in the life of a car engine, calculatedin miles, is normally distributed, with a mean of 17,000 miels and a standard deviation of 16,500 miles, what should be the guarantee period if the company wants less than 2% of the engines to fail while under warranty g

Answer:

A. x-3=0  D. 6=2x  F. x^2=9

Step-by-step explanation:

Substitute x=3 into each equation

A. x-3=0   3-3 =0   0=0  x=3 is a solution

B. 1+ x=2  1+3 =2  4=2  false

C. 9-x=3 9-3 =3  6=3  false

D. 6=2x  6 = 2*3   6=6  x=3 is a solution

E. 15x=3   15*3 =3  45=3  false

F. x^2=9  3^2 = 9   9=9  x=3 is a solution

Answer: i honestly dont know this seems very complicated

Step-by-step explanation:

Answer:

3x^3+12x

Step-by-step explanation:

Answer:

74w+10

Step-by-step explanation:

That's the answer

Answer:

x = 0

Step-by-step explanation:

-7(5-3x)=-35

Divide by -7

-7/-7(5-3x)=-35/-7

5 -3x = 5

Subtract 5 from each side

5-3x-5 = 5-5

-3x=0

Divide by -3

x=0

Answer: x = 0

Step-by-step explanation: Start by distributing the -7 through the parenthses on the left side of the equation.

-7(5) is -35 and -7(-3x) is 21x.

So we have -35 + 21x = -35.

Next, isolate the x term by adding 35 to both sides.

When we do this, we get 21x = 0.

Now divide both sides by 21 and x = 0.

Answer:

I believe that the answer is a cone

Step-by-step explanation:

A cone is a three dimensional figure that has a circular base and a smooth face that goes up into a single point.

Answer:

C). 0.83193

Step-by-step explanation:

There are total of 90 passengers of which 27 are for business.

The probability of passengers for business = 27/90

The probability of passengers for business p = 0.3

The probability of passengers not for business q = 1-The probability of passengers for business

= 1-0.3

= 0.7

Random sample of 5 passenger, probability of at least one business passenger = 1 - probability of no business passenger

probability of no business passenger

= 5C0(0.3)^0 * (0.7)^5

= 1 *1*0.16807

= 0.16807

probability of at least one business passenger = 1 - probability of no business passenger

= 1-0.16807

=0.83193

Answer:

[tex]x = \frac{1}{4}[/tex]

Step-by-step explanation:

[tex]\frac{x}{2} +\frac{3}{4} =\frac{7}{8}[/tex]

→ Find the LCM of the denominators (2,4 and 8)

LCM = 8

→ Multiply the whole equation by 8 to get rid of the fractions

4x + 6 = 7

→ Minus 6 from both sides to isolate 4x

4x = 1

→ Divide both sides by 4 to isolate x

[tex]x = \frac{1}{4}[/tex]

Answer:

Step-by-step explanation:

[tex] \frac{x}{2} + \frac{3}{4} = \frac{7}{8} [/tex]

Multiply both sides of the equation by 8

[tex] \frac{x}{2} \times 8 + \frac{3}{4} \times 8 = \frac{7}{8} [/tex]

[tex]4x + 6 = 7[/tex]

Move constant to R.H.S and change its sign

[tex]4x = 7 - 6[/tex]

Subtract the numbers

[tex]4x = 1[/tex]

Divide both sides of the equation by 4

[tex] \frac{4x}{4} = \frac{1}{4} [/tex]

Calculate

[tex]x = \frac{1}{4} [/tex]

hope this helps..

Best regards!!

Answer:

x is all real numbers

Step-by-step explanation:

5(x-7) + 42 = 5x+7

Distribute

5x - 35 +42 = 5x+7

Combine like terms

5x +7 = 5x+7

Subtract 5x from each side

7=7

This is always true, so x can be any number

Answer:

Hey there!

5(x-7)+42=5x+7

5x-35+42=5x+7

7=7

Infinite solutions.

Hope this helps :)

Answer:

It is 96 square units

Step-by-step explanation:

Step-by-step explanation:

8. As the name implies, a box-and-whisker plot looks like a box with two whiskers.  The box is the middle 50%.  The whiskers are the bottom 25% and the top 25%.

First, we need to sort the numbers from smallest to largest.  Starting with Set A:

Set A = {56, 57, 62, 68, 71, 82, 84, 92, 97, 101, 103, 106}

Now we find the median of the set, or the middle number.  Set A has 12 data points.  Since 12 is an even number, the median will be the average of the 6th and 7th numbers.

M = (82 + 84) / 2 = 83

Next, we find the median of the lower half.  There are 6 numbers in the lower half, so the median is the average of the 3rd and 4th numbers.

Ml = (62 + 68) / 2 = 65

Now we find the median of the upper half.  Again, there are 6 numbers in the upper half, so the median will be the average of the 3rd and 4th numbers.

Mu = (97 + 101) / 2 = 99

So the left whisker is from 56 to 65.

The box is from 65 to 99.

The right whisker is from 99 to 106.

Don't forget to mark the median, 83.

Repeat for Set B.

Set B = {36, 37, 42, 46, 48, 56, 58, 63, 69, 72, 75, 78}

M = (56 + 58) / 2 = 57

Ml = (42 + 46) / 2 = 44

Mu = (69 + 72) / 2 = 70.5

So the left whisker is from 36 to 44.

The box is from 44 to 70.5.

The right whisker is from 70.5 to 78.

The median is 57.

By graphing both on the same number line, we can easily compare them.

9. To make a dot plot, draw a number line starting from the smallest number and ending at the largest number.  For each number, draw a dot every time the number appears in the set.  For example, the number 3 appears twice in Set A, so draw two dots on 3.  You may find it helpful to sort the data first.

10. Draw a dot plot of the set to determine the shape.

Answer:

x= 78

Step-by-step explanation:

Focus on the blue traingle:

∠BHI= 180° -47° -31° (∠sum of triangle)

∠BHI= 102°

x°= 180° -102° (adj. ∠s on a str. line)

x°= 78°

x= 78

Alternatively,

x°= 47° +31° (ext. ∠ of triangle)

x°= 78°

x= 78

Answer:

13/40

Step-by-step explanation:

The period they have played can be divided into 3 parts:

● The time Amy wins

● The time Lily wins

● The time they tie

So the sum of them is the total time of playing.

Let A be the time Amy wins, L the tile Lily wins and T the time they tie .

●●●●●●●●●●●●●●●●●●●●●●●

Since we have expressed the times using fractions then the total period of playing is 1 wich is 100%.

So:

A + P + T = 1

3/8 + 3/10 + T = 1

Multiply 8 by 10 and 10 by 8 so that you get a common denominator.

Cross multiply the numerators and the denominators.

(3*10+3*8)/80 + T = 1

(30 + 24)/80 + T =1

54/80 + T = 1

(27*2)/(40*2) + T = 1

Simplify by 2

27/40 + T = 1

T = 1 - 27/40

Multiply one by 40 to get a common denominator

T = (40-27)/40

T = 13/40

So they have tied 13/40 of the time

Answer:

4

Step-by-step explanation:

f(x) = 4 ^ ( x-2)

Let x=3

f(3) = 4 ^ ( 3-2)

       = 4 ^ 1

       = 4

Answer:

4

Step-by-step explanation:

4^(x - 2)

Plug x as 3.

4^(3 - 2)

Subtract.

4^(1)

4^1 = 4

Hey there! :)

Answer:

118 children

58 students

59 adults

Step-by-step explanation:

We can solve this problem by setting up a system of equations:

Let a = adults

2a = children (since double the # of adults were children), and

s = students

Set up the equations:

1704 = 5(2a) + 7s + 12(a)

1704 = 10a + 7s + 12a

235 = 2a + a + s

Simplify the equations:

1704 = 22a + 7s

235 = 3a + s

Subtract the bottom equation from the top by multiplying the bottom equation by 7 to eliminate the 's' variable:

1704 = 22a + 7s

7(235 = 3a + s)

1704 = 22a + 7s

1645 = 21a + 7s

---------------------- (Subtract)

59 = a

This is the number of adults. Substitute this number into an equation to solve for the number of students:

235 = 3(59) + s

235 = 177 + s

s = 58.

Since the number of children is equivalent to 2a, solve:

2(59) = 118 children.

Therefore, the values for each group are:

118 children

59 adults

58 students.

Answer:

adults: 59, students:58 and children 118

Step-by-step explanation:

let A for adults, and C = children and S for students

There are half as many adults as there are children=

A=C/2 , C=2A

A+C+S=235 or

A+2A+S=235 first equation

3A+S=235

12A+5C+7S =1704 or

12A+10A+7S=1704

22A + 7S=1704 second equation

3A+S=235 first

solve by addition and elimination

22A+7S=1704

21 A+7S=1645 subtract two equations

A=59 adults

C=2A=2(59)=118

substitute in :A+S+C=235

S=235-(118+59)=58

check: 5C+7S+12A=1704

5(118)+7(58)+12(59)=1704

Answer: 5/8

Step-by-step explanation:

Simply do 8/8(1)-3/8 to get 5/8

Hope it helps <3

Answer:

462.61 yards.

Step-by-step explanation:

To solve, you need to find the measurement of the angle that forms a 90 degree angle with the 23.9 degree angle.

90 - 23.9 = 66.1 degrees.

Now that you have the angle, you can use TOA to solve for x (TOA = Tangent; Opposite over Adjacent).

tan(66.1) = x / 205

x / 205 = tan(66.1)

x = tan(66.1) * 205

x = 2.256628263 * 205

x = 462.6087939

So, you are about 462.61 yards from the cabin.

Hope this helps!

Answer:

4 plants

Step-by-step explanation:

If betty has $33 dollars and each plant is $8, than 33/8 ≈ 4

(8 * 4 is 32)

She will have one dollar left but she can't buy another plant since that's not enough.

Answer:

4 plants

Step-by-step explanation:

Take the amount of money she has and divide by the cost per plant

33/8

The amount is 4 with 1 dollar left over

4 plants

Answer:

the answer is x = sqrt 48

Step-by-step explanation:

Answer:

395

Step-by-step explanation:

15.8=d/25

multiply both sides by 25 to remove the denominator

25×15.8=d

d=395

Answer:

20 bags

Step-by-step explanation:

683✖️19=12977

683✖️365=249295

249295/13000=19.17

--> 20 bags

Answer:

The answer is 2.15%  

Step-by-step explanatio

Answer:

We know that for a standard dice the probability of obtain a 6 is:

[tex] P=\frac{1}{6}[/tex]

And for this case our value of x=3 and replacing we got:

[tex] f(x=3) = (1- \frac{1}{6})^{3-1} \frac{1}{6}[/tex]

[tex]f(x=3)=\frac{25}{36} \frac{1}{6}= \frac{25}{216}= 0.116[/tex]

Step-by-step explanation:

For this case we have the following function:

[tex] f(x) = (1-P)^{x-1} P[/tex]

We want to find the approximate probability of rolling a standard die and getting the first 6 on the 3rd try

We know that for a standard dice the probability of obtain a 6 is:

[tex] P=\frac{1}{6}[/tex]

And for this case our value of x=3 and replacing we got:

[tex] f(x=3) = (1- \frac{1}{6})^{3-1} \frac{1}{6}[/tex]

[tex]f(x=3)=\frac{25}{36} \frac{1}{6}= \frac{25}{216}= 0.116[/tex]

Answer:

The last graph (to the far right).

Step-by-step explanation:

As long as each x-value has one y-value, it is a function. However, the last graph has an x-value at -1 where there are two y-values. So, it does not pass the Vertical Line Test, and it is a relation rather than a function.

Hope this helps!

Answer:

a) The rate of change associated with the volume of the box is 54 cubic meters per second, b) The rate of change associated with the surface area of the box is 18 square meters per second, c) The rate of change of the length of the diagonal is -1 meters per second.

Step-by-step explanation:

a) Given that box is a parallelepiped, the volume of the parallelepiped, measured in cubic meters, is represented by this formula:

[tex]V = w \cdot h \cdot l[/tex]

Where:

[tex]w[/tex] - Width, measured in meters.

[tex]h[/tex] - Height, measured in meters.

[tex]l[/tex] - Length, measured in meters.

The rate of change in the volume of the box, measured in cubic meters per second, is deducted by deriving the volume function in terms of time:

[tex]\dot V = h\cdot l \cdot \dot w + w\cdot l \cdot \dot h + w\cdot h \cdot \dot l[/tex]

Where [tex]\dot w[/tex], [tex]\dot h[/tex] and [tex]\dot l[/tex] are the rates of change related to the width, height and length, measured in meters per second.

Given that [tex]w = 6\,m[/tex], [tex]h = 6\,m[/tex], [tex]l = 3\,m[/tex], [tex]\dot w =3\,\frac{m}{s}[/tex], [tex]\dot h = -6\,\frac{m}{s}[/tex] and [tex]\dot l = 3\,\frac{m}{s}[/tex], the rate of change in the volume of the box is:

[tex]\dot V = (6\,m)\cdot (3\,m)\cdot \left(3\,\frac{m}{s} \right)+(6\,m)\cdot (3\,m)\cdot \left(-6\,\frac{m}{s} \right)+(6\,m)\cdot (6\,m)\cdot \left(3\,\frac{m}{s}\right)[/tex]

[tex]\dot V = 54\,\frac{m^{3}}{s}[/tex]

The rate of change associated with the volume of the box is 54 cubic meters per second.

b) The surface area of the parallelepiped, measured in square meters, is represented by this model:

[tex]A_{s} = 2\cdot (w\cdot l + l\cdot h + w\cdot h)[/tex]

The rate of change in the surface area of the box, measured in square meters per second, is deducted by deriving the surface area function in terms of time:

[tex]\dot A_{s} = 2\cdot (l+h)\cdot \dot w + 2\cdot (w+h)\cdot \dot l + 2\cdot (w+l)\cdot \dot h[/tex]

Given that [tex]w = 6\,m[/tex], [tex]h = 6\,m[/tex], [tex]l = 3\,m[/tex], [tex]\dot w =3\,\frac{m}{s}[/tex], [tex]\dot h = -6\,\frac{m}{s}[/tex] and [tex]\dot l = 3\,\frac{m}{s}[/tex], the rate of change in the surface area of the box is:

[tex]\dot A_{s} = 2\cdot (6\,m + 3\,m)\cdot \left(3\,\frac{m}{s} \right) + 2\cdot (6\,m+6\,m)\cdot \left(3\,\frac{m}{s} \right) + 2\cdot (6\,m + 3\,m)\cdot \left(-6\,\frac{m}{s} \right)[/tex]

[tex]\dot A_{s} = 18\,\frac{m^{2}}{s}[/tex]

The rate of change associated with the surface area of the box is 18 square meters per second.

c) The length of the diagonal, measured in meters, is represented by the following Pythagorean identity:

[tex]r^{2} = w^{2}+h^{2}+l^{2}[/tex]

The rate of change in the surface area of the box, measured in square meters per second, is deducted by deriving the surface area function in terms of time before simplification:

[tex]2\cdot r \cdot \dot r = 2\cdot w \cdot \dot w + 2\cdot h \cdot \dot h + 2\cdot l \cdot \dot l[/tex]

[tex]r\cdot \dot r = w\cdot \dot w + h\cdot \dot h + l\cdot \dot l[/tex]

[tex]\dot r = \frac{w\cdot \dot w + h \cdot \dot h + l \cdot \dot l}{\sqrt{w^{2}+h^{2}+l^{2}}}[/tex]

Given that [tex]w = 6\,m[/tex], [tex]h = 6\,m[/tex], [tex]l = 3\,m[/tex], [tex]\dot w =3\,\frac{m}{s}[/tex], [tex]\dot h = -6\,\frac{m}{s}[/tex] and [tex]\dot l = 3\,\frac{m}{s}[/tex], the rate of change in the length of the diagonal of the box is:

[tex]\dot r = \frac{(6\,m)\cdot \left(3\,\frac{m}{s} \right)+(6\,m)\cdot \left(-6\,\frac{m}{s} \right)+(3\,m)\cdot \left(3\,\frac{m}{s} \right)}{\sqrt{(6\,m)^{2}+(6\,m)^{2}+(3\,m)^{2}}}[/tex]

[tex]\dot r = -1\,\frac{m}{s}[/tex]

The rate of change of the length of the diagonal is -1 meters per second.

Answer:

Total cost = $4,873

Therefore, the booking cost of hotel 5 would be $4,873

Step-by-step explanation:

Please refer to the attached table.  

The total cost includes the cost of the room and the cost of buffet dinner.

From the given table hotel 5,

The cost of the room for 120 people is found to be $166 per hour.

The conference will last for 5 hours so the total cost of the room is

Cost of room = 5*$166 = $830

From the given table hotel 5,

The cost of the buffet dinner per head is found to be $30.

Since there are total 120 people so the total cost of dinner is

Cost of dinner = 120*$30 = $3600

Total cost = $830 + $3600 = $4430

We are given that hotel 5 has recently increased the total chargers by 10%

Total cost = $4430*1.10

Total cost = $4,873

Therefore, the booking cost of hotel 5 would be $4,873.

Answer:

-3

Step-by-step explanation:

-3 is the answer

Answer:

-3

Step-by-step explanation:

Answer:

9 in.

Step-by-step explanation:

Given that the 4 in and 10 in. lines are parallel, the two triangles are similar.

As such, the ratio of the sides would give the same results.

Hence,

4/6 = 10/(6 + x)

cross multiplying

4(6 + x) = 60

Dividing both sides by 4

6 + x = 15

collecting like terms

x = 15 - 6

= 9

Answer:

mosses

Step-by-step explanation:

use socratic

Mosses are also known as the amphibian of the plant kingdom. The mosses were the first plant that can even survive on the land.

Conifers, pines, and flowering plants developed much later after the evolution of bryophytes.

Therefore, the mosses were the first plant that can even survive on the land.

Learn more about Bryophytes:

https://brainly.com/question/841138

Answer:

E, needs more info to be determined

Step-by-step explanation:

We know that Kai takes 30 minutes round-trip to get to his school.

One way is uphill and the other is downhill.

He travels twice as fast downhill than uphill.

This means that uphill accounts for 20 minutes of the round-trip and downhill accounts for 10 minutes of his trip.

However, even with this information, we do not know how far his school is.

In order to figure out how far away his school is, we would need more information about the speed at which Kai is traveling.

Simply knowing that he travels twice as fast downhill is not enough.

This question could only be solved by knowing how many miles Kai travels uphill or downhill in a given time.

Answer:

its 23

Step-by-step explanation: