Given that log 2 = 0.3010 and log 7 = 0.8451, find the following (a) log 49 (b) log 560​

Answer:

10:35-3:15

Step-by-step explanation:

Let minimum score on the final exam to earn an A be X

[tex]mean \: = \frac{sum \: of \: observation}{number \: of \: observation} [/tex]

[tex]90 = \frac{83 + 97 + 89 + 82 + x}{5} [/tex]

Further solving :

X = 99 marks

Answer:

10

Step-by-step explanation:

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Answer:

Step-by-step explanation:

The cost of the ends of the can will be ...

  c1 = 0.07(2πr²)

The cost of the side of the can will be ...

  c2 = 0.04(2πrh)

The volume of the can will be ...

  v = πr²h

We want the derivative of the total cost to be zero, and we want the volume to be 550 cm³. We can take the derivatives of both equations to find a relation between r and h.

  d(c1 +c2) = 0.28πr·dr +0.08π(h·dr +r·dh) = 0

  d(v) = 2πrh·dr +πr²·dh = 0

Solving the first equation for dh/dr gives ...

  dh/dr = -π(0.28r +0.08h)/(π(0.08r)) = -(7r+2h)/(2r)

Solving the second equation for dh/dr gives ...

  dh/dr = -2πrh/(πr²) = -2h/r

Equating these expressions, we get ...

  -(7r +2h)/(2r) = -2h/r

  7r +2h = 4h . . . . . . . multiply by -2r

  h = 7/2r . . . . . . . . . . subtract 2h, divide by 2

__

Now, we can find the can dimensions from the volume equation.

  550 = πr²(7/2r)

  r³ = 1100/(7π)

  r ≈ ∛50.02 ≈ 3.685 . . . . . cm

  h = 7/2(3.685 cm) = 12.896 cm

The can cost will be a minimum when the radius is 3.685 cm and the height is 12.896 cm.

_____

Additional comment

You may notice that the ratio of height to diameter is the same as the ratio of end cost to side cost: 7/4. This is the generic solution to this sort of problem.

Is this question complete?

Answer:

Take 5^x as y.  

Now the question becomes a simple equation.  

y + 20y - 125 = 0.

21y = 125.

Thus, y = 125/21.

Now resubstituting we get,

5^x = 125 /21.

Taking log on both sides,

xlog5 = log 125 - log 21

x = (log125/log5) - (log21/log 5)

x= 3- 1.89

Answer:

8

Step-by-step explanation:

4×16=64

[tex] \sqrt{64 } = 8[/tex]

[tex]\sqrt{16}\times\sqrt{12}[/tex]

$=\sqrt{4^2}\times\sqrt{2^2\cdot3}$

$=4\times2\sqrt3=8\sqrt3$

Answer:

236°

Step-by-step explanation:

The circumference of a circle is 360° since <DOC is given as 44° and <COB is given as 80° and the center angles are equal to the arc it sees the the measure of arc DEB would be 360 - 44 - 80 = 236°

Answer:

The greater than symbols looks like this    >    , and the less than symbol looks like? <

Answer:

Greater than symbol: >

Less than symbol: <

Greater than or equal to symbol: ≥

Less than or equal to symbol: ≤

Equal symbol: =

In this case, you are answering with the greater than symbol as well as the less than symbol.

The greater than symbols looks like this > , and the less than symbol looks like < .

If the scale factor is 30, then all you have to do is multiply each measurement by the scale factor. In this case, 4 · 30 = 120.

Answer:

[tex]t = 0.811\,s[/tex] contains the cheapest reference to sugar; [tex]t = 4.511\,s[/tex] contains the most expensive reference to sugar.

Step-by-step explanation:

Let be [tex]s(t) = -0.00003237\cdot t^{5} + 0.0009037\cdot t^{4}-0.008956\cdot t^{3}+0.03629\cdot t^{2}-0.04547\cdot t + 0.4778[/tex], the times when sugar is the cheapest and the most expensive (absolute minimum and maximum) are determined with the help of first and second derivatives of this function (First and Second Derivative Tests):

First Derivative Test

[tex]s'(t) = -0.00016185\cdot t^{4}+0.0036148\cdot t^{3}-0.026868\cdot t^{2}+0.07258\cdot t - 0.04547[/tex]

Let equalize the polynomial to zero and solve the resulting expression:

[tex]-0.00016185\cdot t^{4}+0.0036148\cdot t^{3}-0.026868\cdot t^{2}+0.07258\cdot t - 0.04547 = 0[/tex]

[tex]t_{1} \approx 9.511\,s[/tex], [tex]t_{2}\approx 7.431\,s[/tex], [tex]t_{3}\approx 4.511\,s[/tex] and [tex]t_{4}\approx 0.881\,s[/tex]

Second Derivative Test

[tex]s''(t) = -0.0006474\cdot t^{3}+0.0108444\cdot t^{2}-0.053736\cdot t+0.07258[/tex]

This function is now evaluated at each root found in the First Derivative section:

[tex]s''(9.511\,s) = -0.0006474\cdot (9.511\,s)^{3}+0.0108444\cdot (9.511\,s)^{2}-0.053736\cdot (9.511\,s)+0.07258[/tex]

[tex]s''(9.511\,s) = -0.015[/tex] (A maximum)

[tex]s''(7.431\,s) = -0.0006474\cdot (7.431\,s)^{3}+0.0108444\cdot (7.431\,s)^{2}-0.053736\cdot (7.431\,s)+0.07258[/tex]

[tex]s''(7.431\,s) = 6.440\times 10^{-3}[/tex] (A minimum)

[tex]s''(4.511\,s) = -0.0006474\cdot (4.511\,s)^{3}+0.0108444\cdot (4.511\,s)^{2}-0.053736\cdot (4.511\,s)+0.07258[/tex]

[tex]s''(4.511\,s) = -8.577\times 10^{-3}[/tex] (A maximum)

[tex]s''(0.811\,s) = -0.0006474\cdot (0.811\,s)^{3}+0.0108444\cdot (0.811\,s)^{2}-0.053736\cdot (0.811\,s)+0.07258[/tex]

[tex]s''(0.811\,s) = 0.036[/tex] (A minimum)

Each value is evaluated in order to determine when sugar was the cheapest and the most expensive:

Cheapest (Absolute minimum)

[tex]s(0.811\,s) = -0.00003237\cdot (0.811\,s)^{5}+0.0009037\cdot (0.811\,s)^{4}-0.008956\cdot (0.811\,s)^{3}+0.03629\cdot (0.811\,s)^{2}-0.04547\cdot (0.811\,s)+0.4778[/tex]

[tex]s(0.811\,s) = 0.460[/tex]

[tex]s(7.431\,s) = -0.00003237\cdot (7.431\,s)^{5}+0.0009037\cdot (7.431\,s)^{4}-0.008956\cdot (7.431\,s)^{3}+0.03629\cdot (7.431\,s)^{2}-0.04547\cdot (7.431\,s)+0.4778[/tex]

[tex]s(7.431\,s) = 0.491[/tex]

[tex]t = 0.811\,s[/tex] contains the cheapest reference to sugar.

Most expensive (Absolute maximum)

[tex]s(4.511\,s) = -0.00003237\cdot (4.511\,s)^{5}+0.0009037\cdot (4.511\,s)^{4}-0.008956\cdot (4.511\,s)^{3}+0.03629\cdot (4.511\,s)^{2}-0.04547\cdot (4.511\,s)+0.4778[/tex]

[tex]s(4.511\,s) = 0.503[/tex]

[tex]s(9.511\,s) = -0.00003237\cdot (9.511\,s)^{5}+0.0009037\cdot (9.511\,s)^{4}-0.008956\cdot (9.511\,s)^{3}+0.03629\cdot (9.511\,s)^{2}-0.04547\cdot (9.511\,s)+0.4778[/tex]

[tex]s(9.511\,s) = 0.498[/tex]

[tex]t = 4.511\,s[/tex] contains the most expensive reference to sugar.

The required values are,

[tex]t=0.881199[/tex] at the cheapest.

[tex]t=4.51081[/tex] at the most expensive.

A high point is called a maximum (plural maxima ). A low point is called a minimum (plural minima ).

Given equation is,

[tex]S(t) = -0.00003237t^5 + 0.0009037t^4- 0.008956t^3 + 0.03629t^2-0.04547t + 0.4778[/tex]

Differentiating the given equation we get,

[tex]S'(t)=-0.00003237\times 5t^4+0.0009037\times 4t^3-0.008956\times 3t^2+0.03629\times 2t-0.04547+0\\S'(t)=0\\-0.00003237\times 5t^4+0.0009037\times 4t^3-0.008956\times 3t^2+0.03629\times 2t-0.04547+0=0\\t=0.881199\\t=4.51081\\t=7.43087\\t=9.51137\\[/tex]

Now we can directly plug those fours values of t into given function S(t) to find which one gives max or minimum or you can also use the 2nd derivative test. Although that is not compulsory

[tex]t=0.881199,S(t)=0.46031095\\t=4.51081, S(t)=0.50278423\\t=7.43087, S(t)=0.49096762\\t=9.51137, S(t)=0.49832202\\[/tex]

We see that sugar is cheapest at [tex]t=0.881199[/tex] which is approx 1 and corresponds to the year [tex]1993+1=1994[/tex]

Similarly sugar is most expensive at [tex]t=4.51081[/tex] which is approx 5 and corresponds to year [tex]1993+5=1998[/tex]

Learn more about the topic Minimum or Maximum:

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Answer:

the general equation of parabola is,

y=ax²+bx+c,

you put the given points in the equation since they will satisfy the equation, after that you should get three equations with only a,b,c in them, solve them for a,b,c and find their values, then just put the values in the main equation, which is, y=ax²+bx+c, that's all you have to do

Answer:

1. It would take the car to get from Tucson to Phoenix 12 hours.

2. for the car to go around the equator it would take 637 hours if it is still travelling at 10km/hr.

hope this helps

Step-by-step explanation:

1. 120 km divided by 10 = 12 hours

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Answer:

  x = 5.0

Step-by-step explanation:

The tangent relation is helpful:

  Tan = Opposite/Adjacent

  tan(50°) = x/4.2

  x = 4.2·tan(50°) ≈ 5.0054 . . . . multiply by 4.2

  x ≈ 5.0

Answer:

$20

Step-by-step explanation:

Company A:

Buy 300 shares at $1.45 per share.

Sell 300 shares at $1.65 per share.

Profit: ($1.65 - $1.45) * 300 = $60

Company B:

Buy 200 shares at $1.20 per share.

Sell 200 shares at $1.10 per share.

Loss: ($1.20 - $1.10) * 200 = $20

Net profit:

$40 - $20 = $20

Answer:

Step-by-step explanation:

Profit on Company A =$(1.65−1.45)×300=$60.

Loss on Company B =$(1.20−1.10)×200=$20.

Therefore the total profit Jamal achieved was $60−$20=$40.

Answer:

The value for the Chi -square  test statistics = 1.149

Step-by-step explanation:

The observed value Table can be shown better as:

Observed Value

Age            Favorable          Unfavorable            Neutral              Total

18-30             67                            24                       20                   111

30-45            50                            14                        16                    80

Over 45         69                           21                        26                   116

Total              186                         59                        62                   307

NOTE: when computing the question, in the third row and the second column, there is a mistake , the value is supposed to be 21 and not  41 because :

69 +21+ 26 will eventually give = 116

69 + 41 + 26 = 136  

With that error being fix , let's get started.

Expected Value

The expected value can be determined by using the formula:

[tex]Expected \ Value = \dfrac{ row \ total \times column \ total }{grand \ total }[/tex]

For 67; (111 * 186)/307 = 67.251

For 24 : (111 * 59)/307 = 21.332

For 20 : (111 * 62)/307 = 22.417

For 50 :(80*186)/307 = 48.469

For 14 : (80* 59)/307 = 15.375

For 16 : ( 0 * 62)/307 = 16.156

For 69 : (116 * 186)/307 = 70.280

For 21 : (116* 59)/307 = 22.293

For 26 : (116*62)/307 = 23.427

Expected Value :

Age            Favorable          Unfavorable            Neutral              Total

18-30         67.251                 21.332                     22.417                  111

30-45        48.469                15.375                     16.156                  80

Over 45    70.280                22.293                     23.427               116

Total              186                         59                        62                   307

The Chi - square test statistics = [tex]\dfrac{(observed \ value - Expected \ value)^2}{Expected \ value}[/tex]

For 67.251 : ( 67 - 67.251)²/67.251 = 0.0009

For 21.332 : ( 24 - 21.332)²/21.332 = 0.3337

For 22.417 : ( 20 - 22.417)²/ 22.417 = 0.2606

For 48.469 : ( 50 - 48.469)²/ 48.469 = 0.0484

For 15.375 : ( 14 - 15.375)²/ 15.375 = 0.1230

For 16.156 : ( 16 - 16.156)²/ 16.156 = 0.0015

For 70.280 : ( 69 - 70.280)²/ 70.280 = 0.0233

For 22.293 : ( 21 - 22.293)²/ 22.293 = 0.0750

For 23.427 : ( 26 - 23.427)²/ 23.427 = 0.2826

The chi square table is as follows:

Age            Favorable          Unfavorable            Neutral          Total

18-30          0.0009              0.3337                   0.2606           0.5952

30-45         0.0484               0.1230                   0.0015            0.1729

Over 45     0.0233               0.0750                  0.2826            0.3809

Total          0.0726                0.5317                   0.5447              1.149

The value for the Chi -square  test statistics = 1.149

Answer:

C)slides graph 4 units to the right

Answer:

B

Step-by-step explanation:

The weight of the jar depends on the number of marbles in it, therefore the weight is the dependent variable (y) and the number of marbles is the independent variable (x). The y-intercept is when x = 0 and since the number of marbles is x, the answer is that the y-intercept represents the weight of the jar without the marbles.

Answer:

the lines are perpdicular if you were to get some graph paper and graph u would see

Answer:

50%

Step-by-step explanation:

22 is half of 44.

So, this means 50% of 44 is 22.

Answer:

The probability mass function  that you never win [tex]^xC_o[/tex] = [tex](\dfrac{999999}{1000000})^x[/tex]

Step-by-step explanation:

Given that;

the winning chance of a weekly local lottery = [tex]\dfrac{1}{10^6}[/tex]

= [tex]\dfrac{1}{1000000}[/tex]

The probability of losing = 1 - probability of winning (winning chance)

The probability of losing = [tex]1- \dfrac{1}{1000000}[/tex]

The probability of losing =[tex]\dfrac{999999}{1000000}[/tex]

The probability mass function  that you never win [tex]^xC_o[/tex] = [tex](\dfrac{1}{10^6} )^0 ( \dfrac{999999}{1000000})^x[/tex]

The probability mass function  that you never win [tex]^xC_o[/tex] = [tex](\dfrac{999999}{1000000})^x[/tex]

Answer:

A

Step-by-step explanation:

40/20=2

80/40=2

Therefore the common ration is 2

The correct sequence which has a common ratio of 2 is,

⇒ {20, 40, 80, 160, 320, 640, …}

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

Given that;

The common ratio of sequence is,

⇒ 2

Now, By option 1;

The sequence is,

⇒  {20, 40, 80, 160, 320, 640, …}

Hence, Common ratio = 40 / 20

                                   = 2

And, 80 / 40 = 2

Thus, The correct sequence which has a common ratio of 2 is,

⇒ {20, 40, 80, 160, 320, 640, …}

Learn more about the geometric sequence visit:

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#SPJ2

The answer is $12792

Explanation:

It is known Tessa pays $108.00 to contribute to family coverage every two weeks and this represents 18% of the total payment. This implies the employer pays the 82% missing (100% - 18% = 82%). Additionally, with this information, it is possible to know the amount the employer has to pay every two weeks that represents 82%. The process is shown below:

1. Write the values you know and use x to represent the value you need to find

108 = 18        

  x =   82      

3. Cross multiply

x 18 = 8856

4. Find  the value of x by solving this simple equation

x = 8856 ÷ 18

x = 492 - Amount the employer pays every two weeks for Tessa's family coverage

Now that we know the money the employer pays every two weeks, it is possible to calculate the annual amount of money. Follow the process below.

1. Consider one year has a total of 52 weeks and divide this number of weeks by 2 because the payment for the family coverage occurs every 2 weeks

52 ÷ 2 = 26

2. Finally, multiply the money paid by the employer every two weeks by 26

26 weeks x $492 = $12792- This is the total the employer pays annually

Answer:

Point-slope form: y-4=2(x+1)

Slope intercept form: y=2x+6

I hope this helps!

Answer:

[tex]y-4=2(x+1)[/tex]

Step-by-step explanation:

Point-slope form is equal to

[tex]y-y_1=m(x-x_1)[/tex]

where y and y1 are the known y coordinates of two points on the line, and x and x1 are the known x coordinates of two points on the line. All we need now is m, which is the slope:

[tex]4-2=m(-1-(-2))[/tex]

We can simplify negative one minus negative two as positive 1.

[tex]4-2=m(1)[/tex]

4 minus 2 is 2, so m times 1 is 2. That means m is 2.

Now, we have the slope, so we can convert to point-slope form using one of the two points. Let's use (-1, 4). We can plug those values in for x1 and y1:

[tex]y-4=2(x+1)[/tex]

Answer:

Step-by-step explanation:

A right triangle has one right angle and two acute angles.

A and B are the acute angles.

A+B =  90°

One acute angle is 45 less than twice the other acute angle.

A = 2B-45°

(2B-45°) + B = 90°

3B = 135°

B = 45°

A = 45°

Answer:

330 cm^3

Step-by-step explanation:

Volume of figure=Volume of the cuboid+Volume of the other cuboid

Volume of figure=240+90=330

Answer:

1. add 1/2x to both sides

a. you want to combine the like terms. in this case, it is the x variable.

you are left with 7/6x = 5

2. multiply by 6/7

a. the reciprocal of 7/6 will cancel out the values

Answer: [tex]\dfrac{8}{\pi}[/tex] .

Step-by-step explanation:

We know that the rate of change of function f(x) from x=a to x= b is given by :-

[tex]k=\dfrac{f(b)-f(a)}{b-a}[/tex]

The given points on graph  :  (0, -4) and (pi over 2, 0) and (pi, 4) and (3 pi over 2, 0) and (2 pi, -4).

The rate of change from x = 0 to x = pi over 2 will be :-

[tex]\dfrac{0-(-4)}{\dfrac{\pi}{2}-0}=\dfrac{4}{\dfrac{\pi}{2}}[/tex]     [By using points (0, -4) and (pi over 2, 0) ]

[tex]=\dfrac{8}{\pi}[/tex]

Hence, the rate of change from x = 0 to x = pi over 2 is [tex]\dfrac{8}{\pi}[/tex] .