Suppose that the functions r and a are defined for all real numbers x as follows. r(x)=2x-1 S(x)=5x write the expressions for (r-s)(x)and(r•s)(x)and evaluate(r+s)(-2).

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:

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

Answer:

25% would be the answer

Step-by-step explanation:

Answer: her call lasted for 22 minutes

Step-by-step explanation:

Rita purchased a prepaid phone card for $30. This means that the total credit on her card is $30. Long distance cost 16 cents a minute using the card. Converting to dollars, it costs 16/100 = $0.16

Rita used her card only once to make a long distance call. If the number of minutes if long distance call that she made is x, total cost of x minutes long distance calls will be 0.16 × x = $0.16x

The remaining credit on her card would be 30 - 0.16x

If the remaining credit on her card if $26.48, it means that

30 - 0.16x = 26.48

0.16x = 30 - 26.48 = 3.52

x = 3.52/0.16 = 22 minutes.

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:

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:down t

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

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:

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:

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:

Alien does not take the sample because alien choose the data of a Government's congress and congress contain less women.

On the other hand general population contain women greater than congress

So as compared to general population confidence interval is not representative.

Answer: The sample is not a simple random sample

Step-by-step explanation:

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: 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

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:

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:

[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:

1/14

Step-by-step explanation:

Assuming you mean that there are 2 red, 2 green, and 4 blue marbles, there are a total of 8 marbles.

On the first draw, the probability the marble is red is 2/8.

On the second draw, there's one less marble, so the probability of selecting a green marble is 2/7.

The total probability is:

2/8 × 2/7 = 1/14

The probability that the first marble is red and the second is green is approximately 0.0626 or 6.26%.

To find the probability we need to follow these steps:

The probability of drawing a red marble first is:

P(Red) = Number of Red Marbles / Total Number of Marbles = 222 / 888 = 1/4 or 0.25.

The probability of drawing a green marble after a red one has been drawn is:

P(Green | Red) = Number of Green Marbles / Remaining Marbles = 222 / 887.

The overall probability is:

P(Red then Green) = P(Red) * P(Green | Red) = (222 / 888) * (222 / 887) = (1/4) * (222 / 887).

Therefore, the probability that the first marble is red and the second is green is approximately 0.0626 or 6.26%.

Answer:  The population of the country will be 106 millions in 2014.

Step-by-step explanation:

The exercise gives you the following exponential model, which describes the​ population "A" (in​ millions) of a country "t" years after 2003:

[tex]A=104.8 e^{0.001 t}[/tex]

In this case you must determine when the population of that country will be 106 millions, so you can identify that:

[tex]A=106[/tex]

Now you need to substitute this value into the exponential model given in the exercise:

[tex]106=104.8 e^{0.001 t}[/tex]

Finally, you must solve for "t", but first it is important to remember the following Properties of logarithms:

[tex]ln(a)^b=b*ln(a)\\\\ln(e)=1[/tex]

Then:

[tex]\frac{106}{104.8}=e^{0.001 t}\\\\ln(\frac{106}{104.8})=ln(e)^{0.001 t}\\\\ln(\frac{106}{104.8})=0.001 t(1)\\\\\frac{ln(\frac{106}{104.8})}{0.001}}=t\\\\t=11.38\\\\t\approx11[/tex]

Notice that in 11 years the population will be 106 millions, then the year will be:

[tex]2003+11=2014[/tex]

The population of the country will be 106 millions in 2014.

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

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:

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)

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) [tex](0.035,\ 0.065)[/tex]

Step-by-step explanation:

The confidence interval for proportion (p) is given by :-

[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

, where[tex]\hat{p}[/tex] = Sample proportion

n= sample size.

z* = Critical z-value.

Let p be the true proportion of defective manhole covers, based on this sample.

Given : The workers at Sandbachian, Inc. took a random sample of 800 manhole covers and found that 40 of them were defective.

Then , n= 800

[tex]\hat{p}=\dfrac{40}{800}=0.05[/tex]

Confidence interval = 95%

We know that the critical value for 95% Confidence interval : z*=1.96

Then, the 95% CI for p, the true proportion of defective manhole covers will be :-

[tex]0.05\pm (1.96)\sqrt{\dfrac{0.05(1-0.05)}{800}}\\\\=0.05\pm (1.96)(0.0077055)\\\\=0.05\pm0.01510278\\\\=(0.05-0.01510278,\ 0.05+0.01510278)\\\\=(0.03489722,\ 0.06510278)\approx(0.035,\ 0.065) [/tex]

Hence, the required confidence interval : b) [tex](0.035,\ 0.065)[/tex]

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:

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:

√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:

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:

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:

  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:

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