(25 points) A car rental company's standard charge includes an initial fee plus an additional fee for each mile driven. The standard charge S (in dollars) is given by the function S = 0.40M + 15.75, where M is the number of miles driven.

The company also offers an option to insure the car against damage. The insurance charge I (in dollars) is given by the function I = 0.25M + 3.90.

Let C be the total charge (in dollars) for a rental that includes insurance. Write an equation relating C to M. Simplify your answer as much as possible.

C =

Answer:

a

  [tex] P(X = 0) =  0.6065 [/tex]

b

[tex]P(x <  25 ) =   1.18 *10^{-33} [/tex]

c

 [tex]  P(x \le 5 ) =  0.9994 [/tex]    

Step-by-step explanation:

From the question we are told that

  The rate  is [tex]\lambda =  \frac{1}{2}\   hr^{-1}[/tex]    =  0.5 / hr

  Generally  Poisson distribution formula is mathematically represented as

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

Generally the probability that no error occurred during a day is mathematically represented as  

Here  t =  1  hour according to question a

So

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

Hence

   [tex][tex]P(X = 0) =  \frac{\frac{1}{2} ^0 e^{-\frac{1}{2}}}{0!}[/tex]

=>  [tex] P(X = 0) =  0.6065 [/tex]

Generally the probability that  a critical error occurs since the start of a day is mathematically represented as

Here  t =  1  hour according to question a

So

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

Hence

      [tex]P(x \ge 25 ) =  1 - P(x <  25 )[/tex]

Here

     [tex]P(x <  25 ) = \sum_{x=0}^{24} \frac{e^{-\lambda} * \lambda^{x}}{x!}[/tex]

=>   [tex]P(x <  25 ) =  \frac{e^{-0.5} *0.5^{0}}{0!} + \cdots + \frac{e^{-0.5} *0.5^{24}}{24!}[/tex]

[tex]P(x <  25 ) =  0.6065 + \cdots + \frac{e^{-0.5} *0.5^{24}}{6.204484 * 10^{23}}[/tex]

[tex]P(x <  25 ) =  0.6065 + \cdots + 6.0*10^{-32}[/tex]

[tex]P(x <  25 ) =   1.18 *10^{-33} [/tex]

Considering question c

Here  t =  2  

Gnerally given that the  system just started up and an error occurred  the probability the next reset will occur within 2 hours

[tex]P(x \le 5 ) =  \sum_{n=0}^{5}  \frac{(\lambda t) ^x e^{-\lambda t }}{x!}[/tex]

=> [tex]P(x \le 5 ) =   \frac{(0.5 *  2) ^ 0 e^{- 0.5  * 2 }}{0!} + \cdots  +   \frac{(0.5 *  2) ^ 5  e^{- 0.5  * 2 }}{5!}[/tex]

=> [tex]P(x \le 5 ) =   \frac{1* 2.7183 }{1 } + \cdots  +   \frac{1  *2.7183 }{120}[/tex]

=>  [tex]P(x \le 5 ) =   2.7183 + \cdots  +   0.0226525[/tex]

 [tex]  P(x \le 5 ) =  0.9994 [/tex]    

Answer:

Step-by-step explanation:

The maximum profit will be found in the vertex of the parabola, which is what your equation is. You could do this by completing the square, but it is way easier to just solve for h and k using the following formulas:

[tex]h=\frac{-b}{2a}[/tex] for the x coordinate of the vertex, and

[tex]k=c-\frac{b^2}{4a}[/tex] for the y coordinate of the vertex.

x will be the selling price of each widget and y will be the profit. Usually, x is the number of the items sold, but I'm going off your info here for what the vertex means in the context of this problem.

Our variables for the quadratic are as follows:

a = -10

b = 600

c = -3588. Therefore,

[tex]h=\frac{-600}{2(-10)}=30[/tex] so the cost of each widget is $30. Now for the profit:

[tex]k=-3588-(\frac{(600)^2}{4(-10)})[/tex] This one is worth the simplification step by step:

[tex]k=-3588-(\frac{360000}{-40})[/tex] and

k = -3588 - (-9000) and

k = -3588 + 9000 so

k = 5412

That means that the profit made by selling the widgets at $30 apiece is $5412.

Hence,the profit made by selling the widgets at $[tex]30[/tex] apiece is $[tex]5412[/tex].

What is the maximum profit?

Maximum profit, or profit maximisation, is the process of finding the right price for your products or services to produce the best profit.

Here given that,

A company sells widgets. The amount of profit, [tex]y[/tex], made by the company, is related to the selling price of each widget, [tex]x[/tex], by the given equation.

As the maximum profit found in the vertex of the parabola,

Here, [tex]x[/tex] will be the selling price of each widget and [tex]y[/tex] will be the profit.

The number of items sold is [tex]x[/tex].

So, the quadratic equation is:-

[tex]a = -10b = 600c = -3588.[/tex]

Therefore, so the cost of each widget is $[tex]30[/tex].

For the profit:-

[tex]k = -3588 - (-9000) andk = -3588 + 9000 sok = 5412[/tex]

Hence,the profit made by selling the widgets at $[tex]30[/tex] apiece is $[tex]5412[/tex].

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Answer:

that what

Step-by-step explanation:

Answer:

z=2

Step-by-step explanation:

Just solve

1 + z = 3 (minus 1 on both sides)

z = 2

Plug in

3=(2+1)

3 = 3

Answer:

99.7%

Step-by-step explanation:

Empirical rule formula states that:

• 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.

• 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.

• 99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.

From the question, we have mean of 98.18 F and a standard deviation of 0.65 F

The approximate percentage of healthy adults with body temperatures between 96.23 F and100.13 ​F is

μ - 3σ

= 98.18 - 3(0.65)

= 98.18 - 1.95

= 96.23 F

μ + 3σ.

98.18 + 3(0.65)

= 98.18 + 1.95

= 100.13 F

Therefore, the approximate percentage of healthy adults with body temperatures between 96.23 F and 100.13 ​F which is within 3 standard deviations of the mean is 99.7%

Answer:

You're right!

Step-by-step explanation:

Answer:

Were you right?

Step-by-step explanation:

Answer:hbjnhbgfvrdfghjhgfdfghjhgfghjkl

Answer:

[tex]95 \frac{3}{4} \: inch \leqslant x \leqslant 96 \frac{1}{4} \: inch[/tex]

Step-by-step explanation:

Given that a lumber supplier sells 96 inch Pieces of oak which must be within 1/4 of an inch.

This situation can be represented by the following absolute value inequality:

[tex]|x \: - 96| \: \leqslant \: \frac{1}{4} [/tex].

The absolute value can be thought of as the size of something because length cannot be negative. The length must be no more than 1/4 away from 96.

To simplify this, pretend this is a standard equality, |x-96| = 1/4. 1/4 is the range of acceptable length, 96 is the median of the range, and x is the size of the wood.

First apply the rule |x| = y → x = [tex]\pm[/tex]y

|x-96| = 1/4

x - 96 = [tex]\pm[/tex]1/4

x = [tex]96 \pm 1/4[/tex]

(These are just the minimum, and maximum sizes)

Now with a less than or equal to, the solutions are now everything included between these two values.

Therefore:

[tex]96 - 1/4 \: \leqslant x [/tex] [tex]\leqslant \: 96 + 1/4 [/tex]

With less than inequalities, you must have the lower value on the left, and the higher value on the right.

If x represents the size of the pieces, then the acceptable lengths are represented by this following inequality:

[tex]95 \frac{3}{4} \: inch \leqslant x \leqslant 96 \frac{1}{4} \: inch[/tex]

This is interpreted as x (being the size of the oak) is greater than or equal to 95 3/4, and less than or equal to 96 1/4 in inches.

Answer:

W>16

Step-by-step explanation:

The formula for calculating the perimeter of a rectangle:

P = 2L+2W

L is the length of the rectangle

W is the width of the rectangle:

Given

P = 96m

If the length of a rectangle is 2 times the width, then L = 2W

Substitute into the formula:

Since the perimeter is less than 96m

96 < 2(2W)+2W

96 < 4W+2W

96 < 6W

Divide both sides by 6:

96/6 < 6W/6

16 < W

W>16

Hence the possible values of the width are all values greater than 16.

Answer:

-5/6,-1/4,-0.11,0.567

Step-by-step explanation:

Answer: it would be half the size

Step-by-step explanation:

Answer:

4 students got three answers incorrectly.

The number of students got 3 answers incorrect is 4.

A histogram is a display of statistical information that uses rectangles to show the frequency of data items in successive numerical intervals of equal size.

Now from the given histogram following informations are extracted-

Number of students got 1 answer incorrect = 2

Number of students got 2 answer incorrect = 3

Number of students got 3 answer incorrect = 4

Number of students got 4 answer incorrect = 1  

Number of students got 5 answer incorrect = 2

Thus from above we can conclude that,

Number of students got 3 answer incorrect = 4

Thus, the number of students got 3 answers incorrect is 4.

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Answer:

3 : 1

Step-by-step explanation:

The biggest circle has a radius of 20 cm

So that means, its area will be,

Area = [tex]\pi r^{2}[/tex]

Area = [tex]\pi * 20^{2}[/tex]

A = [tex]\pi * 400[/tex]

=> A = 400[tex]\pi[/tex]

We do not need to solve this because it is nit required

Then, one small circle has an area of,

Area = [tex]\pi r^{2}[/tex]

Area = [tex]\pi *5^{2}[/tex]

Area = [tex]\pi *25[/tex]

=> Area = 25[tex]\pi[/tex]

As there are 4 circles in, we get that the area covered by the small squares,

=> [tex]25\pi * 4[/tex]

=> [tex]100\pi[/tex]

So, the amount shaded = 100/400 (We can omit the [tex]\pi[/tex] at this stage because we are finding out a ratio)

=> 1/4

So, there is 1 cut region and the remaining is the uncut region,

As we need to find uncut to cut, the ratio will be,

=> remaining : 1

=> 3 : 1

If my answer helped, kindly mark me as the brainliest!!

Thanks!!

Answer:

The number of tickets sold at the gate is [tex] G = 211.25[/tex]

The number of tickets sold in advance is  [tex]  A = 311.25 [/tex]

Step-by-step explanation:

From the question we are told that

 The cost of a tickets at the gate is [tex]a =  \$ 5[/tex]  

  The cost of a ticket in advance is  [tex]b =  \$ 3[/tex]

Let the number of ticket sold in the gate be G

Let the number of ticket sold in advance  be   A

From the question we are told that

  One hundred more tickets were sold in advance than at the gate and this can be mathematically represented as

       [tex]G  +  100 =  A[/tex]

From the question we are told that

  The total revenue from ticket sales was $1990  and this can be mathematically represented as

    [tex]5 G  +  3A  =  1990[/tex]

substituting for  A in the equation above

    [tex]5 G  +  3[G  +  100]=  1990[/tex]    

    [tex]5 G  +  3G  +  300=  1990[/tex]    

    [tex] 8G  +  300=  1990[/tex]  

    [tex] 8G  =  1690[/tex]

=>  [tex] G = 211.25[/tex]

Substituting this for G in the above equation

     [tex]5 [211.25]  +  3A  =  1990[/tex]

=>    [tex]  3A  =  1990 - 1056.25[/tex]

=>    [tex]  A = 311.25 [/tex]

Answer:

97.65

Step-by-step explanation:

97.65

Step-by-step explanation

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. The probability of at most 2 red cards is 0.5.

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,

P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)

Where,

x is the number of successes needed,

n is the number of trials or sample size,

p is the probability of a single success, and

q is the probability of a single failure.

Using the given information the number of cards is 24 out of which 12 are red. Therefore, the probability of getting a red card is 0.5.

A) All red cards.

P(X=5) = ⁵C₅ (0.5⁵) (0.5⁰)

            = 0.03125

B.) at least two red cards.

P(X≥2) = 1 - ⁵C₀ (0.5⁰) (0.5⁵) - ⁵C₁ (0.5¹) (0.5⁴)

= 0.8125

C.)  At most 2 red cards.

P(X≤2) = ⁵C₀ (0.5⁰) (0.5⁵) + ⁵C₁ (0.5¹) (0.5⁴) + ⁵C₂ (0.5²) (0.5³)

           = 0.5

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Answer:

-15, -9, -3, 3

Step-by-step explanation:

First One:

y =3(-4)-3 is -15

Second:

y= 3(-2)-3 is -9

Third:

y= 3(0)-3 is -3

Last One:

y= 3(2)-3 is 3

Answer:

Option C: an outline of a pine tree

Step-by-step explanation:

Artists usually use two main types of shapes when drawing. One is geometric shape and the other is bimorphic shape.

A geometric shape simply refers to common regular and precise shapes like triangles, rectangles, squares which are commonly found in man made objects. Whereas, a bimorphic shape is one that is basically rounded or irregular and depicts natural things or living organisms.

Now, from the question, the only thing there that refers to a natural occurring object is "an outline of a pine tree".

Thus, it is a bimorphic shape.

Answer:

C. an outline of a pine tree

Step-by-step explanation:

I just took the test!

Answer:

20°

Step-by-step explanation:

Step 1:

x + 40° = 3x       Vertical ∠'s

Step 2:

40° = 2x      Subtract x on both sides

Step 3:

x = 40° ÷ 2     Divide

Answer:

x = 20°

Hope This Helps :)

Answer:

(6,11)

I can confirm that this question is right.

12/2      22/2

(6   ,        11)

Answer:

52

Step-by-step explanation:

given that the number is a

The expression for Ten less than 5 times the value of a number is given by

5a - 10

10 times the quantity of  12 more than one-fourth of the number.

a/4 is one-fourth  of number

12 more than one-fourth of the number

a/4 + 12

expression for  10 times the quantity of  12 more than one-fourth of the number. is given by

10(a/4 + 12) = 10a/4 + 12*10 = 2.5a + 120

Given that the above two expression are equal

equating them we have

5a - 10 = 2.5a + 120

adding 10 both sides

=>5a - 10+ 10  = 2.5a + 120 + 10

=> 5a = 2.5a + 130

subtracting 2.5a from both sides

=> 5a - 2.5a = 2.5a + 130 - 2.5a

=> 2.5a = 130

dividing both side by 2.5

=> a = 130/2.5 = 52

Thus, value of a is 52

Slope: 1/2

y-intercept(s): (0, 7/3)

x: 0, 7

y: 7/3, 0

Step-by-step explanation:

y=-3 -1/3(1+2)=2/3.3=1.3=3

y=3

Answer:

A) The height of the trapezoid is 6.5 centimeters.

B) We used an algebraic approach to to solve the formula for [tex]b_{1}[/tex].  [tex]b_{1} = \frac{2\cdot A}{h}-b_{2}[/tex]

C) The length of the other base of the trapezoid is 20 centimeters.

D) We can find their lengths as both have the same length and number of variable is reduced to one, from [tex]b_{1}[/tex] and [tex]b_{2}[/tex] to [tex]b[/tex]. [tex]b = \frac{A}{h}[/tex]

Step-by-step explanation:

A) The formula for the area of a trapezoid is:

[tex]A = \frac{1}{2}\cdot h \cdot (b_{1}+b_{2})[/tex] (Eq. 1)

Where:

[tex]h[/tex] - Height of the trapezoid, measured in centimeters.

[tex]b_{1}[/tex], [tex]b_{2}[/tex] - Lengths fo the bases, measured in centimeters.

[tex]A[/tex] - Area of the trapezoid, measured in square centimeters.

We proceed to clear the height of the trapezoid:

1) [tex]A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})[/tex] Given.

2) [tex]A = 2^{-1}\cdot h \cdot (b_{1}+b_{2})[/tex] Definition of division.

3) [tex]2\cdot A\cdot (b_{1}+b_{2})^{-1} = (2\cdot 2^{-1})\cdot h\cdot [(b_{1}+b_{2})\cdot (b_{1}+b_{2})^{-1}][/tex] Compatibility with multiplication/Commutative and associative properties.

4) [tex]h = \frac{2\cdot A}{b_{1}+b_{2}}[/tex] Existence of multiplicative inverse/Modulative property/Definition of division/Result

If we know that [tex]A = 91\,cm^{2}[/tex], [tex]b_{1} = 16\,cm[/tex] and [tex]b_{2} = 12\,cm[/tex], then height of the trapezoid is:

[tex]h = \frac{2\cdot (91\,cm^{2})}{16\,cm+12\,cm}[/tex]

[tex]h = 6.5\,cm[/tex]

The height of the trapezoid is 6.5 centimeters.

B) We should follow this procedure to solve the formula for [tex]b_{1}[/tex]:

1) [tex]A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})[/tex] Given.

2) [tex]A = 2^{-1}\cdot h \cdot (b_{1}+b_{2})[/tex] Definition of division.

3) [tex]2\cdot A \cdot h^{-1} = (2\cdot 2^{-1})\cdot (h\cdot h^{-1})\cdot (b_{1}+b_{2})[/tex] Compatibility with multiplication/Commutative and associative properties.

4) [tex]2\cdot A \cdot h^{-1} = b_{1}+b_{2}[/tex] Existence of multiplicative inverse/Modulative property

5) [tex]\frac{2\cdot A}{h} +(-b_{2}) = [b_{2}+(-b_{2})] +b_{1}[/tex] Definition of division/Compatibility with addition/Commutative and associative properties

6) [tex]b_{1} = \frac{2\cdot A}{h}-b_{2}[/tex] Existence of additive inverse/Definition of subtraction/Modulative property/Result.

We used an algebraic approach to to solve the formula for [tex]b_{1}[/tex].

C) We can use the result found in B) to determine the length of the remaining base of the trapezoid: ([tex]A= 215\,cm^{2}[/tex], [tex]h = 8.6\,cm[/tex] and [tex]b_{2} = 30\,cm[/tex])

[tex]b_{1} = \frac{2\cdot (215\,cm^{2})}{8.6\,cm} - 30\,cm[/tex]

[tex]b_{1} = 20\,cm[/tex]

The length of the other base of the trapezoid is 20 centimeters.

D) Yes, we can find their lengths as both have the same length and number of variable is reduced to one, from [tex]b_{1}[/tex] and [tex]b_{2}[/tex] to [tex]b[/tex]. Now we present the procedure to clear [tex]b[/tex] below:

1) [tex]A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})[/tex] Given.

2) [tex]b_{1} = b_{2}[/tex] Given.

3) [tex]A = \frac{1}{2}\cdot h \cdot (2\cdot b)[/tex] 2) in 1)

4) [tex]A = 2^{-1}\cdot h\cdot (2\cdot b)[/tex] Definition of division.

5) [tex]A\cdot h^{-1} = (2\cdot 2^{-1})\cdot (h\cdot h^{-1})\cdot b[/tex] Commutative and associative properties/Compatibility with multiplication.

6) [tex]b = A \cdot h^{-1}[/tex] Existence of multiplicative inverse/Modulative property.

7) [tex]b = \frac{A}{h}[/tex] Definition of division/Result.

Answer:

hi to what. good bye???????

Answer:

10%

Step-by-step explanation:

(a) What percentage of meals had less than 10 grams of fat?

(b) Round your answer to the nearest tenth of a percent.

To find the percentage of meals with less than 10 grams of fat, count the number of meals with less than 10 grams of fat and divide by the total number of meals; multiply this figure by a hundred.

(A) Total number of meals = 550

Number of meals having less than 10 grams of fat = 77

Percentage of meals having less than 10 grams of fat = 77/550 × 100

= 0.14 × 100 = 14%

(B) Rounding the answer to the nearest tenth of a percent means approximating it to the nearest multiple of 10 that is not more than 100 (where 100 here represents a full cent or 'percent').

The multiples of 10 that are close to 14 are 10 and 20. The closest being 10, your answer becomes 10%

Answer:

2 2/3 or 8/3

Step-by-step explanation:

Formula for each side = 2/3 x 2/3

2/3 x 2/3 = 4/9

6 sides

4/9 x 6 or 4/9 + 4/9 + 4/9 + 4/9 + 4/9 + 4/9

=2 2/3 or 8/3

Answer:

2 2/3

Is the answer

Answer:

x = 9°

y = 119°

Step-by-step explanation:

Given,

y° = 61°+58° { the exterior angle formed by producing the side of triangle is equal to two non-adjacent angle}

or, y° = 119°

therefore, y° = 119°

Now,

52°+y°+x° = 180°{the sum of angle if triangle is 180°}

or, 52°+119°+x°= 180°

or, 171°+x° = 180°

or, x° = 180°-171°

or, x° = 9°

therefore, x° = 9°

Answer:

i am pretty sure it would be 8

Step-by-step explanation:

when it rounds to 2 but also rounds to 100, 8 would be the best bet.