A new Firestone tire is guaranteed to last for 40,000 miles. The actual mean life of the tires is 47,000 miles with a standard deviation of 4,000 miles.
a) What percent of the tires will last for at least 40,000 miles?
b) What percent of the tires will not last for at least 40,000 miles?
c) What is the probability that a tire will last for more than 50,000 miles?
d) The Firestone Company wants to advertise how long some of their tires last. They decide to state how long the top 3% of their tires will last. How many miles will the top 3% of their tires last?

Answer:

√56/8

Step-by-step explanation:

Let the number be x

f(x) = 8x + 7(1/x)

f(x) = 8x + 7/x

Differentiate f(x) with respect to x

f'(x) = 8x - 7/x = 0

8 - 7/x^2 = 0

(8x^2 - 7)/2 = 0

8x^2 - 7 = 0

8x^2 = 7

x^2 = 7/8

x = √7/8

x = √7 /√8

x = (√7/√8)(√8/√8)

x = (√7*√8) / √8*√8)

x = √56/8

Answer:

0.00597

Step-by-step explanation:

Given,

Total number of cards = 52,

In which flush cards = 20,

Also, the number of spade flush cards = 5,

Since,

[tex]\text{Probability}=\frac{\text{Favourable outcomes}}{\text{Total outcomes}}[/tex]

Thus, the probability of a hand containing a spade flush, if each player has 5 cards

[tex]=\frac{\text{Ways of selecting a spade flush card}}{\text{Total ways of selecting five cards}}[/tex]

[tex]=\frac{^{20}C_5}{^{52}C_5}[/tex]

[tex]=\frac{\frac{20!}{5!15!}}{\frac{52!}{5!47!}}[/tex]

[tex]=\frac{15504}{2598960}[/tex]

= 0.00597  

Answer:

10.54 pounds is right answer

Step-by-step explanation:

bananas 2.26  pounds

Grapes  1.5 pounds

water melon 6.78 pounds

total weight = 10.54 pounds

Answer:

10.54 pounds

Step-by-step explanation:

Answer:

option A and C, (-0.7, 0.5) and (0.7, 0.5)

Step-by-step explanation:

The two equations are equal means, the points at which the  two graphs meet.

In that case the x and y coordinates satisfy both the graphs.

let the coordinates at the intersection point be (a,b).

Inserting in first equation,

[tex]b = -a^{2} + 1[/tex]

Inserting in second equation,

[tex]b = a^{2}[/tex]

Inserting value of b from second to first equation, we get

[tex]b = -b + 1[/tex]

[tex]b = \frac{1}{2} = 0.5[/tex]

Now inserting the value of b second equation, we get

[tex]\frac{1}{2} = x^{2}[/tex]

[tex]x = \sqrt{\frac{1}{2} } = +\frac{1}{1.414} or -\frac{1}{1.414}  = +0.7  or  -0.7[/tex]

Thus points are, (-0.7, 0.5) and (0.7, 0.5)

Answer:

D. [tex]f(t)=300+0.20t[/tex]

Step-by-step explanation:

We have been given that Mikayla is a waitress who makes a guaranteed $50 per day.

Since Miklaya works  6 days per week, so the guaranteed income for one week would be [tex]\$50\times 6=\$300[/tex]  

We are also told that she gets tips of 20% of all her weekly customer receipts, t. So amount earned from tips would be 20% of t, that is [tex]\frac{20}{100}t=0.20t[/tex].

Total amount earned in one week would be guaranteed income for 1 week plus 20% of t:

[tex]300+0.20t[/tex]

Therefore, our required function is [tex]f(t)=300+0.20t[/tex] and option D is the correct choice.

Answer: it will take 2.7 hours to get to the surface

Step-by-step explanation:

A submarine was stationed 700 feet below sea level. It means that the height of the submarine from the surface is 700 feet.

It ascends 259 feet every hour.

If the submarine continues to ascend at the same rate, the time it will take for it to get to the surface will be the distance from the surface divided by its constant speed.

Time taken to get to the surface

700/259 = 2.7 hours

Using related rates and the Pythagorean theorem, we can find that dy/dt, the rate of change of the y-coordinate, is 0 ft/s.

To find dy/dt, we need to determine the rate of change of the y-coordinate of the jogger. Since the jogger is running on a circular track, we can use the concept of related rates to solve this problem.

Let's assume that the jogger completes a full lap around the track in a time interval of Δt. During this time interval, the x-coordinate of the jogger changes by Δx, the y-coordinate changes by Δy, and the distance traveled along the track is Δs.

Since the jogger is running at a constant speed, the distance Δs is equal to the distance traveled in a straight line, which is the hypotenuse of a right triangle with legs Δx and Δy. Using the Pythagorean theorem, we have:

Δs^2 = Δx^2 + Δy^2

Taking the derivative with respect to time, we have:

2Δs(dΔs/dt) = 2Δx(dΔx/dt) + 2Δy(dΔy/dt)

Substituting the given values, Δx is 15 ft/s, Δy is 0 (since the y-coordinate is not changing), and Δs is the distance around the circular track, which is equal to the circumference of the circle:

2π(55ft) = 2(15ft)(dΔx/dt) + 2(0)(dΔy/dt)

Simplifying, we have:

dΔx/dt = π(55ft)/15s = 11π/3 ft/s

Therefore, dy/dt = dΔy/dt = 0 ft/s, since the y-coordinate is not changing.

Answer:

[tex]P(A\ or\ B)=\frac{7}{9}[/tex]

Step-by-step explanation:

We need to use the formula to calculate the probability of (A or B) where  

A=Probability a student likes pepperoni

B=Probability a student likes olive

A and B =Probability a student likes both toppings in a pizza

A or B =Probability a student likes pepperoni or olive (and maybe both), a non-exclusive or

The formula is

[tex]P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)[/tex]

Since 6 students like pepperoni out of 9:

[tex]P(A) = \frac{6}{9}[/tex]

Since 4 students like olive out of 9:

[tex]P(B) = \frac{4}{9}[/tex]

Since 3 students like both toppings out of 9

[tex]P(A\ and\ B) = \frac{3}{9}[/tex]

Then we have

[tex]P(A\ or\ B)=\frac{6}{9}+\frac{4}{9}-\frac{3}{9}[/tex]

[tex]P(A\ or\ B)=\frac{7}{9}[/tex]

Answer:

[tex]P=M(1-e^{-kt})[/tex]

Step-by-step explanation:

The relation between the variables is given by

[tex]\frac{dP}{dt} = k(M- P)[/tex]

This is a separable differential equation. Rearranging terms:

[tex]\frac{dP}{(M- P)} = kdt[/tex]

Multiplying by -1

[tex]\frac{dP}{(P- M)} = -kdt[/tex]

Integrating

[tex]ln(P-M)=-kt+D[/tex]

Where D is a constant. Applying expoentials

[tex]P-M=e^{-kt+D}=Ce^{-kt}[/tex]

Where [tex]C=e^{D}[/tex], another constant

Solving for P

[tex]P=M+Ce^{-kt}[/tex]

With the initial condition P=0 when t=0

[tex]0=M+Ce^{-k(0)}[/tex]

We get C=-M. The final expression for P is

[tex]P=M-Me^{-kt}[/tex]

[tex]P=M(1-e^{-kt})[/tex]

Keywords: performance , learning , skill , training , differential equation

The differential equation dp/dt = k(M - P) can be solved via separating variables, integrating and applying the initial condition. Result provides the equation for performance over time: P(t) = M(1 - e-kt).

The subject of the question is around a differential equation. Firstly, you will rewrite the given equation dp/dt = k(M - P) in the form necessary for separation of variables: dp/(M - P) = k dt. Then, integrate both sides: ∫dp/(M - P) = ∫k dt. The left-hand side integral results in -ln|M - P|, and the right side is k*t + C, where C is the constant of integration. Finally, solve for P(t) by taking the exponential of both sides, and rearranging. The procedure results in the performance level equation.

P(t) = M - Ce-kt

Since we're given P(0) = 0, we can determine that C = M. Hence, we finally have the solution:

P(t) = M(1 - e-kt)

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Answer:

The ratio is 2 to 3.

Step-by-step explanation:

The jar is comprised of only red and green jelly beans. We are given the number of total beans and the number of red beans. We calculate the number of green beans by doing 800-320 = 480.

The problem is asking for the ratio of red to green jelly beans, which is 320 to 480, or 320/480. Simplified, this is 2/3.

The ratio of red to green jellybeans will be 1/3.

Ratio is a quantitative relation between two amounts showing the number of times one value contains or is contained within the other. A statement expressing the equality of two ratios A:B and C:D is called a proportion. We can express proportion as -

A : B ∷ C : D

AND

A x D = B x C

Product of extremes equal to product of means

We have a jar that contains 800 red and green jelly beans. Of those, 320 are red and the rest are green.

Number of red beans = 320

Number of green jelly beans = 800 - 320 = 480

Ratio of red to green jellybeans = 320/480 = 1/3

Therefore, the ratio of red to green jellybeans will be 1/3.

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Answer:

Step-by-step explanation:

The triangle is a right angle triangle. This is because one of its angles is 90 degrees.

Let us determine x

Taking 47 degrees as the reference angle,

x = adjacent side

11 = hypotenuse

Applying trigonometric ratio,

Cos # = adjacent side / hypotenuse

# = 47 degrees

Cos 47 = x/11

x = 11cos47

x = 11 × 0.6820

x = 7.502

Let us determine y

Taking 47 degrees as the reference angle,

y = opposite side

11 = hypotenuse

Applying trigonometric ratio,

Sin # = opposite side / hypotenuse

# = 47 degrees

Sin 47 = y/11

x = 11Sin47

x = 11 × 0.7314

x = 8.0454

I don't think that's correct

Step-by-step explanation:

Why are you splitting the $50? you'd end up paying more than the bill and he'd be getting back more money than he put in. Sounds like a rip off. If he had given you each $50 than maybe you'd each owe $140. I assume there is 3 friends, the original bill price would have been $110 for each of you. But then one friend gave $50 to help pay the bill, if you had split the $50 you'd still not be paying back that much. Also why are YOU paying so much more? Everyone else is paying $140 and you're paying $165? You would not be giving him that much, all of you would not be paying an extra $30 either. you'd be splitting it to where it equals $50 all around, so instead it'd be around $93.00. Not $140 or $165. $16.7 multipled by 3 = $50.1

But at the end of the day, just tell him to take his money back. He really didn't help pay the bill that much with his $50, he still owes you $60 if he too had participated in whatever you guys were doing. So instead of going through the trouble, just tell him to take back his money.

Answer:

  90 feet

Step-by-step explanation:

The perimeter is the sum of the side lengths of the enclosure. The length is given as 80 ft, but only one side that long counts as part of the 260 ft of fence. So, we have ...

  260 ft = 2×W + L = 2×W + 80 ft . . . . . length of fence for 3 sides

  180 ft = 2×W . . . . . . subtract 80

  90 ft = W . . . . . . . . . divide by 2

The width of the enclosure is 90 feet.

Final answer:

To find the width of the farmer's rectangular enclosure, we subtract the length of the barn (80 ft) from the total amount of fencing available (260 ft) to get the length available for the other three sides. Dividing this by two (because there are two widths), we find that the width of the enclosure will be 90 feet.

Explanation:

The question asks about creating a rectangular enclosure using a fixed length of fencing and a barn as one of the sides. With 260 feet of fencing available and the barn covering one side of 80 feet, the farmer must use the remaining fencing for the other three sides of the rectangle.

To find the width of the rectangular enclosure, we need to subtract the length of the barn side from the total amount of fencing available, and then divide by two (because there are two widths in a rectangle), as follows:

260 ft - 80 ft = 180 ft for both widths, so each width will be

180 ft / 2 = 90 ft.

Therefore, the width of the rectangular enclosure will be 90 feet.

Answer:

The Proof is given below.

Step-by-step explanation:

Given:

LJ ≅ MK

LK ≅ MJ

To Prove:

∠ L ≅ ∠ M

Proof:

In  Δ LKJ  and Δ MJK

    LK ≅ MJ      ……….{Given}

    KJ ≅ KJ       ………..{Reflexive Property}

    LJ ≅ MJ       ……….{Given}

Δ LKJ ≅ Δ MJK  ....….{Side-Side-Side test}

∴∠ KLJ ≅ ∠ JMK  .....{corresponding angles of congruent triangles (c.p.ct)}

i.e ∠ L ≅ ∠ M ............Proved.

Answer:

running distance =   78,18 m

swimmingdistance  =  92m

Step-by-step explanation:

Ann has to run a distance 100 - x    and swim  √ (50)² + x²

at speed of 5 m/sec   and 2 m/sec

As distance  = v*t       t  = d/v

Then running she will spend time doing d = ( 100-x)/5    

and   √[(50)² + x² ] / 2   swimming

Therefore total time of biathlon

t(x)  =  ( 100 - x )/5    +  √[(50)² + x² ] / 2

Taking derivatives both sides of the equation we get

t´(x)  =  - 1/5  + [1/2 ( 2x)*2] / 4√[(50)² + x²]

t´(x)  =  - 1/5  + 2x / 4√[(50)² + x²]      t´(x)  =  - 1/5  + x/2√(50)² + x²

t´(x)  = 0           - 1/5  + x/2√(50)² + x²  = 0

  - 2√[(50)²+  x²]   +  5x     =  0

  - 2√(50)²+  x² ) =  -5x

       √(50)²+  x²   = 5/2 *x

squared

        (50)²  +  x²   = 25/4 x²

             2500 - 21/4 x²  =  0

                           x²  =  2500*4/21

 x  =  21,8 m

Therefore she has to run  100 - 21,82  = 78,18 m

And swim    √(50)² + (78,18)²   =  92m

The question pertains to Physics and involves calculating the optimal path in a swim-and-run biathlon to minimize total time, which would typically involve physics and calculus. However, the scenario is incomplete and lacks necessary information for a precise solution.

The subject of this question is Physics, as it involves concepts of speed, velocity, and optimization of travel paths in a biathlon, which includes both swimming and running. To answer the question on the optimal path Ann should take in the swim-and-run biathlon, we would use principles of physics and calculus to find the path that minimizes the total time. The calculation would involve deriving the functional relationship between swimming and running speeds, and the distances covered in each stage, then determining the point at which Ann should exit the water to reach the end point in the shortest total time. However, since the problem in the question is incomplete and requires additional information, such as the current of the river or whether Ann swims at a constant speed relative to the water, we cannot solve it without making assumptions that may be incorrect.

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Answer:

  (-4, 0)

Step-by-step explanation:

The scale factor of 1/2 means each "dilated" point is 1/2 the distance from the center of dilation that the original point is. That is, the dilated point is the midpoint between the original and the dilation center.

If O is the origin of the dilation, then ...

  (O + X)/2 = P . . . . . P is the dilation of point X

  O +X = 2P

  O = 2P -X = 2(0, 2) -(4, 4)

  O = (-4, 0)

The center of dilation is (-4, 0).

_____

Another way to find the center of dilation is to realize that dilation moves points along a radial line from the center. Hence the place where those radial lines converge will be the center of dilation. See the attachment for a solution that way.

Answer:

b(x)=24(1/2)x

Step-by-step explanation:

The situation can be modeled by the exponential function will be y = 24 (0.5)ˣ.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

There are 24 ball groups contending in a competition. After each round around 50% of the groups is dispensed with.

Then the value of the b will be 1/2 and the value of the variable 'a' will be 24. Then the exponential equation is given as,

y = 24 (1/2)ˣ

y = 24 (0.5)ˣ

The situation can be modeled by the exponential function will be y = 24 (0.5)ˣ.

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Answer:

Step-by-step explanation:

It can be helpful to draw a diagram. In the attached diagram, point H represents the harbor, point B represents the position of the boat, and point N represents a point directly north of the harbor and west of the boat.

The bearing N56E means the direction of travel is along a path that is 56° clockwise (toward the east) from north.

__

The mnemonic SOH CAH TOA reminds you of the relationships between the sides of a right triangle. Here, we are given the length of the hypotenuse, and we want to know the lengths of the sides opposite and adjacent to the angle. One of the useful relations is ...

  Sin = Opposite/Hypotenuse

In our diagram, this would be ...

  sin(56°) = BN/BH

We want to find length BN, so we can multiply by BH to get ...

  BN = BH·sin(56°) = 150·0.829038 = 124.4 . . . . miles (east)

__

For the adjacent side, we use the relation ...

  Cos = Adjacent/Hypotenuse

  cos(56°) = HN/HB

  HN = HB·cos(56°) = 150·0.559193 = 83.9 . . . . miles (north)

The boat has traveled 124.4 miles north and 83.9 miles east of the harbor entrance.

Answer:

Remainder = 64

Step-by-step explanation:

Given equation,

[tex]x^4+3x^3-6x^2-12x-8[/tex]

Remainder theorem says a polynomial can be reset in terms of its divisor (a) by evaluating the polynomial at x=a

Plug x=3,

[tex]=3^4+3(3)^3-6(3)^2-12(3)-8\\=81+81-54-36-8\\=162-54-36-8\\=64[/tex]

Thus the remainder is 64 at x=3 ,using polynomial remainder theorem.

Answer:

Step-by-step explanation:

The total cost of producing a cylindrical can with radius r and height h will be ...

  cost = (lateral area)×(side cost) +(end area)×(end cost) +(seam length)×(seam cost)

__

The lateral area (LA) is ...

  LA = 2πrh

Since the volume of the can is fixed, we can write the height in terms of the radius using the volume formula.

  V = πr²h

  h = V/(πr²)

Then the lateral area is ...

  LA = 2πr(V/(πr²)) = 2V/r = 2·500/r = 1000/r

__

The end area (EA) is twice the area of a circle of radius r:

  EA = 2×(πr²) = 2πr²

__

The seam length (SL) is twice the circumference of the end:

  SL = 2×(2πr) = 4πr

__

So, the total cost in cents of producing the can, in terms of its radius, is ...

  cost = (1000/r)(0.01) +(2πr²)(.012) +(4πr)(0.015)

We can find the minimum by setting the derivative to zero.

  d(cost)/dr = -10/r² +0.048πr +.06π = 0

Multiplying by r² gives the cubic ...

  0.048πr³ +0.06πr² -10 = 0

  r³ +1.25r² -(625/(3π)) = 0 . . . . . . divide by .048π

This can be solved graphically, or using a spreadsheet to find the value of r to be about 3.671 cm. The corresponding value of h is ...

  h = 500/(π·3.671²) ≈ 11.810 . . . cm

The minimum-cost can will have a radius of about 3.671 cm and a height of about 11.810 cm.

_____

A graphing calculator can find the minimum of the cost function without having to take derivatives and solve a cubic.

Answer:

25% would be the answer

Step-by-step explanation:

Answer:

  9.6 units

Step-by-step explanation:

The area of the parallelogram is the product of the base length and distance between parallel sides, either way you figure it.

  16 × 6 = area = 10 × h

  96 = 10h

  h = 96/10 = 9.6 . . . . units

Answer:

 = 12169 rs

Step-by-step explanation:

Asha invest total=rs 8000  

Total years = 3

Amount after 1 year= 9200 rs

Interest on first year =9200-8000= 1200 rs

So for second and third years

A= P (1 + R/100)ⁿ

9200= 8000( 1+  R/100)¹

9200= 8000( 100+  R/100)  

115= 100 +R

R = 15  

So amount after second year  

A= 8000 (1 +15/100)²

A= 10580

Interest on second is = 10580 –P-interest on ist  

                                      =10580-8000-1200

                                   = 1380 rs

So total amount at the end  

A =  8000 ( 1 +15/100) ³

 =12169 rs

Step-by-step explanation:

We need to find new area of bakery.

Old length = 15 feet

Old width = New width = 5 x  Old length = 5 x 15 = 75 feet

New length = Old length + 5 feet = 15 + 5 = 20 feet

New area = New length x New width

New area = 75 x 20 = 1500 square feet.

New area of bakery = 1500 square feet.

Answer:

26 socks

Step-by-step explanation:

There are a total of 48 socks here. Let us assume you pulled out 24 socks at a go and all are red. Now, you would have exhausted the number of red socks here. You would be left with only blue socks which you can pull one after the other to give a total of  26 socks pulled out to have 2 blue socks at least.

Answer with Step-by-step explanation:

We are given that a matrix B .

The eigenvalues of matrix are 0, 1 and 2.

a.We know that

Rank of matrix B=Number of different eigenvalues

We have three different eigenvalues

Therefore, rank of matrix B=3

b.

We know that

Determinant of matrix= Product of eigenvalues

Product of eigenvalues=[tex]0\times 1\times 2=0[/tex]

After transpose , the value of determinant remain same.

[tex]\mid B^TB\mid=\mid B^T\mid \mid B\mid =0\times 0=0[/tex]

c.Let  

B=[tex]\left[\begin{array}{ccc}0&-&-\\-&1&-\\-&-&2\end{array}\right][/tex]

Transpose of matrix:Rows change into columns or columns change into rows.

After transpose of matrix B

[tex]B^T=\left[\begin{array}{ccc}0&-&-\\-&1&-\\-&-&2\end{array}\right][/tex]

[tex]B^TB=\left[\begin{array}{ccc}0^2&-&-\\-&1^2&-\\-&-&2^2\end{array}\right][/tex]

[tex]B^TB=\left[\begin{array}{ccc}0&-&-\\-&1&-\\-&-&4\end{array}\right][/tex]

Hence, the eigenvalues of [tex]B^TB[/tex] are 0, 1 and 4.

d.Eigenvalue of Identity matrix are 1, 1 and 1.

Eigenvalues of [tex]B^2+I=(0+1),(1+1),(2^2+1)=1,2,5[/tex]

We know that if eigenvalue of A is [tex]\lambda[/tex]

Then , the eigenvalue of [tex]A^{-1}[/tex] is [tex]\frac{1}{\lambda}[/tex]

Therefore, the eigenvalues of [tex](B^2+I)^{-1}[/tex] are  

[tex]\frac{1}{1},\frac{1}{2},\frac{1}{5}[/tex]

The eigenvalues of [tex](B^2+I)^{-1}[/tex] are 1,[tex]\frac{1}{2}[/tex] and [tex]\frac{1}{5}[/tex]

Answer:

first, second, and fourth are correct

Step-by-step explanation:

2(-4) + 0 = -8; this is correct because -8 + 0 = -8

(-4) - 0 = -4; this is correct because -4 - 0 = -4

We know that they are both true, so the fourth choice is true as well.

Statements first, second, and fourth are true about the ordered pair (−4, 0) and the system of equations, 2x+y=−8 and x−y=−4.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that,

2x+y=−8

x−y=−4

The correct statements for the ordered pair (−4, 0) are,

Because it makes the first equation true, the ordered pair (4, 0) is a solution to the first equation.

⇒2(-4) + 0 = -8

⇒-8 + 0 = -8

Because it makes the second equation true, the ordered pair (4, 0) is a solution to the second equation.

⇒(-4) - 0 = -4

⇒-4 - 0 = -4

The ordered pair (4, 0) makes both equations true, making it a solution to the problem.

Thus, statements first, second, and fourth are true about the ordered pair (−4, 0) and the system of equations, 2x+y=−8 and x−y=−4.

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Answer:

18 fastballs

Step-by-step explanation:

Let x represent each throw

fastball : curve ball = 3:2

For fastball we have 3x while for curve ball we have 2x

If Rick makes a relief appearance of 30 pitches with the same ratio,

3x + 2x = 30

5x = 30

x = 30/5

x = 6

fastball, 3x= 3*6

= 18

curveball = 2x = 2*6

= 12

Rick will throw 18 fast balls

Answer:down t

Step-by-step explanation: j this is world. Theo t sit with this

Answer:

2

Step-by-step explanation:

Terms are products separated by +'s and −'s.  Here, there are 2 terms:

2 tan(1/t) / (1/t)

sec²(1/t)