Precision manufacturing: A process manufactures ball bearings with diameters that are normally distributed with mean 25.0 millimeters and standard deviation 0.07 millimeter. Round the answers to at least four decimal places. (a) Find the 60th percentile of the diameters. (b) Find the 67th percentile of the diameters. (c) A hole is to be designed so that 2% of the ball bearings will fit through it. The bearings that fit through the hole will be melted down and remade. What should the diameter of the hole be

Answer:  [tex]y=\frac{1}{4}x-7[/tex]

Step-by-step explanation:

The perpendicular slope of the line(m) = [tex]-\frac{1}{m}[/tex]:

The function formula is y = mx + b, where the y-intercept(b) is found by substituting in the values of a point on the line ⇒ (4, -6):

[tex]y=\frac{1}{4}x+b\\-6=\frac{1}{4}(4)+b\\-6=1+b\\b=-6-1=-7[/tex]

So the perpendicular equation is [tex]y=\frac{1}{4}x-7[/tex].

Answer:

Yes it is. Graph will go down as it moves from left to right.

Step-by-step explanation:

Answer: D: The minimum value of A occurs 7 units lower than minimum of function B.

Step-by-step explanation: The minimum of function A is at (3,-2), while the minimum of function B would be at (-3,5). So, you do 5-(-2) to get 7.

The minimum value of A occurs 7 units lower than the minimum of function B.

We have given that,

Statement best compares the two functions

The maxima and minima of a function, known collectively as extrema, are the largest and smallest value of the function, either within a given range, or on the entire domain.

The minimum of function A is at (3,-2), while the minimum of function B would be at (-3,5). So, you do 5-(-2) to get 7.

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Hi there!

[tex]\large\boxed{\text{Choice 4}}[/tex]

We can look at each function, f(x) and g(x), to determine which is exponential.

Use slope formula: m = y2-y1/x2-x1

f(x) starts off with a slope at about $1800/year, but becomes about $1100/year.

g(x) starts off with a slope of about $1500/year, but becomes about $1874/year.

Thus, g(x) is exponential, because g(x)'s slope is increasing across the interval.

Given:

Edge of a cubic box = n inches.

He decided to make the box 1 inch taller and 2 inches longer, while keeping its depth at n inches.

To find:

How many cubic inches greater than the box he originally planned to build?

Solution:

Edge of a cubic box is n inches, so the volume of the original cube is:

[tex]V_1=(edge)^3[/tex]

[tex]V_1=n^3[/tex]

According to the given information,

New width of the box = n+1

New length of the box = n+2

New height of the box = n

So, the volume of the new box is:

[tex]V_2=Length\times width\times h[/tex]

[tex]V_2=(n+2)(n+1)n[/tex]

[tex]V_2=(n^2+2n+n+2)n[/tex]

[tex]V_2=(n^2+3n+2)n[/tex]

[tex]V_2=n^3+3n^2+2n[/tex]

Now, the difference between new volume and original volume is:

[tex]V_2-V_1=n^3+3n^2+2n-n^3[/tex]

[tex]V_2-V_1=3n^2+2n[/tex]

So, the volume of new box is 3n^2+2n cubic inches more than the original box.

Therefore, the correct option is A.

Answer:

.0668

Step-by-step explanation:

Formula:

z=(x-average)/standard deviation

(2.5-2.8)/.2= -1.5

Go to a ztable and find the value for 1.5  (.9332) and take the compliment of this (we can do this because the normal distribution is symmetrical)

1-.9332= .0668

Answer:

[tex]b=h=\sqrt{6}[/tex] m

Step-by-step explanation:

Let

Bas length of box=b

Height of box=h

Material used in constructing of box=36 square m

We have to find the height h and base length b of the box to maximize the volume of box.

Surface area of box=[tex]2b^2+4bh[/tex]

[tex]2b^2+4bh=36[/tex]

[tex]b^2+2bh=18[/tex]

[tex]2bh=18-b^2[/tex]

[tex]h=\frac{18-b^2}{2b}[/tex]

Volume of box, V=[tex]b^2h[/tex]

Substitute the values

[tex]V=b^2\times \frac{18-b^2}{2b}[/tex]

[tex]V=\frac{1}{2}(18b-b^3)[/tex]

Differentiate w. r.t b

[tex]\frac{dV}{db}=\frac{1}{2}(18-3b^2)[/tex]

[tex]\frac{dV}{db}=0[/tex]

[tex]\frac{1}{2}(18-3b^2)=0[/tex]

[tex]\implies 18-3b^2=0[/tex]

[tex]\implies 3b^2=18[/tex]

[tex]b^2=6[/tex]

[tex]b=\pm \sqrt{6}[/tex]

[tex]b=\sqrt{6}[/tex]

The negative value of b is not possible because length cannot be negative.

Again differentiate w.r.t b

[tex]\frac{d^2V}{db^2}=-3b[/tex]

At  [tex]b=\sqrt{6}[/tex]

[tex]\frac{d^2V}{db^2}=-3\sqrt{6}<0[/tex]

Hence, the volume of box is maximum at [tex]b=\sqrt{6}[/tex].

[tex]h=\frac{18-(\sqrt{6})^2}{2\sqrt{6}}[/tex]

[tex]h=\frac{18-6}{2\sqrt{6}}[/tex]

[tex]h=\frac{12}{2\sqrt{6}}[/tex]

[tex]h=\sqrt{6}[/tex]

[tex]b=h=\sqrt{6}[/tex] m

Answer:

Time of flight of first rocket = 60 seconds

Time of flight of second rocket = 40 seconds

Step-by-step explanation:

Let the time of flight of first rocket be t1.

Since the second rocket is launched 20 seconds later, then it means that;

t1 = t2 + 20

Where t2 is the time of flight of the second rocket.

When destruction has occurred, it means that both of the rockets would have covered the same distance.

We know that;

Distance = speed × time

Thus;

2000t1 = 3000t2

We know that t1 = t2 + 20

Thus;

2000(t2 + 20) = 3000t2

2000t2 + 40000 = 3000t2

3000t2 - 2000t2 = 40000

1000t2 = 40000

t2 = 40000/1000

t2 = 40 seconds

Thus;

t1 = 40 + 20

t1 = 60 seconds

SOLUTION:

10•10= 100

Answer:

it can not cleared clear but it can not cleared

Answer:

455 ways

Step-by-step explanation:

Given

[tex]n = 15[/tex] --- friends

[tex]r = 3[/tex] -- available postcard kinds

Required

Ways of sending the cards

The question is an illustration of combination and the formula is:

[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]

So, we have:

[tex]^{15}C_3 = \frac{15!}{(15 - 3)!3!}[/tex]

[tex]^{15}C_3 = \frac{15!}{12!*3!}[/tex]

Expand

[tex]^{15}C_3 = \frac{15*14*13*12!}{12!*3*2*1}[/tex]

[tex]^{15}C_3 = \frac{15*14*13}{3*2*1}[/tex]

[tex]^{15}C_3 = \frac{2730}{6}[/tex]

[tex]^{15}C_3 = 455[/tex]

Answer:

C. 3rd quartile

Step-by-step explanation:

Percentile:

A data belonging to the xth percentile means that the data is greater than x% of the values of the data-set, and smaller than (100 - x)%.

Point below 75% of the cases lie:

This is the 75th percentile, which is the 3rd quartile, as 75 = 3*100/4. Thus, the correct answer is given by option c.

Answer: 12

Step-by-step explanation:

The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed.

Answer:

Step-by-step explanation:

I always advise my students to make a table of information for these story problems because trying to keep track of the information otherwise is a nightmare. The table will look like this:

           d      =      r      *      t

m

c

m is motorcycle and c is car.

First thing we are told is that the ratio of m's speed to c's speed is 5:4; that means that we can divide 5/4 to find out how many times faster m is going than c.

5/4 = 1.25 so we have a couple of values to put into the table right away, along with the fact that they are both traveling the same distance of 160 miles.

             d      =     r      *      t

m        160     =   1.25r

c         160     =     r

The last thing we have to fill in is the time. If m travels a half hour less than c, c is driving a half hour more than m, right? Filling that in:

            d      =      r      *      t

m       160     =   1.25r   *     t

c        160     =      r       *  t + .5

Now we have our 2 equations. Looking at the top row of the table gives us the formula we need to solve this problem. It tells us, in other words, what we are going to be doing with these columns of numbers. Distance equals the rate times the time. For the motorcycle, the equation is:

160 = (1.25r)t  and that seems pretty useless since we still have 2 unknowns in there and you can only have 1 unknown in 1 equation. Let's see what the equation for the car is.

160 = (t + .5)r  Same problem.

Let's go back to the equation for the motorcycle and since we are looking for the rates of each, let's solve that equation for time in terms of rate (solve it for t):

[tex]t=\frac{160}{1.25r}[/tex] and sub that into the car's equation in place of t:

[tex]160=r(\frac{160}{1.25r})+.5r[/tex] and simplify. The r's to the left of the plus sign cancel out leaving us with:

[tex]160=(\frac{160}{1.25})+.5r[/tex] and divide those numbers inside the parenthesis to get:

160 = 128 + .5r and subtract 128 from both sides to get:

32 = .5r and finally divide by .5 to get

r = 64 miles/hour

The car goes 64 mph and the motorcycle goes 1.25 times that so,

m = 1.25(64) and

m = 80 mph

9514 1404 393

Answer:

  1,222,200

Step-by-step explanation:

A search using a computer program found ...

  5432 × 225 = 1,222,200

__

1000 mod 225 = 100

4 × 225 = 900

This suggests that if we have some number of thousands whose digits total 9, that we will have the number of interest. Of course, we can add 200 to some number of thousands with a digit total of 7. The smallest such digit total will be had with the number 1222 using the specified digits {0, 1, 2}. This gives rise to the result above: 1222×1000 +200 = 1,222,200. It also explains why moving the 1 to the right will also give a multiple of 225.

Answer:

hi, option C is correct because it has a right angel. please give brainliest

Answer:

1=83.08

Step-by-step explanation:

mean=summation of number divided by number

Answer:

<A = 47.7°

<B = 99.4°

<C = 32.9

Step-by-step explanation:

When given the measurements of all three sides, you can calculate the angles using the Cosine Law.

c² = a² + b² - 2ab cos C

(based on Pythagorean Theorem)

If we say: a = 15

b = 20

c = 11

11² = 15² + 20² - 2(15)(20) cos C

121 = 625 - 2(15)(20) cos C

121 = 625 - 600 cos C

⁻504 = ⁻600 cos C

cos⁻¹ (504 ÷ 600) = C

< C = 32.9°

a² = b² + c² - 2bc cos A

15² = 20² + 11² - 2(20)(11) cos A

225 = 521 - 2(20)(11) cos A

225 = 521 - 440 cos A

⁻296 = ⁻440 cos A

cos⁻¹ (296 ÷ 440) = A

<A = 47.7°

Then, since we know the sum of all three angles of a triangle equals 180°:

180° - 32.9° - 47.7° = 99.4°

<B = 99.4°

Answer:

You have a total of $11.50

Step-by-step explanation:

We first subtract $19.75 by $8.25 and the result will be $11.50

Answer:

11.50

Step-by-step explanation:

19.75-8.35= 11.50

May I have the brainiest?

Answer:

D. No angle opposite the sides is given

Step-by-step explanation:

Given

See attachment for triangle

Required

Why the law of sines cannot be used

From the attached image of a triangle, we can see that all sides are given while none of the angles are given.

Since none of the angles are given, then law of sines doesn't apply

Answer:

The 96% CI on the death rate from lung cancer is (0.4177, 0.4823).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

Of 1000 randomly selected cases of lung cancer, 450 resulted in death within 5 years.

This means that [tex]n = 1000, \pi = \frac{450}{1000} = 0.45[/tex]

96% confidence level

So [tex]\alpha = 0.04[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.04}{2} = 0.98[/tex], so [tex]Z = 2.054[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.45 - 2.054\sqrt{\frac{0.45*0.55}{1000}} = 0.4177[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.45 + 2.054\sqrt{\frac{0.45*0.55}{1000}} = 0.4823[/tex]

The 96% CI on the death rate from lung cancer is (0.4177, 0.4823).

Answer:

14=-2x-4

18=-2x

x=-9

Hope This Helps!!!

[tex] cos(A) = \frac{ {b}^{2} + {c}^{2} - {a}^{2} }{2bc} [/tex]

The cos A will be b/c

Cosine function in a triangle is the ratio of the adjacent side to that of the hypotenuse

The steps are as follow:

AB = c

BC = a

AC = b

Cos A = Adjacent side to A / Hypoteneous

Cos A = AC / AB

Cos A = b / c

Therefore the value of Cos A in given figure will be b / c

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Answer:

Step-by-step explanation:

                    Statements                                        Reasons

1). ΔABC with side lengths a, b, c, and h      1). Given

2). Area = [tex]\frac{1}{2}bh[/tex]                                                 2). Triangle area formula

3). [tex]\text{sin}C=\frac{h}{a}[/tex]                                                    3). Definition of sine

4). asin(C) = h                                                4). Multiplication property of

                                                                          equality.

5). Area = [tex]\frac{1}{2}ba\text{sin}C[/tex]                                         5). Substitution property

6). Area = [tex]\frac{1}{2}ab\text{sin}C[/tex]                                         6). Commutative property of

                                                                           multiplication.

Hence, proved.