The life span of a graphing calculator manufactured by Texas Instruments has a normal distribution with a mean of 54 months and a standard deviation of 8 months. The company guarantees that any calculator that starts malfunctioning within 36 months of the purchase will be replaced by a new one. You apply the normal model and discover that this is approximately 1.22% of their graphing calculators. Texas Instruments has sold 75 million graphing calculators world- wide. How many of these would you expect to malfunction within 3 months (and thus need to be replaced)? Explain.

Answers

Answer 1

Answer:

The expected number of graphing calculators that malfunctions within 3 months and need to be replaced is 915,000.

Step-by-step explanation:

Let X represents the number of graphing calculator that starts malfunctioning within 36 months of the purchase and needs to be replaced by a new one.

It is provided that X follows a normal distribution with a mean of 54 months and a standard deviation of 8 months.

Also, using the normal model it was determined that 1.22% of graphing calculator manufactured by Texas Instruments malfunctions and needs replacement.

That is,

P (X) = 0.0122

Texas Instruments has sold 75 million graphing calculators world- wide.

Compute the expected number of graphing calculators that malfunctions within 3 months and need to be replaced as follows:

E (X) = n × P (X)

        = 75 × 10⁶ × 0.0122

        = 915000

Thus, the expected number of graphing calculators that malfunctions within 3 months and need to be replaced is 915,000.


Related Questions

There is a box with an area of 112 sq inches and a height of 3.5 inches. What is the width of the box?

Answers

Answer:

32 inches

Step-by-step explanation:

Because height times width equals area,

we can divide 112 by 3.5 to get the width

So it is 32 inches

If a, b and c are positive integers for which (a,b,c) is the only
ordered triple such that 6a +9b + 20c = 61, then what is
a+b+c?

Answers

If a, b, and c are all positive integers and 6a + 9b + 20c = 61, then right away you know c < 3, because if c = 3, then 20c = 60, and there are no solutions for a and b.

So consider two cases:

• If c = 2, then we're left with 6a + 9b = 21.

• If c = 1, then 6a + 9b = 41.

We have gcd(6, 9) = 3, but 41 is prime and 3 does not divide 41. So we throw out the second case.

This leaves us with 6a + 9b = 21. Notice that if a = b = 1, then 6a + 9b = 15. Add 6 to both sides to get 21. So a = 2, b = 1, and c = 2, and hence a + b + c = 5.

How much mixed spice will she need for 6 spice

Answers

Answer:

who

Step-by-step explanation:

Rectangle ABCD has a perimeter represented by the expression 9x + 3. Rectangle PQRS has a
perimeter represented by the expression 6x + 2. Write the expression that represents the
difference in the perimeters of Rectangle ABCD and Rectangle PQRS. Write the steps and
solution.

Answers

Answer:

D. [tex] 3x + 1 [/tex]

Step-by-step explanation:

Perimeter of Rectangle ABCD = [tex] 9x + 3 [/tex]

Perimeter of Rectangle PQRS = [tex] 6x + 2 [/tex]

Difference between perimeter of Rectangle ABCD and Perimeter of Rectangle PQRS:

[tex] (9x + 3) - (6x + 2) [/tex]

Open Parentheses

[tex] 9x + 3 - 6x - 2 [/tex]

Collect like terms

[tex] 9x - 6x + 3 - 2 [/tex]

[tex] 3x + 1 [/tex]

Write an inequality representing the following phrase:
One-tenth of a number h is less than or equal to ten

Answers

Answer:

[tex]\frac{1}{10} h\leq 10[/tex]

Step-by-step explanation:

Basically, we are just translating the phrase into an algebraic expression.

please help explain if you can​

Answers

Answer:

A

Step-by-step explanation:

58-90 bc its a right triangle

hope this helps

Determine how many solutions the following equation has using quadratic formula x^2+5x=-8

Answers

Answer:

I will be using differentiation method

Step-by-step explanation:

x^2+5x =-8

2×x ×x^2-1 +5x = -8

2x +5x = -8

7x = -8

divide both sides by the co-efficient of x

7x÷7=-8÷7

x =-1.5

name the type of triangle of a b is equal to BC BC is equals to see a is equals to 6 CM​

Answers

Given ,

AB = BC

BC = CA

CA = 6 cm

This is an equilateral triangle as the first side is equal to the second side and the third side is equal to the second side which is equal to the first side . As all the sides are equal to 6 cm , this triangle is said to be an equilateral triangle .

Triangle ABC is an equilateral triangle , where :- AB = BC = CA = 6 cm .

f(x) = x^3- 9x
What is the average rate of change of f over the interval [1, 6]

Answers

Answer:

Step-by-step explanation:

[tex]\frac{f(b)-f(a)}{b-a}[/tex] This is the formula for the average rate of change

over the interval (a, b)

a and b are x values

f(a) ad f(b) think of them as y values

Start calculating f(a) and f(b) a=1 b=6

replace all x's in formula with a, (1)

f(1)=1³-9(1) = 1-9= -8    f(1) = -8

Now do : b (6)

f(6) = 6³ - 9 (6) = 216-54=162 f(6) = 162

now plug everything into your equation

[tex]\frac{f(6)-f(1)}{6-1} =\frac{162- (-8)}{5} =\frac{170}{5} =34[/tex] average rate of change.

notice the 162 - (-8) In math there is no subtraction, and you would change it to + and when you do that you much change the sign of the next value making -8 a +8.

Hope this helps. Good luck!

324 soldiers queued up such that the number of queues is equal to the number of soldiers in each queue. find the number of queues

Answers

I think so answer will be 164.

I NEED HELP PLEASE AND SHOW THE WORK PLEASE

Answers

Answer:

6. x = 28 degrees

7.  z = 1.6 cm

Step-by-step explanation:

6.  

Notice that you can use the property that tells us that the addition of all internal angles of a triangle must give 180 degrees, then you write the following equation:

50 + 69 + (2 x +5) = 180

combine like terms:

119 + 2 x + 5 = 180

124 + 2 x = 180

subtract 124 from both sides:

2 x = 56

divide by 2 both sides:

x = 56 / 2

x = 28 degrees

Problem 7.

If the two triangles are congruent, then the side MN must equal side RS.

Since MN  measure 1,8 cm, then RS must also measure 1.8 cm

and we can write the equation:

1.8 = 3 z - 3

adding 3 to both sides:

1.8 + 3 = 3 z

4.8 = 3 z

dividing both sides by 3:

z = 4.8 / 3

z = 1.6 cm

Write a positive or negative integer that represents the situation.

An elevator goes down 8 floors.

Answers

Negative because it is going down

What’re these two problems simplified?

Answers

Step-by-step explanation:

-2(3x-12)+4-13

=-6x+24+4-13=-7x-15

=6x-15

4(5x-1)+8x-20=20x-4+8x-20

=28x-24

So this is ur solution.

But if u wnt to solve these eq. together thn it will be:-

6x-15=28x-24

6x-28x=-24+15

-22x=-9

x=22/9=2.44

Hope u like it.

Answer:

-8+9 is problem one

Step-by-st-ep explanation:

1. You are eating on a Tootsie Roll Lollipop that is in the shape of a sphere. It is giving up volume at a steady rate of 0.25 in3 /min. How fast will the radius be decreasing when the Tootsie Roll Pop is .75 inches across?

Answers

Answer:

Step-by-step explanation:

Since the Tootsie Roll lollipop is a sphere

volume of sphere= [tex]\frac{4}{3}piR^3[/tex] = -0.25 [tex]in^3/min[/tex]

the negative sign indicates that the volume is decreasing

upon differentiating

as the diameter given is =0.75 so radius will be = 0.375

[tex]dV/dt = 4piR^2*dR/dt[/tex]

so [tex]dR/dt = 0.25/4*3.14 *(0.375)^2[/tex]

So the radius is decreasing at the rate of dR/dt= 0.142in/min

Find the surface area of a right cone with a diameter of 6 inches and a slant height of 5 inches.

Answers

Answer:

about 172.82

Step-by-step explanation:

Answer:

83.23

Step-by-step explanation:

to work out surface area of a  right cone u

A=πr(r+h2+r2)

hope this helps

im not sure if its right tho


A person with a height of 2 meters stand near a tree. The tree casts a shadow that is 30 meters long and the person has a shadow that is 3
meters long. What is the height of tree

Answers

9514 1404 393

Answer:

  20 m

Step-by-step explanation:

The 30 m shadow of the tree is 10 times the 3 m length of the person's shadow. We expect the tree to be 10 times as tall as the person:

  10(2 m) = 20 m . . . height of the tree

Helpppppp!!! PLEASE
:((

Answers

Answer:

Using the vertical line test, the functions are b, c, d, and f

Step-by-step explanation:

a and e both fail the vertical line test, therefore, it's not a functions.

B, c, d, and f are functions because they pass the vertical line test. If you were to draw a straight line down the graph, the points would only touch the line once. A and E however, touch the line two or more times.

Aging workers of the Neotropical termite, Neocapritermes taracua, develop blue crystal containing glands ("backpacks") on their backs, When they fight intruding termites and are hampered, these "blue" termites explode, and the glands spew a sticky liquid (Sobotnik et al. 2012). The following data are from an experiment that measured the toxicity of the blue substance. A single drop of the liquid extracted from blue termites was placed on individuals of a second termite species, Labiotermes labralis, and the number that were immobilized (dead or paralyzed) within 60 minutes was recorded. The frequency of this outcome was compared with a control treatment in which liquid from glands of "white" termites lacking the blue crystals was dropped instead.
Is the blue liquid toxic compared to liquid from white termites?
Liquid source Unharmed Immobilized
Blue workers 3 37
White workers 31 9

Answers

Answer:

The blue liquid is toxic

Step-by-step explanation:

From the calculations I have done and attached to this problem

Null hypothesis:

H0 : p1 <= p2

Alternate hypothesis:

H1 : p1 > p2

^p1 = 0.925

^p2 = 0.2250

^P = (x1 + x2)/(n1+n2)

= 0.575

After calculating, I got test statistics = 6.33 ( check attachment)

P(z > 6.33) = 0.0000

In conclusion, our pvalue has been found to be less than the level of significance 0.05 so we reject null hypothesis and accept that we have enough sample evidence that the blue liquid is more toxic in comparison to white one.

Please check attachment for calculated test statistics.

if m<2 = 115 degrees what is m<1 ? (There you go)

Answers

Answer:

65

Step-by-step explanation:

180 - 115 = 65

This is the easiest way to think about and do it but your teacher might want you to do it a different way.

Answer:

65

Step-by-step explanation:

twice a number is three more than nine​

Answers

Answer:

6

Step-by-step explanation:

Let that number be x.

[tex]2x = 9 + 3[/tex]

[tex]2x = 12[/tex]

[tex]x = 6[/tex]

A juice box has a length of 2 inches, a width of 1 inch, and a height of 4 inches. What is the volume of the juice box?

Answers

Answer:

8 in

Step-by-step explanation:

L × W × H = V2 × 1 × 4 = 8 in

I hope this helps!

Find the slope of the line passing through the points (8,-4) and (-6,-3).

Anybody know this ?

Answers

Answer:

= -1/14

Step-by-step explanation:

We can use the slope formula

m = ( y2-y1)/(x2-x1)

    = ( -3 - -4)/( -6 -8)

   = ( -3+4)/( -6-8)

   1/-14

= -1/14

solve the quadratic equation 3x^2-5x-7=0

Answers

Step-by-step explanation:

[tex]3x^{2} -5x -7 = 0 \\ 3x^{2} -5x = 7 \\ x^{2} -\frac{5}{3}x = \frac{7}{3} \\ x^{2} -\frac{5}{3}x +\frac{25}{36} = \frac{7}{3} +\frac{25}{36} \\ (x -\frac{5}{6})^{2} = \frac{84 +25}{36} \\ (x -\frac{5}{6})^{2} = \frac{109}{36} \\ x -\frac{5}{6} = ±\sqrt{\frac{109}{36}} \\ x -\frac{5}{6} = ±\frac{\sqrt{109}}{6} \\ x = ±\frac{\sqrt{109}}{6} +\frac{5}{6}[/tex]

Equation from the positive root:

[tex]x = \frac{\sqrt{109}}{6} +\frac{5}{6} \\ x = \frac{\sqrt{109} +5}{6}[/tex]

Equation from the negative root:

[tex]x = -\frac{\sqrt{109}}{6} +\frac{5}{6} \\ x = \frac{-\sqrt{109} +5}{6}[/tex]

Answer:

[tex]x = \frac{\sqrt{109} +5}{6}\\[/tex] and [tex]x = \frac{-\sqrt{109} +5}{6}\\[/tex] satisfy your quadratic equation.

Given : A quadratic equation is given to us . The equation is 3x² - 5x - 7 = 0 .

To Find : The roots of the equation .

Solution : Given quadratic equation is 3x²-5x-7=0. So , let's factorise it to get the zeroes of the equation .

⇒ 3x² -5x - 7 = 0.

Here now , use Quadratic formula , of the quadratic equation in standard form of ax² + bx + c = 0.

[tex]\boxed{\red{\bf x\:\:=\:\:\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}}}[/tex]

On substituting respective values ,

⇒ x = -(-5) ± √ (-5)² - 4×3×(-7) / 2 × 3.

⇒x = 5 ± √ [ 25 + 84 ]/ 6 .

⇒ x = 5 ± √ 109 / 6 .

x = 5 + 109 / 6 , 5 - 109 / 6.

[tex]\purple{\underbrace{\underline{\boxed{\red{\tt \purple{\longmapsto} x = \dfrac{5+\sqrt{109}}{6}, \dfrac{5-\sqrt{109}}{6}}}}}}[/tex]

find the value of x.
The answer is 13, but I need to show my work

Thank you guys

Answers

Answer:

Know the properties of vertical angles.

Step-by-step explanation:

Vertical angles are equal to each other, so we must make them equal to each other in an equation:

6x+2=80

6x=78

x=13

A regular hexagon is rotated about its center. By which angle could the hexagon be rotated so that it is mapped onto itself?
30°
45°
600
90°
Previous

Answers

Answer: 60

Step-by-step explanation:

What is 5 8/100
as a decimal?
O
A. 5.008
0
B. 5.08
O
C. 5.8
0 D. 58

Answers

Answer:

5.08

Step-by-step explanation:

5   8/100

Since there are 2 zero's in 100, we need two numbers in the top

Replace 8 with 08 which is the same number

5  08/100

Now write as a decimal

5.08

Answer:

B. 5.08

Step-by-step explanation:

[tex]5\frac{8}{100} = \frac{508}{100}[/tex]  508 ÷ 100 = 5.08

I hope this helps!

4 1/8÷2 3/4 convert the mixed numbers to improper fractions​

Answers

Answer:

Check picture

Step-by-step explanation:

9514 1404 393

Answer:

  1 1/2

Step-by-step explanation:

  [tex]\dfrac{4\dfrac{1}{8}}{2\dfrac{3}{4}}=\dfrac{\left(\dfrac{4\cdot8+1}{8}\right)}{\left(\dfrac{2\cdot4+3}{4}\right)}=\dfrac{\left(\dfrac{33}{8}\right)}{\left(\dfrac{11}{4}\right)}=\dfrac{\left(\dfrac{33}{8}\right)}{\left(\dfrac{22}{8}\right)}=\dfrac{33}{22}=\dfrac{3}{2}[/tex]

Then the improper fraction 3/2 can be written as the mixed number 1 1/2.

  (4 1/8) / (2 3/4) = 1 1/2

_____

Comment on division of fractions

Fractions can be divided several ways. Two ways that are commonly taught are "invert and multiply", or "match denominators". Here, we have used the second of these methods.

If we were to "invert and multiply", the computation would be ...

  (33/8)(4/11) = (33/11)(4/8) = 3(1/2) = 3/2

Instead, we multiplied 11/4 by 2/2 to make it be 22/8, so having a denominator of 8 matching that of the numerator. Then the value of the compound fraction is the ratio of the numerators:

  (33/8)/(22/8) = 33/22 = (3/2)(11/11) = 3/2

· At what point does the value of f(x) exceed the value of g(x) if
f(x)=200(1.194) and g(x) = 8x + 225? Justify your answer with a graph.
Someone help I’m dying

Answers

Step-by-step explanation:

hope this helps, good Luck xD.

Hi Guys

Please answer this question. I will choose Brainliest.

Also please do a step by step method.

Worth 10 points and it is a Maths question.

Cheers,
Jake

Answers

Answer:

In simplifying this is simple.

2-4 x + 3x-12.2x+9x2-x-12

8x - 9 = - 2x + 11 ​

Answers

Answer:

10/3

3.333333

3  1/3

Step-by-step explanation:

hope this helps

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