Alonso's family rented a car when they flew to
Orlando for a 4-day vacation. They paid $39
per day and $0.09 for each mile driven. How
much did it cost to rent the car for 4 days and
drive 350 miles, not including tax?

From the given graph the value of μ is 530 and the value of σ is 15.

In the Normal Curve the value at which the shape of the graph is highest is called it's mean(μ) and the value on the left of mean is μ-σ and the value on the right of the mean is μ + σ .

In the Given question

the shape of the graph is highest at 530,

hence the value of mean(μ) = 530.    ....(i)

we know that the value on the left of mean is μ-σ .....(ii)

From the graph the value to the left of mean(μ) is 515.    ...(iii)

Equating equation (ii) and (iii) we get ,

μ-σ = 515

Substituting the value of  μ from equation (i) we get ,

530 - σ = 515

σ = 530 - 515

σ = 15

Therefore , From the graph the value of μ is 530 and the value of σ is 15.

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The missing side of the figure if the perimeter is 35 2/3 cm, is calculated as: 10.9 cm.

The perimeter of a figure is the total length surrounding the figure.

We are given that the figure shown below has a perimeter of 35 2/3 cm, which means all the total length of all its sides equals 35 2/3 cm.

To find the missing length, sum all the given lengths and subtract it from the perimeter of the figure.

Sum of all the given lengths =  4 3/4 + 3 1/2 + 1 1/3 + 1 1/3 + 3 1/2 + 9.25 + 6.6 = 4.75 + 2.3 + 1.3 + 1.3 + 2.3 + 9.25 + 6.6

Sum of all the given lengths =  27.8 cm

The missing side = 38 2/3 - 27.8 = 38.7 - 27.8

The missing side = 10.9 cm.

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Answer: 7x-6

Step-by-step explanation:

P=perimeter. L=length. W=width

P=2L+2W

P=2(x+1)+2(2.5x-4)

P=2x+2+5x-8

P=2x+5x+2-8

P=7x-6

Step-by-step explanation:

sadly you skipped the key word in the question.

should we check under what circumstances plan A costs more than plan B ? or costs less than plan B ?

so, I don't know which inequality to solve.

but I can tell you the facts, and you need to pick the right direction for your answer.

cost of plan A for used minutes m :

cA(m) = 1.9 + 0.06m

plan B

cB(m) = 0 + 0.07m = 0.07m

to find the intersecting point, where both plans cost the same :

1.9 + 0.06m = 0.07m

1.9 = 0.01m

m = 1.9 / 0.01 = 190 minutes

up until 190 minutes plan B is cheaper.

if there are more than 190 minutes, than plan A is cheaper.

so,

m < 190 B is cheaper

m > 190 A is cheaper

m = 190 A and B cost the same

The equation that represents Diego's cash flow is cash flow = $3,000-$2,715.

Cash flow is the difference between cash inflows and cash outflows. Cash inflow are additions to the cash flow. An example of cash inflow is monthly income. Cash outflow would reduce the cash flow. An example of cash inflow is expenses.

Cash inflow = income - expense

$3,000 - $2,715

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Answer:

If your number was 250,000,000,000

The amount of social security would be 52,000,000,000

Step-by-step explanation:

Answer:

Step-by-step explanation:

100 more than 365 is equal to 65more then

we can solve with an equation

100 + 365 = 65 + x

100 + 365 - 65 = x

465 - 65 = x

400 = x

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

check

100 + 365 = 65 + 400

465 = 465

the answer is good

Answer: f'(x)=6x

Step-by-step explanation:

f'(x)= lim (h->0) [f(x+h) - f(x)] /h

f'(x)= lim (h->0) [3(x+h)^2 + 1 - (3x^2 + 1)] /h

f'(x)= lim (h->0) [3(x^2+2hx+h^2) + 1 - 3x^2 - 1] /h

f'(x)= lim (h->0) [3x^2+6hx+3h^2 - 3x^2] /h

f'(x)= lim (h->0) [6hx+3h^2] /h

f'(x)= lim (h->0) [6x+3h]

f'(x)= [6x+3(0)]

f'(x)=6x

Answer:

The width is 3 feet and the height is 6 feet.

Step-by-step explanation:

Answer:

1, 0.75, 1.25, 3, 0

Step-by-step explanation:

To find the value of the function, we find the y coordinate of the point with the given x value.

The solution to each division problem is;

1) 4

2) 2

3) 3

4) 3

5) 3

1) We are given the expression;

(5 * 3) * ___ = 60

To get the blank answer, we will divide both sides by (5 * 3) to get;

60/(5 * 3) = 4

2) We are given the expression;

4 *( ___ * 9) = 72

To get the blank answer, we will divide both sides by (4 * 9) to get;

72/(4 * 9) = 2

3) We are given the expression;

7 * (2 * ___) = 42

To get the blank answer, we will divide both sides by (7 * 2) to get;

42/(7 * 2) = 3

4) We are given the expression;

(___ * 5) * 5 = 75

To get the blank answer, we will divide both sides by (5 * 5) to get;

75/(5 * 5) = 3

5) We are given the expression;

(3 * 3) * ___ = 27

To get the blank answer, we will divide both sides by (3 * 3) to get;

27/(3 * 3) = 3

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The simplified value of the expression given as 3^2018 + 3^2015 / 3^2017 + 3^2016 is 7/3

The expression is given as:

3^2018 + 3^2015 / 3^2017 + 3^2016

Factor out 3^2015 in the expression

So, we have

3^2015(3^3 + 1)/3^2015(3^2 + 3)

Cancel out the common factor

(3^3 + 1)/(3^2 + 3)

Evaluate the exponents

(27 + 1)/(9 + 3)

This gives

28/12

Simplify

7/3

Hence, the simplified value of the expression given as 3^2018 + 3^2015 / 3^2017 + 3^2016 is 7/3

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There are 5548 students majoring in computer science.

This problem is related to percentage we have to calculate the number of students with the percentage given. After multiplying the percent given to the total number of students we will get the required number of students.

Given that the total number of students in the university class is =7600

Also 73% of students are majoring in computer science.

Number of students majoring in computer science is = (73/100) of 7600

                                                                                   = 73×76

                                                                                   = 5548 students

So, the total number of students majoring in computer science is 5548.

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Answer:

5250.

Step-by-step explanation:

Consistent = Population of deer increases 5% each year.

This year = 5000

105% of 5000 = 5250

Answer:

x=6

Step-by-step explanation:

2(x+3)-8=10

use 2 to multiply the one in the bracket

(2x+6)-8=10

group like terms

2x-2=10

send all constant terms to one side of the equation

2x=10+2

2x=12

divide both side by the coefficient of x

2x/2=12/2

x=6

Answer:

f(x) = $65x + $50

f(4.5) = $342.5

  The real-world interpretation of f(4.5) would be an emergency service call where they have to work for 4.5 hours.

Step-by-step explanation:

         We will write a function where x is the hours. Since you pay $65 for every hour, we will multiply $65 by x. Next, there is a fee of $50 so we will add that onto the end.

     f(x) = $65x + $50

         Now, we will plug 4.5 into the function for x and solve.

     f(x) = $65x + $50

     f(4.5) = $65(4.5) + $50

     f(4.5) = $292.5 + $50

     f(4.5) = $342.5

         The real-world interpretation of f(4.5) would be an emergency service call where they have to work for 4.5 hours.

The value of my car one year ago was $35,714.3

INTEREST FORMULA: The interest formula includes two types of interests - simple interest and compound interest. Interest is the cost a borrower pays a lender for a loan. This additional sum, or the interest, must be paid in addition to the loan itself. The compound interest formula and the simple interest formula are both discussed in the interest formula.

Present value of the car = A = $25,000

Depreciation rate = r = 30% per annum

Time = t = 1 year

Let the initial value be p

We know the formula, A = P(1 – r/100)^t

$25,000 = P [1 – 30/100] ^1

$25,000 = P (7/10)

P = (25,000 * 10) / 7

P = $35,714.3

Therefore, One year ago, my car's value was worth $35,714.3.

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Using the Empirical Rule, the percentages are given as follows:

a) 68%.

b) 5%.

c) 0.15%.

It states that, for a normally distributed random variable, approximately:

For item a, 80 and 120 are within one standard deviation of the mean, hence:

68% of people has an IQ score between 80 and 120.

For item b, the bounds are within two standard deviations of the mean, hence 5% of the observations are outside this interval, that is:

5% of people has an IQ score less than 60 or greater than 140.

For item c, 160 is three standard deviations above the mean. Considering the symmetry of the normal distribution, 0.3/2 = 0.15% of people has an IQ score greater than 160​?.

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7y+2=3x-5 is the given equation. Finding the point that does not lie on the specified line, 7y+2=3x-5, is the next step.

To determine whether or not the point meets the provided equation, we will simply enter in the supplied point.

Check for (2,-1/7)

Connect it to 7y+2=3x–5.

7(-1/7)+2=3(2)-5

-1+2=6-5

1=1

Which is correct; as a result, this point is on the line 7y+2=3x-5.

Verify (3,-2/7)

Connect it to 7y+2=3x–5.

7(-2/7)+2=3(3)-5

-2+2=09-5

1=4

Which is False; as a result, the supplied line 7y+2=3x-5 does not include this point.

Connect it to 7y+2=3x–5.

7(-1)+2=3(0)-5

-7+2=0-5

-5=-5

Which is correct; as a result, this point is on the line 7y+2=3x-5.

Verify (1, -4, 7)

Connect it to 7y+2=3x–5.

7(-4/7)+2=3(1)-5

-4+2=3-5

-2=-2

This is why I'm making this point

lies on the line 7y+2=3x-5 that is presented.

Verify (-1, -10/7)

Connect it to 7y+2=3x–5.

7(-10/7)+2=3(-1)-5

-10+2=-3-5

-8=-8

Which is correct; as a result, this point is on the line 7y+2=3x-5.

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Brief The Question Please, Thank You

Answer:

Step-by-step explanation:

Given function:

[tex]y=\dfrac{x-3}{x^2-2x-3}[/tex]

The domain is the set of all possible input values (x-values).

Factor the denominator of the function:

[tex]\implies y=\dfrac{x-3}{(x-3)(x+1)}[/tex]

The domain of the given function is restricted as the function is undefined when the denominator equals zero, and when both the numerator and denominator equal zero.  

Therefore, the function is undefined when x = -1 and x = 3.

Therefore, the domain is (-∞, -1) ∪ (-1, 3) ∪ (3, ∞).

The range is the set of all possible output values (y-values).

As the domain is restricted, the range is also restricted.

Therefore, the range is (-∞, 0) ∪ (0, ¹/₄) ∪ (¹/₄, ∞).

A function f(x) is continuous when, for every value [tex]c[/tex] in its domain:

[tex]\text{$f(c)$ is de\:\!fined \quad and \quad $\displaystyle \lim_{x \to c} f(x) = f(c)$}[/tex]

Point Discontinuity (holes): When a rational function has a factor with an x that is in both the numerator and the denominator.

Therefore, there is a point discontinuity at x = 3.

Infinite Discontinuity: A vertical asymptote occurs when the denominator of a rational function is zero. This is considered an infinite discontinuity when the graph exists on both sides of the asymptote.

Therefore, there is an infinite discontinuity at x = -1.

Stationary points occur when the gradient of a graph is zero.

Therefore, to find the x-coordinate(s) of the stationary points of a function, differentiate the function, set it to zero and solve for x.

[tex]\begin{aligned}y & =\dfrac{x-3}{x^2-2x-3}\\\\\implies \dfrac{\text{d}y}{\text{d}x} & = \dfrac{(x^2-2x-3)(1) - (x-3)(2x-2)}{\left(x^2-2x-3\right)^2}\\\\ & = \dfrac{(x-3)(x+1)-(x-3)(2x-2)}{\left((x-3)(x+1)\right)^2}\\\\& = \dfrac{(x-3)[(x+1)-(2x-2)]}{(x-3)^2(x+1)^2}\\\\ & = \dfrac{(x-3)(-x+3)}{(x-3)^2(x+1)^2}\\\\ & = \dfrac{-(x-3)^2}{(x-3)^2(x+1)^2}\\\\& = \dfrac{-1}{(x+1)^2}\end{aligned}[/tex]

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & = 0\\\implies \dfrac{-1}{(x+1)^2} & = 0\\ -1 & \neq 0\end{aligned}[/tex]

Therefore, there are no stationary points and no minimum/maximum points.

[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}} \implies \dfrac{\text{d}y}{\text{d}x} > 0[/tex]

[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies \dfrac{\text{d}y}{\text{d}x} < 0[/tex]

Increasing

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & > 0\\\implies \dfrac{-1}{(x+1)^2} & > 0\\ \dfrac{1}{(x+1)^2} & < 0\\ \textsf{If $\dfrac{1}{a} < 0$ then $a < 0$}:\\(x+1)^2 & < 0\\ \textsf{As $(x+1)^2\geq 0$, no solution.}\end{aligned}[/tex]

Decreasing

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & < 0\\\implies \dfrac{-1}{(x+1)^2} & < 0\\ \dfrac{1}{(x+1)^2} & > 0\\ \textsf{If $\dfrac{1}{a} > 0$ then $a > 0$}:\\(x+1)^2 & > 0\\ \end{aligned}[/tex]

[tex]\textsf{For $a^n > 0$, if $n$ is even then $a < 0$ or $a > 0$}[/tex]

[tex]\implies x+1 < 0 \implies x < -1[/tex]

[tex]\implies x+1 > 0 \implies x > -1[/tex]

Combine the intervals:

(-∞, -1) ∪ (-1, ∞)

Therefore:

[tex]\textsf{A function is \underline{even} when $f(x) = f(-x)$ for all $x$.}[/tex]

[tex]\textsf{A function is \underline{odd} when $-f(x) = f(-x)$ for all $x$.}[/tex]

As there is no symmetry about the y-axis (even symmetry) and no origin symmetry (odd symmetry), the symmetry of the function is neither.

Answer:

Domain: (-∞, -1) ∪ (-1, 3) ∪ (3, ∞)

Range: [0, ∞)

Continuity: Point discontinuity (hole) at x = 3.

Infinite discontinuity (vertical asymptote) at x = -1.

None

Decreasing function: (-∞, -1) ∪ (-1, ∞)

Symmetry: Neither

The percent of the days in month that the cash will run out is given as: 23.33%. See the computation below.

Money put in ATM per day=$7750

We have to find the percent of days in a month you should expect to run out of cash.

From the given information

There are 7 days in which you run out cash more than $7750

Assuming that the total number  of days in a month = 30

Hence, we can arrive at the above value by saying:
(Corresponding days/Total number of Days) * 100

From we above we state:

(7/30) * 100

= 23.33%

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Answer:

y= -3x-4.

Step-by-step explanation:

1) the slope-interception form is:

y=slope*x+i, where i - interception;

2) using the given two points it is possible to calculate the slope:

[tex]slope=\frac{5+1}{-3+1}=-3;[/tex]

then the required equation has the form:

y=-3x+i;

3) in order to calculate the 'i', it is enough to substitute the coordinates of the one point into this form of the required equation:

-1=-3*(-1)+i; ⇒ i=-4.

4) finally, the required equation is:

y=-3x-4.

P.S. the suggested way is not the shortest one.

Answer: Parentheses

Step-by-step explanation: Parentheses always go first because if you look at the work PEMDAS, P= parentheses, E= exponents, M= Multiplication, D= division, A= addition, and S= subtraction.

Answer:

4cm

Step-by-step explanation:

the ratio of the two scales is 100,000:300,000 which simplifies to 1/3

1/3 x 12 =4