Bob has decided to make his move to his new house easier, so he is going to rent a truck to get it all moved in one trip. He is looking at two truck rental companies. U-Haul rents a 32 ft truck for $19.95 plus 49 cents per mile driven. The formula to calculate the cost with U-Haul is C = 19.95 + 0.49x, where x represents the number of miles driven. Penske rents a truck for 69 cents per mile but has no extra fees. The formula to calculate costs for Penske is C = 0.69x, where x represents miles driven. How many miles indicate that the cost of renting a truck from U-Haul is equal to the cost of renting a truck from Penske?

According to the given table the line of best fit is

f(x)=4.54x+77.84

The term "line of best fit" describes a line that passes across a scatter plot of data points and best captures their connection. Statisticians often utilise regression analysis software or manual computations to arrive at the geometric equation for the line using the least squares approach. A straightforward linear regression study of two or more independent variables will provide a straight line. 

Hence, as asked by the question we need to find the time at which the tempurature will become 100°C.

To find that let us put f(x)=100 and find out the value of x for which it is satisfied.

4.54x+77.84=100

⇒[tex]x=\frac{100-77.84}{4.54}=4.88[/tex]

⇒x≈5

Therefore the time at which the tempurature is 100°C is 5 minutes.

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Answer:

Inequality:  x + 6 ≤ 24

Solution:  x ≤ 18

Step-by-step explanation:

Plus:  "+" →  to add something to something else

Less than or equal to:  "≤" → the expression on the left side of the inequality sign is smaller than the expression on the right side of the sign.

Let x be the unknown number.

A number plus 6 is less than or equal to twenty-four:

x + 6 ≤ 24

To solve the found inequality, subtract 6 from both sides:

⇒ x + 6 - 6 ≤ 24 - 6

⇒ x ≤ 18

Therefore, the solution to the inequality is x ≤ 18.  The unknown number x can be any real number equal to or less than 18.

No be n

Solve

Solution set

Answer:

15cd(1 + 2cd)

Step-by-step explanation:

greatest common factor is 15cd

[tex]15cd*1 + 15cd*2cd\\= 15cd(1 + 2cd)[/tex]

The solution for the system of equations is: (99/13, 150/13)

Given the two expression 2/3x+3/5y=12 and 5/2y-3x=6

We have to find solution of two given expression.

To find the value of x, we have to eliminate y by making y the subject of formula in any of the equations.

Multiply equation A by 5/3 t.o get,

5/3(2/3x) + 5/3(3/5y) = 5/3(12)

10/9x + y = 20

y = 20 - 10/9x

substituting for y into equation b, we have:

5/2(20 - 10/9x) - 3x = 6

50 - 25/9x - 3x = 6

52/9x = 44

52x = 396

The expression that gives the value of x is: 52x = 396

Hence, x = 396/52 = 99/13

y = 20 - 10/9(99/13) = 20 - 110/13 = 150/13

Hence The solution for the system of equations is: (99/13, 150/13)

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Answer:

-6/11 goes with -1/2

-7/9 goes with -3/4

-3/13 goes with -1/4

Step-by-step explanation:

6/11 is close to 6/12 which is the same as 1/2, so -6/11 goes with -1/2

7/9 is close to 6.75/9 which is 3/4, so -7/9 is close to -3/4

3/13 is close to 3/12 which is the same as 1/4, so -3/13 goes with -1/4

The probability that exactly 4 are cured from 7 dolphins is 0.0128

Probability is the likeliness of an event to occur and it has a range of 0 to 1, where 0 means unlikely and 1 indicates certainty of the event to happen.

It is given that the 92% of all the dolphins are cured of an ear infection ,When treated with an antibiotic

If there are total dolphins given as 7

On the basis of given data

The dolphin that cannot be cured is given by

1 - p = 1 - (92/100) = 0.08 = 8/100

q = (8/100)
n= 7

r = 4

Therefore by Binomial Distribution

[tex]P = ^nC_r p^r q^{n-r}[/tex]

Putting the values

[tex]P = ^7C_4 (\dfrac{92}{100})^4 (\dfrac{8}{100})^{7-4}[/tex]

[tex]P = \dfrac{7!}{4! \;3!} (\dfrac{92}{100})^4 (\dfrac{8}{100})^{7-4}[/tex]

P =  0.0128

Therefore the probability is 0.0128.

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Answer: [tex]y=x-9[/tex]

Step-by-step explanation:

To find the inverse of a function you must first swap the places of x and y

[tex]x=y+9[/tex]

Now solve for y

Step 1: Flip the equation.

[tex]y+9=x[/tex]

Step 2: Subtract 9 from both sides.

[tex]y+9-9=x-9\\y=x-9[/tex]

We can subtract the function that represents the cost in 2000 from the function that represents the cost in 1990.

Doing this gives us [tex](-20t^{2}+1000)-(-10t^{2}+1500)=\boxed{-10t^{2}-500}[/tex]

In solving minimum and maximum problems, result we are looking for would be the constant, k.

When looking for the minimum functional value, we are looking for the constant, k because it can be thought of as the absolute minimum value.

An open parabola would then have k as the maximum functional value which means that the constant k is the value being sought.

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Answer:

false

Step-by-step explanation:

the answer is x=70

Answer:

In standard form thats 4.4024

In standard form, 4+0.4+0.0024 can be written as 4.4024

Concept: Any number we can write as a decimal number, between 1.0 and 10.0, multiplied by 10, is said to be in the normal range. 1.23 × 108;

If you look closely, 1.23 is a decimal number between 1.0 and 10.0 so we have a standard form 123,000,000 as 1.23 × 108.

Given: 4+0.4+0.0024

In this case,4 is the integral value and 0.4 is at the first decimal place followed by 0.0024 at the third and 4th decimal place so combining them all together and writing them in standard form we get,4.4024

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

1) Cancel [tex]x^5[/tex].

[tex]\frac{9y^{16} }{45y^4}[/tex]

2) Take out the constants.

[tex]\frac{9}{45} \times\frac{y^{16} }{y^4}[/tex]

3) Simplify [tex]\frac{9}{45}[/tex] to [tex]\frac{1}{5}[/tex].

[tex]\frac{1}{5} \times\frac{y^{16} }{y^4}[/tex]

4) Simplify.

[tex]\frac{y^{16} }{5y^4}[/tex]

5) Use Quotient Rule: Use Quotient Rule: [tex]\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}[/tex].

[tex]\frac{{y}^{16-4}}{5}[/tex]

6)  Simplify [tex]16-4[/tex] to [tex]12[/tex].

[tex]\frac{y^{12} }{5}[/tex]

distance = speed * time

the first bus speed = x

second bus = x - 12

the sum of distance = 765 miles

first distance = 6x

second distance = 6 (x -12)

6x + 6(x-12) = 765

x + x -12 = 127.5

2x = 139.5

x = 69.75 mi/h which is the faster bus

the second bus speed = 57.75 mi/h

Th equation that can be used to find the umber of minutes Teri ran is m + 2 = 28 minutes.

Addition is a mathematical operation that is used to determine the sum of two or more numbers.

The total minutes run by Julie = minutes ran by Teri + 2

28 = m + 2

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Answer:

C=55m + 30

Step-by-step explanation:

You would multiply 55 by the number of months so you'd get 55m, and since 30 is a one time fee you would just add 30 to your monthly payment.

Answer:

1. F

2. F

3. T

4. F

5. F

6. T

7. T

8. F

9. F

10. T

Step-by-step explanation:

1. For the rays to be opposite, they need to have the same starting point and go in different directions. Rays AP and BP use Point A and Point B, respectively, for their starting points.

2. They do not lie on the same line.

3. Points A, B, C, D all lie in the same plane therefore making them coplanar.

4. Points X, Y do not lie in the same plane as A, B.

5. Point X does not lie in the same plane as C, D, B

6. A, P, B are all points on the same line therefore any two of them could be used to represent the same line.

7. PX and PY start at the same point and go in the opposite directions, defining them as opposite rays.

8. Plane AXY cannot be defined as point X and Y are not in a plane.

9. Lines AB and CD cannot both be in a different plane.

10. Both rays sum up to equal Line XY.

Answer:

the measure of line AD is 8

Step-by-step explanation:

lines AD and BC are equal, due to the markings on the lines
this means that if line BC is 8, than line AD is also 8

Answer:

the answer is 4gn Puig IT in

Answer: Option 1

Step-by-step explanation:

The graphs intersect at x=0 and x=2, meaning f(2)=g(2) and f(0)=g(0).

The functions have the intersecting points at x = 2 and x = 0 and the relation is f ( 0 ) = g ( 0 ) and f ( 2 ) = g ( 2 )

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the first function be represented as f ( x )

Let the second function be represented as g ( x )

Now , the function f ( x ) is a parabolic function and g ( x ) is a linear function

And , the intersecting points of both f ( x ) and g ( x ) are

x = 2 and x = 0

So , both the functions f(x) and g(x) intersect at two points, one at x = 2 at the x-axis in the graph and one at y = 4 at y-axis of the graph

Therefore , f ( 0 ) = g ( 0 ) and f ( 2 ) = g ( 2 )

Hence , the functions are solved

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Answer: 180 degrees

Step-by-step explanation:

Angles on a line add to 180 degrees since they form a straight angle.

The difference in price between the two companies is $81-$79.56 = $1.44

Fire side Shop

Price of Chimney cap =$120

First Discount = 25% of(120)=$30

Price after 1st Discount = $120-$30=$90

Second Discount = 10% of 90=$9

Price after 2nd Discount = $90-$9=$81

Builders' Supply

Price of Chimney Cap= $111

First Discount= 25% of 111 = $27.75

Price after 1st Discount = $111 - $27.75 = $83.75

Second Discount = 5% of $83.75 = $ 4.1875

Price after 2nd Discount = $83.75 - $4.1875 = $79.5625 ≈ $79.56

Therefore,

a) Builders supply offers the lower price.

b) Difference in price = $81-$79.56 = $1.44

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The flux is 9.

Flux is the presence of a force field in a specified physical medium, or the flow of energy through a surface.

Given:

2x+2y+z= 1

F = 2i+2j + 2k

Now,

r = xi + yj + z( 1-2x-2y) K

dr/dx= i - 2k

dr/dy = j-2k

dr/dx* dr/dy

= ( i - 2k) * (j-2k)

= 2i + 2j + k

F(x)= 2i+2j + 2k

F(x). da = 4 +4 +2 = 10 dxdy

Hence, flux

= [tex]\int\limits^1_0 {\int\limits^{1-2y}_0 {10 } \, dx dy } \,[/tex]

=  [tex]\int\limits^1_0[/tex]  10(1-2y) dx

= [tex]\int\limits^1_0[/tex] 10-2y

= 10(1) - (1)²

=9

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The plane has intercepts (1/2, 0, 0), (0, 1/2, 0), and (0, 0, 1). Parameterize [tex]S[/tex] by the vector function

[tex]\vec s(u,v) = \dfrac{(1-u)(1-v)}2 \, \vec\imath + \dfrac{u(1-v)}2 \, \vec\jmath + v \,\vec k[/tex]

with [tex]0\le u\le1[/tex] and [tex]0\le v\le1[/tex]. (More explicitly, we have the parameterization

[tex]\vec s(u,v) = (1-v)((1-u) p_1 + u p_2) + v p_3[/tex]

where [tex]p_i[/tex] denote the given points.)

The normal vector to [tex]S[/tex] is

[tex]\vec n = \dfrac{\partial\vec s}{\partial u} \times \dfrac{\partial\vec s}{\partial v} = \dfrac{1-v}2\,\vec\imath + \dfrac{1-v}2\,\vec\jmath + \dfrac{1-v}4\,\vec k[/tex]

Then the flux of [tex]\vec F = 2\,\vec\imath+2\,\vec\jmath+2\,\vec k[/tex] across [tex]S[/tex] is given by the surface integral,

[tex]\displaystyle \iint_S \vec F \cdot d\vec\sigma = \iint_S \vec F \cdot \vec n \, dA[/tex]

[tex]\displaystyle = \int_0^1 \int_0^1 \left(2\,\vec\imath+2\,\vec\jmath+2\,\vec k) \cdot \left(\frac{1-v}2\,\vec\imath + \frac{1-v}2\,\vec\jmath + \frac{1-v}4\,\vec k\right) \, du \, dv[/tex]

[tex]\displaystyle = \frac52 \int_0^1 \int_0^1 (1-v) \, du \, dv[/tex]

[tex]\displaystyle  = \frac52 \int_0^1 (1-v) \, dv = \boxed{\frac54}[/tex]

Answer:

One solution

Step-by-step explanation:

The equation can be rewrite as 3x - 6 = 22 - x

so we try to get all the x on one side so we add x and 6 to both sides so we get 4x = 28 then we divide by 4 both side and get x=7

Answer:

3:11 or 8:11

Step-by-step explanation:

I think your missing some imformation! I'm guessing the ratio of picking a red marble is 3:8 while a blue marble is 8:3

Answer:

0.339

Step-by-step explanation:

Hope it helped!

Hii!

___________________________________________________________

Answer: 0.339

Explanation:

There are two rounding rules that will help us whenever we need to round a number! These are the rules.

---

Now that we know the rules, let's get down to solving our problem! ^^

The nearest thousandth is 3 decimal places.

_._ _ _ <==== Nearest thousandth

The third number after the decimal point is 9. After it is a digit that is less than 5. According to the rounding rules, we should round down.

[tex]\boldsymbol{0.3391=== > 0.339}[/tex]

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Hope that this helped! Best wishes.

--

Answer:

2+3+4 = 9

Add the three numbers of the three school districts that project to lose.

The probability of failure for Luis will be 0.18.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

The probability of passing is = 0.82

We know that the maximum probability of happening any event is 1 or 100 per cent if the probability of passing of the person is 0.82 then the probability of failure will be calculated as:-

Probability of failing = 1 - probability of passing

Probability of failing = 1 - 0.82

Probability of failing = 0.18

Therefore the probability of failure for Luis will be 0.18.

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The probability that a female chosen runs = 0.24

We are given;

Number of adults surveyed = 100

Total number of females = 45

Total Number of Males = 55

Number of female adults that go to gym = 30

Number of adults that run = 35

Number of males that cycle = 9

Thus;

From the probability table attached, we can say that;

Number of females that can run = 11

Probability that she runs = 11/45

Probability that she runs = 0.24

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