1. Write the equation of a line given the point and the slope.
(0,3); m = -2

Answer:

5.6 and 3,043.2

Step-by-step explanation:

The probability that the randomely selected fertilized egg will hatch between 15 days to 17 days as 0.5.

The probability of an event is a number that indicates how likely the event is to occur.

It is expressed as a number in the range from 0 and 1 or it can be expressed using percentage notation, in the range from 0% to 100%

Given is that the probability of a randomely selected fertilized egg will take 21 days to hatch is 0.028.

We can write the probability that the randomely selected fertilized egg will hatch between 15 days to 17 days as -

P{E} = {0.028 + (1 - 0.028)}/2

P{E} =  1/2

P{E} = 0.5

Therefore, the probability that the randomely selected fertilized egg will hatch between 15 days to 17 days as 0.5.

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Step-by-step explanation:

a = k/m    or       ma = k    

using 4 and 9     4* 9 = k = 36

then the equation becomes:

    ma = 36    

  using a = 6

      6 * m = 36     shows m = 6 kg

Answer:

cioè x ≥ 1; si avrà pertanto x > 0

Step-by-step explanation:

EXERCISE 2. Risolvere le seguenti disuguaglianze:

(1) | x−1 |< 3

(2) | x+1 |> 2

(3) | 2x+1 |< 1

(4) | x−1 |<| x+1 |

Caso: (a): | x−1 |< 3, risolvo

x−1 < 3

x ≥ 1

∪

−x+1 < 3

x < 1

, si avrà quindi

x < 4

x ≥ 1

cioè 1 ≤ x < 4 e

x > −2

x < 1

cioè −2 < x < 1. L’unione tra le due dà la soluzione −2 < x < 4

Caso: (b):

x+1 > 2

x ≥ −1

∪

−x−1 > 2

x < −1

, si avrà quindi

x > 1

x ≥ −1

cioè x > 1 e

x < −3

x < −1

cioè x < −3,

pertanto x < −3 ∪ x > 1

Caso: (c):

2x+1 < 1

x ≥ −1

2

∪

−2x−1 < 1

x < −

1

2

, si avrà quindi

x < 0

x ≥ −1

2

cioè −

1

2 ≤ x < 0 e

x > −1

x < −

1

2

cioè

−1 < x < −

1

2

. pertanto −1 < x < 0

Caso: (d): in questo caso,

−x+1 < −x−1

x < −1

∪

−x+1 < x+1

−1 ≤ x < 1

∪

x−1 < x+1

x ≥ 1

, si avrà quindi

0 < −2

x < 1

cioè non si hanno soluzioni e

x > 0

−1 ≤ x < 1

cioè 0 < x < 1 e

0 < 2

x ≥ 1

cioè x ≥ 1; si avrà pertanto x > 0

Answer:

h²=b²+p²

15²=6²+p²

225-36=p²

189=p²

13.74=p

Answer: 12/5

Step-by-step explanation:

The 12-pound bag has to be split between 5 pots, so to find out how much is in one bag, the equation is 12/5=x (x being the amount of soil in each pot)

Answer:

+18,000

Step-by-step explanation:

Answer:

population of a certain city is increased by 10,000 people. write

a signed number to represent this population change.

a car corporation produced 920 fewer cars this month than last. write a signed number to represent this months change in production

Step-by-step explanation:

The quadrilateral you're describing is a Kite. A kite is a quadrilateral with two pairs of consecutive congruent sides, and its diagonals meet at a right angle.

Percentage is expressed in terms of 100

We were told that in the 1st hour, 225 people purchased admission tickets and in the 2nd hour, 30% more people purchased admission tickets than in the 1st hour. This means that the number of extra tickets purchased in the 2nd hour is

30/100 * 225 = 67.5

Thus, the number of people that purchased tickets in the 2nd hour is

225 + 67.5 = 292.5

Since the number of people must be whole number, it is appoximately 293 people. Thus, the total number of ticket sales after the first two hours is

225 + 293 = 518

If each ticket costs $22.25, then the total amount of money that the ballet made from ticket sales after the first 2 hours is

518 * 22.25 = $11525.5

Answer:

d

Step-by-step explanation:

Answer:

C 25%

Step-by-step explanation:

The reason why its C because 24 divided by 6 is 4 and then 6 times 4 is 24 so its C

Answer:

C

Step-by-step explanation:

For these types of problems, its important that we focus on the base as well as the lengths of the base and any other given lengths.

Here, the net has a base that forms a square with side lengths of 8mm.

So automatically, we can eliminate choices a and d as both have a base that is a triangle rather than a square.

We've also noticed that the base has a length of 8mm

If we look at B and C closely, we can tell that B has base lengths of 10mm while C has base lengths of 8mm.

So C is the correct answer choice.

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Answer:

\(w(z(7))=189\)

Step-by-step explanation:

\(z(7)=7+5=12 \\ \\ w(z(7))=w(12)=12^2+4(12)-3=189\)

Answer:

70

Step-by-step explanation:

The angle next to 105 is 75 degrees because it is a linear angle

The angle at the top of the triangle is 35 because it is alternate interior of the 2 parallel lines

The 3 angles must add to 180

75 + 35 + x = 180

x = 70

Answer:

y = -16

Step-by-step explanation:

y = kx for proportion questions like this

y = kx

y = 64, x = -8

64 = -8k

Divide by -8 on each side

64/-8 = -8k/-8

-8 = k

Then to find y when x = 2, use y = kx again

y = kx

k = -8

x = 2

y = 2(-8)

y = -16

At x = 2 , the value of y will be ; y = -16.

It is given that y is directly proportional to the value of x and at x = - 8 , value of y is ; y = 64.

We have to calculate the value of y at x = 2.

What will be the value of y ; if x = 4 in equation x - y = 2 ?

The value of y will be , y = 2 .

Let's assume ;

y = k × x  ----- ------ ------ -------- ------ ----- ---- -------- Equation 1

It is given in the question that ;

at x = -  8 , y = 64

Putting these values in equation 1 to find the value of k.

⇒ 64 = - 8 × k

Dividing on both sides by - 8

⇒ k = - 8

Now , to find value of y at x = 2, we need to use equation 1 again ;

⇒ y = - 8 × 2

⇒ y = -16

Thus , at x = 2 , the value of y will be ; y = -16.

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Answer:

Step-by-step explanation:

You have to use the tangent.

Tan(y) = opposite / adjacent

tan(10) = x / 500

tan(10) = 0.1763

0.1763 = x / 500

500 * 0.1763 = x

x = 88.1635

x = 88.2

Answer:

A. g(x) = x²/3

Step-by-step explanation:

Step-by-step explanation:

According to question, the initial value, the y-intercept is b = 8 and the rate of change, the slope is m = 2.

This gives us the equation:

Plot the y-intercept (0, 8) and one more point:

Connect the points to get the line.

See attached graph

Answer:

Linear second-order differential equation F(x, y, y′, y″) = 0

y¹¹( -3 x⁴ )+ y¹12 x³ - 12 x² y= 0  

Step-by-step explanation:

Step(i):-

Given differential equation

y = c₁x + c₂x⁴  ...(i)

Differentiating equation (i) with respective to 'x', we get

y¹ = c₁(1) +  c₂ ( 4 x³ ) ...(ii)

Differentiating equation (ii) with respective to 'x', we get

y¹¹ =   c₂ ( 12 x² )

\(C_{2} = \frac{y^{11} }{12 x^{2} }\) ...(a)

Step(ii):-

Substitute (a) in equation (ii)

\(y^{l} = C_{1} + (\frac{y^{ll} }{12x^{2} } ) (4 x^{3} )\)

\(C_{1} = y^{l} - (\frac{y^{ll} }{12 x^{2} } ) (4 x^{3} )\) ...(b)

\(C_{2} = \frac{y^{11} }{12 x^{2} }\)

Step(iii):-

\(y = (y^{l} - (\frac{y^{ll} }{12 x^{2} } ) (4 x^{3} ) x + \frac{y^{ll} }{12 x^{2} } x^{4}\)

12 x² y = (y¹12 x³ - 4 x⁴ y¹¹) + x⁴ y¹¹

x⁴ y¹¹ - 4 x⁴ y¹¹ + y¹12 x³ - 12 x² y= 0

y¹¹( -3 x⁴ )+ y¹12 x³ - 12 x² y= 0

After simplification we got the above expression in the form 3f + 16m -56

The word "simplify" implies to turn something in a simpler form.

In mathematics, simplify an expression means write an expression in such a way that is comparatively less complicated than before. The main purpose of simplify an expression is to make it easy to solve as well as calculation.

3f + 8(2m-7)

we rearrange the expression by removing the parenthesis.

we remove the parenthesis by multiplying the factors.

3f + 8 × 2m - 8 × 7

3f + 16m -56

the above expression has no like terms to add or subtract so it is kept in this form.

Hence, 3f + 16m -56 is the simpler form.

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Answer:

Step-by-step explanation:

To find the two consecutive natural numbers whose sum is 575, we can set up the following equation:

x + (x+1) = 575

where x and x+1 are the two consecutive natural numbers.

We can solve this equation by combining like terms:

2x + 1 = 575

Subtracting 1 from both sides, we get:

2x = 574

Dividing both sides by 2, we get:

x = 287

Therefore, the two consecutive natural numbers are 287 and 288. Our final answer is 287, 288.

Answer:

287,288

Step-by-step explanation:

Question

The sum of two consecutive natural numbers is 575. Find the numbers

soln

x +( x + 1) = 575

x + x + 1 = 575

2x + 1 = 575

2x = 575 – 1

2x = 574

\( \frac{2x}{2} = \frac{574}{2} \)

x = 287

since we got x as 287, lets solve(x+1)

by substituting

287 + 1 = 288

hence the consecutive numbers are 287,288

Check

287 + 288 = 575

we are correct.

i hope this helps

Step-by-step explanation:

Divergence Test: use this when the limit as n approaches infinity of a sequence isn't 0.

If lim(n→∞) an ≠ 0, then an diverges.

(Note this only tests divergence, not convergence.)

P Test: use this when the series is a p-series.

For an = 1 / nᵖ, if p > 1, then the series converges.  Otherwise, it diverges.

Geometric Test: use this when the series is a geometric series.

For an = a₁ (r)ⁿ, if -1 < r < 1, then the series converges.  Otherwise, it diverges.

Integral Test: use this when the sequence can be easily integrated.

If ∫₁°° f(x) dx converges, then ∑₁°° f(n) converges.

If ∫₁°° f(x) dx diverges, then ∑₁°° f(n) diverges.

Comparison Test: use this when a sequence is similar to a p-series or a geometric series.

If bn > an and bn converges, then an converges.

If bn < an and bn diverges, then an diverges.

Otherwise, inconclusive.

Limit Comparison Test: use this when comparison test is inconclusive.

If an ≥ 0 and bn > 0, and lim(n→∞) an/bn > 0 and finite, then an and bn either both converge or both diverge.

Alternating Series Test: use this when the series is alternating.  This usually includes (-1)ⁿ or (-1)ⁿ⁺¹, but might use trig functions instead.

If an = (-1)ⁿ bn or (-1)ⁿ⁺¹ bn, where bn ≥ 0, and if lim(n→∞) bn = 0, and bn is decreasing, then an converges.

(Notice this only tests for convergence, not divergence.)

Answer:

10.756 esa seria la respuesta

Step-by-step explanation:

HOPE IT HELPS (◕‿◕✿)

Answer:

In triathlon an athlete swims 750meter in 15minutes cycles at an average speed of 40km/h for 30minutes and runs 5km at an average speed of 3meter/second find his average speed for the entire competition giving your answer in km/h

The average speed for the entire triathlon = 21.229 km/hr

Step-by-step explanation:

Calculate the distance covered and time taken in the first part of the Triathlon in Kilometers and hours respectively - Swimming

Distance 750 meters ⇒  750/100= 0.75Km

Time = 15 minutes ⇒  15/60      =  0.25 hours

Calculate the distance and time in Km and hours in the second phase:

Time is 30 minutes = 30/60 = 0.5 hours

Speed = 40km/hr

Distance = speed × time = 40km/hr × 0.5 = 20km

Calculate the distance covered and time taken in the last phase of the triathlon: Running

Runs 5 Km - this is the distance

5km = 5000m

Speed = 3 meters/sec

Time = Distance / speed

      = 5000 m / 3m/s

      = 1666.66666667 s

Convert to hours

1666.66666667 /3600 = 0.46 hours

Final step is to calculate the average speed:

Average speed = total distance travelled / total time taken

Total distance in Km = 0.75 km + 20 km + 5 km = 25.75 km

Total time taken = 0.25 hours + 0.5 hours + 0.46 hours = 1.21296296296 hours

Average speed of the athlete = 25.75 km / 1.21296296296 hours

                                             = 21.229 Km/hr

The average speed for the entire triathlon = 21.229 km/hr

Complete Question

The complete question is shown on the first uploaded image  

Answer:

The point of diminishing returns (x , y ) is  (11, 21462)

Step-by-step explanation:

From the question we are told that

     The function is  \(R(x) = 10,000 -x^3 - 33x^2 + 800x , \ \ 0 \le x \le 20\)

Here R(x)  represents revenue (in thousands of​ dollars) and  x  represents the amount spent on advertising​ (in thousands of​ dollars).

           Now  differentiating  R(x) we have  

               \(R'(x) = -3x^2 +66x + 800\)

Finding the second derivative of R(x)

              \(R''(x) = -6x +66\)

at  inflection point    \(R''(x) = 0\)

    So      \(-6x +66 = 0\)

=>           \(x= 11\)

    substituting value of x into R(x)

     \(R(x) = 10,000 -(11)^3 - 33(11)^2 + 800(11) ,\)

      \(R(x) = 21462\)

Now the point of diminishing returns (x , y ) i.e (x , R(x) ) is

     (11, 21462)

Answer: 9.2 inches

Step-by-step explanation: 15.1 - 5.9 = 9.2

Answer:

It snowed 9.2 more inches in Janurary then in December.

Step-by-step explanation:

Take December's snow fall and subtract it by January's snow fall.

15.1 - 5.9 = 9.2

The daily percentage rate (DPR) for the given Annual Percentage Rate (APR) on credit card is 17.8% is equal to 0.048%.

Given the Annual Percentage Rate (APR) on credit card is 17.8%.

Now, we need to find the daily percentage rate (DPR) for the given yearly percentage on credit card.

To find your current annual percentage rate, look at your monthly statements. To determine the daily percentage rate (DPR), divide the annual percentage rate (APR) by 365 (the number of days in a year).

So, given APR = 17.8%

Now, daily percentage rate will be:

⇒ Daily percentage rate = Annual Percentage Rate ÷ 365

⇒ DPR = APR / 365

⇒ DPR = 17.8% ÷ 365

⇒ DPR = 0.048%

Therefore, daily percentage rate (DPR) is equal to 0.048%.

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we can see that Kiran is farthest from home (6 blocks away) at time 5, when he reaches the bank. He spends the most time away from home (9 minutes) during his entire journey.

How to make graph?

To make a graph showing Kiran's distance from home over time, we can use the following steps:

Divide the journey into three parts: from home to store, from store to bank, and from bank to home.

Calculate the time taken for each part of the journey based on the distance and speed.

Use a coordinate system to plot Kiran's distance from home on the y-axis and time on the x-axis.

Plot the points corresponding to Kiran's position at different times for each part of the journey.

Connect the dots to form a continuous line.

Let's go through each part of the journey in more detail:

Home to store: Kiran is driving at a speed of 1 block per minute, and the distance is 3 blocks. Therefore, he reaches the store in 3 minutes.

Store to bank: After spending 2 minutes at the store, Kiran continues driving at a speed of 1 block per minute, and the distance is 3 blocks. Therefore, he reaches the bank in 5 minutes.

Bank to home: After spending 4 minutes at the bank, Kiran drives at a speed of 2 blocks per minute, and the distance is 6 blocks. Therefore, he reaches home in 9 minutes.

To plot the graph, we can use a coordinate system where the x-axis represents time in minutes and the y-axis represents Kiran's distance from home in blocks. We can label the points on the graph corresponding to Kiran's position at different times, as follows:

At time zero, Kiran is at home, which is 0 blocks away from home.

At time three, Kiran reaches the store, which is 3 blocks away from home.

At time five, Kiran reaches the bank, which is 6 blocks away from home (3 blocks from the store plus 3 blocks from home).

At time nine, Kiran reaches home again, which is 0 blocks away from home.

To create the graph, we can plot these points and connect them with a line, as shown in the attached image.

Graph showing Kiran's distance from home over time

From the graph, we can see that Kiran is farthest from home (6 blocks away) at time 5, when he reaches the bank. He spends the most time away from home (9 minutes) during his entire journey.

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Answer:

\(\textsf{B)} \quad f(x) = 5 \sin (16x) + 7}\)

Step-by-step explanation:

The sine function is periodic, meaning it repeats forever.

\(\boxed{f(x) = A \sin (B(x + C)) + D}\)

where:

Given values:

Calculate the value of B:

\(\dfrac{2\pi}{B}=\dfrac{\pi}{8}\implies 16\pi=B\pi\implies B=16\)

Substitute the values of A, B C and D into the standard formula:

\(f(x) = 5 \sin (16(x + 0)) + 7\)

\(f(x) = 5 \sin (16x) + 7\)

Therefore, the sine function with an amplitude of 5, a period of π/8, and a midline at y = 7 is:

\(\Large\boxed{\boxed{f(x) = 5 \sin (16x) + 7}}\)

Answer:

2

Step-by-step explanation:

2*3+3*4 x 1/3 power 2

6+12 x 1/9

18 x 1/9

2 x 1 (because 9 and 18 are cutted by each other)

2

2

To evaluate the expression (2b+3a)×(c^2) when a=4, b=3, and c=1/3, we substitute the given values into the expression and perform the indicated arithmetic operations:

(2b + 3a) × (c^2)

= (2(3) + 3(4)) × ((1/3)^2) (substitute a=4, b=3, c=1/3)

= (6 + 12) × (1/9) (evaluate 2(3) + 3(4) and (1/3)^2)

= 18/9

= 2

Therefore, when a=4, b=3, and c=1/3, the expression (2b+3a)×(c^2) equals 2.