(1.25)

25 = 1.56625a + 1.25b

Maximum/minimum point of quadratic function can be found with dy/dx = 0, dy/dx is differential:

y = ax^2 + bx

dy/dx = 2ax + b

0 = 2ax + b

0 = 2a(1.25) + b

0 = 2.5a + b

-2.5a = b

After we know the ratio a and b, we can substitute b with -2.5a in previous equation:

25 = 1.5625a + 1.25b

25 = 1.5625a + 1.25(-2.5a)

25 = 1.5625a - 3.125a

25 = -1.5625a

15/-1.5635 = a

a = 15/-1.5625

a = 16

We got a = 16. Then we just substitute it in a b ratio equation:

b = -2.5a

b = -2.5(-16)

b = 40

After we know a, b, c, just substitute that three numbers in the function:

y = ax^2 + bx + c

y = -16x^2 + 40x

So, the function can be used in launching of the object is y = -16x^2 + 40x.

Where is the object in 1.00 seconds after launched? Just substitute x with 1.

y = -16x^2 + 40x

y = -16(1)^2 + 40(1)

y = -16 + 40

y = 24 feet

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The number of sequence of 0s and 1s of length 19 are there that begin with a 0, end with a 0 are 65 .

In the question ,

After any particular 0, the next 0 in sequence must appear exactly 2 or 3 positions down.

In this case, we start at position 1 and end at position 19,

that is , we move a total of 18 positions down the line.

So , we must add the series of 2s and 3s to get 18.

There are several number of ways to do this:

Case 1: nine 2s - there is only 1 way to arrange them.

Case 2: two 3s and six 2s - there are ⁸C₂ ways = 28 ways

Case 3: four 3s and three 2s - there are ⁷C₄ ways = 35 ways

Case 4: six 3s - there is only 1 way to arrange them.

So , the number of sequences is = 1 + 28 + 35 + 1 = 65 .

Therefore , the total number of sequence is = 65 .

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Answer:

x-intercept: (7/5, 0)

y-intercept: (0, 14)

Step-by-step explanation:

The x intercept is when y is equal to 0.

1/2(0) + 5x = 7

5x = 7

x = 7/5

Put this into point form, where x is 7/5 and y is 0.

(7/5, 0)

The y intercept is when x is equal to 0.

1/2y + 5(0) = 7

1/2y = 7

y = 14

Put this into point form, where x is 0 and y is 14.

(0, 14)