The probability that a certain make of car will need repairs in the first eight months is 0.6. A dealer sells three such cars. What is the probability that at least one of them will require repairs in the first eight months? Round your final answer to four decimal places.

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

Answer:

x < 1.39285714286

Step-by-step explanation:

5(5x+2x/5x8)<78

             x5      x5

5(5x+2x(8))<390

             /8    /8

5(5x+2x)<48.75

5(7x)<48.75

/5         /5

7x < 9.75

/7       /7

x < 1.39285714286

Finance charge = $93.00

The interest you'll pay on a loan is defined as a finance charge, and it's most commonly used in the context of credit card debt. A financing fee is computed by taking your annual percentage rate, or APR, the amount you owe, and the time period into account.

Given that,

Interest rate = 15.5%

Date: 1-3 (3 days)

Average daily balance = amount paid × days

                                      = $200 × 3 = $600  

Date: 4-20 (17 days)

Average daily balance = amount paid × days

                                      = $300 × 17 = $5100  

Date: 21-30 (10 days)

Average daily balance = amount paid × days

                                      = $150 × 10 = $1500  

So, total average daily balance for the month

= $(600+5100+1500)

= $7200

Now, the finance charge = $7200 × (15.5÷12)

                                         = $93.00

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Answer:

Convert the mixed numbers to improper fractions, then find the LCD and combine.

Exact Form:

17

6

Decimal Form:

2.8

¯

3

Mixed Number Form:

2

5

6

Step-by-step explanation:

Answer:

2 5/6 is your answer

Step-by-step explanation:

5 3/4 - 2 11/12

23/4-35/12

(23×3-35)/12

34/12

2 5/6

9514 1404 393

Answer:

  g(x) = |x -13| -7

Step-by-step explanation:

The transformation ...

  g(x) = f(x -h) +k

represents a translation h units to the right and k units up. Here, we are translating 13 units to the right and -7 units up (that is, 7 units down). Then the transformed function is ...

  g(x) = f(x -13) -7

  g(x) = |x -13| -7

The area A of the region between the two curves x = y^3–4y^2+3y and x+y=y^2 is 11.8334.

The graph of the question is given below:

We have to evaluate the integral needed to determine the area A of the region between the two curves x = y^3–4y^2+3y and x+y=y^2 i.e. x = y^2-y.

Now the area A of the given region is:

A = \(\int^1_{y=0}\left[g(y)-f(y)\right]dy+\int^4_{y=1}\left[g(y)-f(y)\right]dy\)

A = \(\int^1_{y=0}\left[(y^3-4y^2+3y)-(y^2-y)\right]dy+\int^4_{y=1}\left[(y^2-y)-(y^3-4y^2+3y)\right]dy\)

A = \(\int^1_{y=0}\left[y^3-4y^2+3y-y^2+y)\right]dy+\int^4_{y=1}\left[y^2-y-y^3+4y^2-3y)\right]dy\)

A = \(\int^1_{y=0}\left[y^3-5y^2+4y\right]dy+\int^4_{y=1}\left[5y^2-y^3-4y)\right]dy\)

Further simplification

A = \(\left[\frac{y^4}{4}-\frac{5y^3}{3}-\frac{4y^2}{2}\right]^1_{y=0}+\left[\frac{5y^3}{3}-\frac{y^4}{4}-\frac{4y^2}{2}\right]^4_{y=1}\)

A = \(\left[(\frac{1}{4}-\frac{5}{3}-2)\right-(0-0+0)]+\left[(\frac{320}{3}-64-32)\right-(\frac{5}{3}-\frac{1}{4}-2)]\)

A = (3-20+24)/12 + 320/3 - 96 - (20-3-24)/12

A = 7/12 + 32/3 + 7/12

A = (7+128+7)/12

A = 142/12

A = 11.8334

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(a) The algebraic expression, -5x - 2 + 5x + 2 is simplified as 0.

(b) The algebraic expression, 5x -2  - (5x + 2) is simplified as -4.

The given algebraic expression is simplified by adding similar terms together, as it will make the expression to be in simplest form.

The given algebraic expressions are;

-5x - 2 + 5x + 2

5x -2  - (5x + 2)

The first algebraic expression is simplified as follows;

-5x - 2 + 5x + 2

collect similar terms;

(-5x + 5x) + (-2 + 2)

= 0 + 0

= 0

The second algebraic expression is simplified as follows;

5x - 2 - (5x + 2)

= 5x - 2 - 5x - 2

collect similar terms;

= (5x - 5x) + (-2 - 2)

= 0 - 4

= - 4

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Answer:

540

Step-by-step explanation:

Since the surface area is 408, we can set up the equation

2*9*6 + 2*r*9 + 2*r*6 = 408

108 + 30r = 408

30r = 300

r = 10

The volume is length * width * height

9*6*10 = 540

Answer:

The value of y is 216

(and the value of x is 12)

Step-by-step explanation:

The general formula for a geometric sequence is,

\(a_n = a_1(r)^{n-1}\)

Where n represents the nth term, a_1 is the first term and r is the common ratio,

we see that,

r = 6,

the first term is,

a_1 = (x-6)

the 2nd term is,

a_2 = 3x,

the 3rd term is,

a_3 = y, finding y,

first we find x, using the above given formula we have,

\(a_2 = a_1(6)^{2-1}\\3x = (x-6)(6^1)\\3x = 6x -36\\36 = 6x - 3x\\36 = 3x\\x=36/3\\x=12\)

x = 12,

Now, for y we can use the relation between a_3 and a_2,

\(a_3 = a_1(6)^{3-1}\\y = (x-6)(6)^2\\y = (12-6)(6^2)\\y = 6(6^2)\\y = 6^3\\y = 216\)

y = 216

Answer: 20

Step-by-step explanation: c(68) = 5/9 (68-32)

i.  The position vector of X is 2b - a.

ii.  The position vector of Y is (3b + c)/4.

iii.  The ratio XY : Y Z is \(|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|\). Simplifying this expression will give us the final ratio.

i. To find the position vector x of point X, we can use the concept of vector addition. Since AB : BX = 2 : 1, we can express AB as a vector from A to B, which is given by (b - a). To find BX, we can use the fact that BX is twice as long as AB, so BX = 2 * (b - a). Adding this to the vector AB will give us the position vector of X: x = a + 2 * (b - a) = 2b - a.

ii. Similar to the previous part, we can express BC as a vector from B to C, which is given by (c - b). Since BY : YC = 1 : 3, we can find BY by dividing the vector BC into four equal parts and taking one part, so BY = (1/4) * (c - b). Adding this to the vector BY will give us the position vector of Y: y = b + (1/4) * (c - b) = (3b + c)/4.

iii. Z is the midpoint of AC, so we can find Z by taking the average of the vectors a and c: z = (a + c)/2. The ratio XY : YZ can be calculated by finding the lengths of the vectors XY and YZ and taking their ratio. Since XY = |x - y| and YZ = |y - z|, we have XY : YZ = |x - y|/|y - z|. Plugging in the values of x, y, and z we found earlier, we get XY : YZ =\(|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|\).

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Answer:

54 inches

Step-by-step explanation:

Area = 50, let Perimeter = P

50 = 23 + ½P

Therefore

P = 2(50 - 23) = 54

Therefore, the label represented by the rectangle in the figure is 62.4π square inches that is option D.

The lateral surface area of a three-dimensional object is the area of all its faces except for the top and bottom faces (i.e., the base(s) and the top(s)). In other words, it is the surface area of the object's lateral or side faces. The lateral surface area is typically used to describe the surface area of certain geometric solids such as cylinders, cones, and prisms. In the case of a cylinder, for example, the lateral surface area is the area of the curved side of the cylinder, excluding the top and bottom circular faces. For a cone, the lateral surface area is the area of the curved side of the cone, excluding the circular base.

Here,

From the given figure, we can see that the rectangle represents the lateral surface area of the cylinder, which can be calculated using the formula:

Lateral surface area = height x circumference

The circumference of the circle can be calculated as 2πr, where r is the radius. In this case, the radius is given as 4 inches. Therefore, the circumference is 2π(4) = 8π inches.

Substituting the given values, we get:

Lateral surface area = 7.8 x 8π

= 62.4π square inches

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The value of x is 4 if the  AG =2x +10 and CF =5x-2 which are opposite sides of a parallelogram option (d) is correct.

In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.

The question is incomplete:

The complete question is in the picture please refer to the picture.

We have given the side measure of a parallelogram:

AG =2x +10 and CF =5x-2

As we know in the parallelogram the opposite sides are equal in measure.

AG = CF

2x + 10 = 5x - 2

3x = 12

x = 4

CF = 5x - 2 = 5(4) - 2 = 20 - 2 = 18

Thus, the value of x is 4 and value of CF is 18if the  AG =2x +10 and CF =5x-2 which are opposite sides of a parallelogram.

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Answer:

y=10

Step-by-step explanation:

1

Rearrange terms

5

+

=

1

5

+

5

=

1

5

2

Subtract

5

5

5

from both sides of the equation

+

5

=

1

5

+

5

−

5

=

1

5

−

5

3

Simplify

Subtract the numbers

Subtract the numbers

Solution

=10

The solution is the point (0, 1/6) y = 1/6

Given the equation y = (-3/4)x + 1/6, which represents a linear equation, there is no "system" of equations involved since there is only one equation.

In this case, the equation is in slope-intercept form (y = mx + b),

where m represents the slope (-3/4) and b represents the y-intercept (1/6).

The slope-intercept form allows us to determine various properties of the equation.

Since there is only one equation, the solution to this equation is a single point on the Cartesian plane.

Each pair of x and y values that satisfy the equation represents a solution.

For example, if we choose x = 0, we can substitute it into the equation to find the corresponding y value:

y = (-3/4)(0) + 1/6

y = 1/6

Therefore, the solution is the point (0, 1/6).

In summary, the given equation has a unique solution, represented by a single point on the Cartesian plane.

Any value of x plugged into the equation will yield a corresponding y value, resulting in a unique point that satisfies the equation.

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Based on the given information, the second brand, Cola, is the more affordable option in terms of cost per milliliter compared to Co Fizz.

To determine which brand of cola is more expensive, we need to compare the cost per unit volume for each brand.

For the first brand, Co Fizz, a pack contains 4 bottles, and each bottle has a volume of 500 ml. The cost of the pack is $2.50. Therefore, the total volume in a pack is 4 * 500 ml = 2000 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2.50 / 2000 ml = $0.00125 per ml.

For the second brand, Cola, a pack contains 10 bottles, and each bottle has a volume of 330 ml. The cost of the pack is $2. Therefore, the total volume in a pack is 10 * 330 ml = 3300 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2 / 3300 ml ≈ $0.000606 per ml.

Comparing the two brands, we can see that the cost per milliliter for Co Fizz is $0.00125, while the cost per milliliter for Cola is approximately $0.000606.

Since the cost per milliliter for Co Fizz is higher than the cost per milliliter for Cola, it can be concluded that Co Fizz is more expensive in terms of price per unit volume.

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Answer:

The numbers are 1/10 & 11/10

Answer:

yes means yes

Step-by-step explanation:

Answer:84

Step-by-step explanation:

Answer:

84 hamburgers were sold

The equation in terms of x that represents the given relationship is 114 = (1 + 3x) * (Width)

Let's break down the information given:

Height of the rectangular box = 7 ft

Length of the rectangular box = 1 ft longer than thrice the width (x)

Volume of the rectangular box = 798 ft³

To write an equation that represents the given relationship, we need to relate the length, width, and height to the volume.

The volume of a rectangular box is given by the formula: Volume = Length * Width * Height.

Given that the height is 7 ft, we can substitute this value into the equation.

Volume = (Length) * (Width) * (7)

Now, let's focus on the length. It is described as 1 ft longer than thrice the width.

Length = 1 + (3x)

Substituting this value into the equation, we have:

Volume = (1 + (3x)) * (Width) * (7)

Since the volume is given as 798 ft³, we can set up the equation as follows:

798 = (1 + (3x)) * (Width) * 7

Simplifying further, we get:

798 = 7 * (1 + 3x) * (Width)

Dividing both sides of the equation by 7, we have:

114 = (1 + 3x) * (Width)

Therefore, the equation in terms of x that represents the given relationship is:

114 = (1 + 3x) * (Width)

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The distance from point A to point B is 2744.1 feet.

Define Trigonometric ratio

The ratios of the sides of a right triangle are called trigonometric ratios. Three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan).

Given, horizontal distance = 1357 feet

Let h  = height of the lighthouse

tan(A) = perpendicular / base

where, perpendicular = h

base = 1357 feet

Angle is 9°

so now, put these value in trigonometric ratio

tan(9) = h / 1357

where, tan(9) = 0.1584

h = 1357 * 0.1584

h = 214.9 feet

Let d = distance from point B to the Lighthouse base

Angle is 3°

h = 214.9 feet

so, tan(3) = 214.9 / d

where, tan(3) = 0.0524

0.0524 = 214.9 / d

d = 214.9 / 0.0524

d = 4101.1 feet

Distance between point A to B = 4101.1 - 1357

                                                    = 2744.1 feet

Therefore, the distance from point A to point B is 2744.1 feet

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Answer:

The answer is x=y-7/9+10

Step-by-step explanation:

hope that helps

Answer:

184

Step-by-step explanation:

2*(6*5+6*14+5*14)=184

Answer:

See below.

Step-by-step explanation:

4x + 12y = 4(x + 3y)

35x + 50y = 5(7x + 10y)

18x + 9y = 9(2x + y)

32x + 8y = 8(4x + y)

100x + 700y = 100(x + 7y)

Answer:

b.x2(squared) +2x+4x+8

Answer:

C. X2 (squared) +6x +8

Step-by-step explanation:

I hope this helps

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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The cost function is:

We can say:

87t is the variable cost, depends on what "t" is

32 is the fixed cost

From the problem, we can infer that "32" is the cost of oil change [fixed]

87t is the cost of t tires [variable cost]

Since t is the number of tires, then 87 would be the cost of 1 tire