solve the differential equation dy/dx 3x^2/5y y(2)=-3

Answer:

Slope: 1/2

Step-by-step explanation:

Use rise over run.

Please mark BRAINLIEST! Thanks!

Answer:

$100

Step-by-step explanation:

we can do comparing fractions

1800/300=600/x

Now cross multiply

1800(x)=300(600)

1800x=180000

/1800.  /1800

x=100

He spent $100

Hopes this helps please mark brainliest

The quadratic residues for the given integers are as follows: a) For the integer 3, the quadratic residues are 0 and 1.

b) For the integer 5, the quadratic residues are 0 and 1.

c) For the integer 13, the quadratic residues are 0, 1, 3, 4, 9, and 10.

d) For the integer 19, the quadratic residues are 0, 1, 4, 5, 6, 7, 9, 11, 16, and 17.

In number theory, a quadratic residue of an integer n is an integer x such that there exists an integer y satisfying x^2 ≡ y (mod n), where "≡" denotes congruence.

To find the quadratic residues of a given integer, we can calculate the square of each integer between 0 and n-1 (inclusive) and check if the result is congruent to a residue modulo n.

For example, let's consider the integer 13. We calculate the squares of integers from 0 to 12:

0^2 ≡ 0 (mod 13)

1^2 ≡ 1 (mod 13)

2^2 ≡ 4 (mod 13)

3^2 ≡ 9 (mod 13)

4^2 ≡ 3 (mod 13)

5^2 ≡ 12 (mod 13)

6^2 ≡ 10 (mod 13)

7^2 ≡ 10 (mod 13)

8^2 ≡ 12 (mod 13)

9^2 ≡ 3 (mod 13)

10^2 ≡ 9 (mod 13)

11^2 ≡ 4 (mod 13)

12^2 ≡ 1 (mod 13)

From these calculations, we can see that the quadratic residues of 13 are 0, 1, 3, 4, 9, and 10.

Similarly, we can apply this process to the other given integers (3, 5, and 19) to determine their quadratic residues.

To know more about number click here

brainly.com/question/28210925

#SPJ11

Answer:

37

Step-by-step explanation:

x = (9 · 37) - (8 · 37)

x = 333 - 296

x = 37

Answer:

THERES ONE MORE 37 THAN 8

Step-by-step explanation:

as the question say, shw drove 32 miles in 4 hours, but for the unit rate you need to simplify it:

32/4=8

she drove 8 miles in 1 hour

so the answer is: option C

Let's consider the specific product of packaged food items, such as canned goods and dry goods, which are transported from a warehouse to a grocery store.

Distance: The distance between the warehouse and grocery store will affect the transportation cost. The farther the distance, the higher the freight rate will be.

Weight: The weight of the packaged food items will also impact the freight rate. The heavier the items, the higher the cost of transportation.

Density: The density of the packaged food items is a measure of how much space they occupy in relation to their weight. If the items are low in density, they may take up more space on a truck, and therefore, the freight rate will be higher.

Stowability: The stowability of the packaged food items refers to how easy they are to store and stack on a truck. If the items are difficult to stack, more space may be required, and the freight rate will be higher.

Handling: The handling of the packaged food items is also a factor in determining the freight rate. If the items require special handling, such as refrigeration or careful stacking, the freight rate will be higher.

Liability: Liability refers to the risk of damage or loss of the packaged food items during transportation. If the items are fragile or perishable, the freight rate will be higher to cover the higher risk of damage or loss.

Market: The market conditions, such as supply and demand, will also influence the freight rate. If there is a high demand for transportation services or a shortage of trucks, the freight rate will be higher.

Overall, the freight rate for transporting packaged food items will depend on multiple factors, including distance, weight, density, stowability, handling, liability, and market conditions. Transport companies will consider all of these factors when determining the freight rate for a particular shipment.

to know ore about product

brainly.com/question/22852400

#SPJ1

Answer:

119 is the value of x when y = 7

Step-by-step explanation:

Since y varies inversely with x, we can use the following equation to model this:

y = k/x, where

Step 1:  Find k by plugging in values:

Before we can find the value of x when y = k, we'll first need to find k, the constant of proportionality.  We can find k by plugging in 49 for y and 17 for x:

Plugging in the values in the inverse variation equation gives us:

49 = k/17

Solve for k by multiplying both sides by 17:

(49 = k / 17) * 17

833 = k

Thus, the constant of proportionality (k) is 833.

Step 2:  Find x when y = k by plugging in 7 for y and 833 for k in the inverse variation equation:

Plugging in the values in the inverse variation gives us:

7 = 833/x

Multiplying both sides by x gives us:

(7 = 833/x) * x

7x = 833

Dividing both sides by 7 gives us:

(7x = 833) / 7

x = 119

Thus, 119 is the value of x when y = 7.

The probability that all three balls drawn from the bag are red is 6/273.

Prοbability is a measure οf the likelihοοd οr chance that a particular event will οccur. It quantifies the uncertainty assοciated with an οutcοme in a given situatiοn οr experiment.

Given:

- Total number of balls in the bag: 4 white + 5 red + 6 blue = 15 balls

- Number of red balls: 5

For the first draw, the probability of selecting a red ball is 5 red / 15 total balls = 1/3.

After the first red ball is drawn, there are 4 red balls left and 14 total balls remaining in the bag. Therefore, for the second draw, the probability of selecting another red ball is 4 red / 14 total balls = 2/7.

After the second red ball is drawn, there are 3 red balls left and 13 total balls remaining in the bag. Therefore, for the third draw, the probability of selecting the final red ball is 3 red / 13 total balls.

To find the probability of all three balls being red, we multiply the individual probabilities together:

P(all red) = (1/3) * (2/7) * (3/13)

Simplifying the expression, we get:

P(all red) = 6/273

Therefore, the probability that all three balls drawn from the bag are red is 6/273.

To know more about probability, refer here:

https://brainly.com/question/31828911

#SPJ4

The value of x and y in the equation 8(a+4)= xa + y are 8 and 32 respectively.

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

for example 2(x+2) is a linear equation and can be expressed in another form by multiplying the factor by all terms in the bracket. i.e = 2x+4

Similarly 8( a+4) can be written in another form form by multiplying 8 by a and +4

therefore 8( a+4) = 8a+ 32

therefore the two unknowns are 8 and 32 respectively.

learn more about linear equations from

https://brainly.com/question/2030026

#SPJ1

The weaker inequality 1/2 · 3/4 ··· 2n-1/2n < 1/√(3n) holds for all positive integers n, but using mathematical induction, the basis step works, although the inductive step fails.

a) If we try to prove the inequality 1/2 · 3/4 ··· 2n-1/2n < 1/√(3n) using mathematical induction, we can see that the basis step works. When n = 1, we have 1/2 < 1/√3, which is true.

Now, let's consider the inductive step. Assuming that the inequality holds for some positive integer k, we need to show that it also holds for k+1, i.e., we assume 1/2 · 3/4 ··· 2k-1/2k < 1/√(3k) and we want to prove 1/2 · 3/4 ··· 2k-1/2k · (2k+1)/(2k+2) < 1/√(3k+3).

If we attempt to manipulate the expression, we can simplify it to (2k+1)/(2k+2) < 1/√(3k+3). However, we cannot proceed further to prove this inequality, as it is not necessarily true. Therefore, the inductive step fails, and we cannot establish the original inequality using mathematical induction.

b) However, mathematical induction can still be used to prove the stronger inequality 1/2 · 3/4 ··· 2n-1/2n < 1/√(3n+1) for all integers greater than 1. We can start by verifying the case where n = 1, which gives us 1/2 < 1/√4, which is true.

Now, assuming the inequality holds for some integer k, we can multiply both sides of the inequality by (2k+3)/(2k+2) to get:

(1/2 · 3/4 ··· 2k-1/2k) · (2k+3)/(2k+2) < 1/√(3k+1) · (2k+3)/(2k+2).

Simplifying the expression on both sides, we have:

(2k+3)/(2k+2) < 1/√(3k+1) · (2k+3)/(2k+2).

We can observe that the right side of the inequality is less than 1/√(3k+3) by multiplying the denominator of the right side by (2k+3)/(2k+3). Hence, we obtain:

(2k+3)/(2k+2) < 1/√(3k+3).

This establishes the inequality for k+1, and thus, we have proven the stronger inequality using mathematical induction.

By verifying the case where n = 1 separately, we can conclude that the weaker inequality 1/2 · 3/4 ··· 2n-1/2n < 1/√(3n) holds for all positive integers n, as it follows from the proven stronger inequality using mathematical induction.

Learn more about mathematical induction here:

https://brainly.com/question/29503103

#SPJ11

Answer:

B.

Step-by-step explanation:

Table B has x values that go to multiple y values. A function has inputs that only go to one output.

(Assuming all these lines are parallel to each other)

Angle x = 70, because it is corresponding to the 70 angle.

Angle y = 70, because it is corresponding to x

Angle z = 70, because angle z and angle y are alternate angles

(corresponding angles and alternate angles are equal to each other with the condition of parallel lines)

The given statement "the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring." is False.

The union of two events A and B represents the event that at least one of the events A or B occurs. The probability of the union of two events can be calculated using the formula:

P(A or B) = P(A) + P(B) - P(A and B)

On the other hand, the intersection of two events A and B represents the event that both events A and B occur. The probability of the intersection of two events can be calculated using the formula:

P(A and B) = P(A) * P(B|A)

where P(B|A) is the conditional probability of B given that A has occurred.

It is possible for the probability of the union of two events to be greater than the probability of the intersection of two events if the two events are not mutually exclusive.

In this case, the probability of both events occurring together (the intersection) may be relatively small, while the probability of at least one of the events occurring (the union) may be relatively high.

In summary, the probability of the union of two events occurring can sometimes be greater than the probability of the intersection of two events occurring, depending on the relationship between the events.

To learn more about probability click on,

https://brainly.com/question/30648713

#SPJ4

At the first day: the visitor hiked the South Kaibab Trail and the River Trail on one day

so, the length for the first day = 10.1 + 2.7 = 10.1 + 2.7 = 12.8 km

At the second day: the visitor hiked the Bright Angel Trail

so, the length of the second day = 12.6 km

We will answer the questions:

How much farther did she hike the first day than the second day?

it will be = 12.8 - 12.6 = 0.2 kilometers

How much longer was her total route than if she had hiked the North Kaibab Trail?

The total route = 12.8 + 12.6 = 25.4

if she had hiked the North Kaibab Trail, the difference will be = 25.4 - 22.9 =

= 2.5 kilometers

​

Answer:

C

Step-by-step explanation:

Given

3\((x+9)^{\frac{3}{4} }\) = 24 ( divide both sides by 3 )

\((x+9)^{\frac{3}{4} }\) = 8

Raise both sides to the power of \(\frac{4}{3}\)

x + 9 = \(8^{\frac{4}{3} }\) = \((\sqrt[3]{8}) ^{4}\) = \(2^{4}\) = 16 ( subtract 9 from both sides )

x = 7 → C

Answer:

above sea level

Step-by-step explanation:

Therefore, the equation \(+3 + 5(2n - 1)^2 + n^2 + D(n + 2)\) is true for every positive integer n.

To verify the equation for every positive integer n using induction, we'll follow the steps of mathematical induction.

Step 1: Base Case

Let's check if the equation holds true for n = 1.

For n = 1:

\(3 + 5(2(1) - 1)^2 + 1(1) + D(1 + 2)\)

\(3 + 5(1)^2 + 1 + D(3)\)

3 + 5 + 1 + D(3)

9 + D(3)

At this point, we don't have enough information to determine the value of D. However, as long as the equation holds for any arbitrary value of D, we can proceed with the induction.

Step 2: Inductive Hypothesis

Assume that the equation holds true for an arbitrary positive integer k. That is:

\(3 + 5(2k - 1)^2 + k^2 + D(k + 2)\)

Step 3: Inductive Step

We need to prove that the equation also holds true for n = k + 1, based on the assumption in the previous step.

For n = k + 1:

=\(3 + 5(2(k + 1) - 1)^2 + (k + 1)^2 + D((k + 1) + 2)\\3 + 5(2k + 1)^2 + (k + 1)^2 + D(k + 3)\)

Expanding and simplifying:

=\(3 + 5(4k^2 + 4k + 1) + (k^2 + 2k + 1) + D(k + 3)\\3 + 20k^2 + 20k + 5 + k^2 + 2k + 1 + Dk + 3D\)

Combining like terms:

=\(21k^2 + 22k + 9 + Dk + 3D\)

Now, we compare this expression with the equation for n = k + 1:

=\(3 + 5(2(k + 1) - 1)^2 + (k + 1)^2 + D((k + 1) + 2)\)

We can see that the expression obtained in the inductive step matches the equation for n = k + 1, except for the constant terms 9 and 3D.

As long as we choose D in a way that makes 9 + 3D equal to zero, the equation will hold true for n = k + 1 as well. For example, if we set D = -3, then 9 + 3D = 9 - 9 = 0.

Step 4: Conclusion

Since the equation is true for the base case (n = 1) and we have shown that if it holds for an arbitrary positive integer k, it also holds for k + 1, we can conclude that the equation is true for every positive integer n.

To know more about positive integer,

https://brainly.com/question/30212857

#SPJ11

The unit rate in acres of land planned by the workers per day is found is 16/35 acres.

For the mentioned question-

Total acres of land planted = 2/5 acres.

Total time taken = 7/8 days.

Thus, unit rate in acres per day = Total acres of land planted / Total time taken

unit rate in acres per day = (2/5) / (7/8)

unit rate in acres per day = (2*8)/(5*7)

unit rate in acres per day = 16/35

Thus, unit rate in acres of land planned by the workers per day is found is 16/35 acres.

To know more about the rate of doing work, here

https://brainly.com/question/25864308

#SPJ1

Answer:

1594

Step-by-step explanation:

9514 1404 393

Answer:

  -2 5/9

Step-by-step explanation:

w +(-x) -2/3 = w -x -2/3 = -5/9 -4/3 -2/3

  = -(5/9 +4/3 +2/3) = -(5/9 +(4+2)/3) = -(5/9 +2)

  = -2 5/9

Answer:

use photomath

Step-by-step explanation:

ur welcome

The length of the arc intercepted by a central angle of pi/6 radians in a circle with a radius of 5 meters is approximately 2.6 meters.

The length of the arc intercepted by a central angle, we can use the formula: s = rθ, where s is the length of the arc, r is the radius of the circle, and θ is the central angle in radians.

Given that the radius of the circle is 5 meters and the central angle is pi/6 radians, we can substitute these values into the formula:

s = (5 meters) * (pi/6 radians)

 ≈ (5 meters) * (0.5236 radians)

 ≈ 2.618 meters

Rounding to the nearest tenth, the length of the arc intercepted by a central angle of pi/6 radians in a circle with a radius of 5 meters is approximately 2.6 meters.

Learn more about radius  : brainly.com/question/24051825

#SPJ11

Answer:

a) To calculate the future value of the GIC at maturity, we can use the formula:

FV = P(1 + r/n)^(n*t)

where:

P = principal amount = $3000

r = annual interest rate = 5.6% = 0.056

n = number of times interest is compounded per year = 1 (annually)

t = number of years = 10

Plugging in the values, we get:

FV = $3000(1 + 0.056/1)^(1*10)

= $3000(1.056)^10

= $5,020.93

Therefore, the future value of the GIC at maturity is $5,020.93.

b) To estimate how long it will take for the GIC to be worth at least $12,000, we can use the same formula as above and solve for t:

FV = $12,000

P = $3000

r = 0.056

n = 1

$12,000 = $3000(1 + 0.056/1)^(1*t)

4 = 1.056^t

t = log(4) / log(1.056)

t ≈ 25.58

Therefore, it will take approximately 25.58 years for the GIC to be worth at least $12,000.

i) If the compounding frequency is monthly, then n = 12 and the formula becomes:

FV = $3000(1 + 0.056/12)^(12*10)

= $5,124.82

The future value of the GIC will be slightly higher because compounding is occurring more frequently.

ii) If the interest rate is 2.8%, compounded semi-annually, then r = 0.028/2 = 0.014 and n = 2. Plugging in the values, we get:

FV = $3000(1 + 0.014/2)^(2*10)

= $4,012.92

The future value of the GIC will be lower because the interest rate is lower and compounding is occurring less frequently.

d) To find the minimum interest rate with daily compounding that would be needed to have a future value that is $100 greater than the future value in part a, we can use the formula:

FV = P(1 + r/n)^(n*t)

where:

FV = $5,120.93

P = $3000

n = 365 (number of times interest is compounded per year with daily compounding)

t = 10

We can solve for r as follows:

$5,120.93 = $3000(1 + r/365)^(365*10)

1.707 = (1 + r/365)^3650

log(1.707) = log(1 + r/365)*3650

log(1.707)/3650 = log(1 + r/365)

0.000108166 = r/365

r = 0.0395

Therefore, the minimum interest rate with daily compounding that would be needed to have a future value that is $100 greater than the future value in part a is 3.95%

Answer:

Step-by-step explanation:

The random sample of size =36

Taken from a population with mean= 64

Standard deviation=4  

Standard error of the mean = 4/6=0.66

To learn more about standard deviation click here

https://brainly.com/question/475676  

#1234

The standard error of the mean is calculated to be 0.66

The formula for the standard error of the mean is expressed as:

SE = σ/√n

SE = standard error of the sample

σ = sample standard deviation

n = sample size

Note that σ is the Greek letter sigma and ​​√ is the square root symbol.

Given that,

The size of the random sample is 36.

based on a population whose mean was 64.

Standard deviation is 4

Standard error equals 4/\(\sqrt{36}\)=4/6 = 0.66

According to calculations, the standard error of the mean is 0.66.

Click here for additional information about standard error of the mean :

brainly.com/question/28583871

#SPJ4

Answer:

54 mph

Step-by-step explanation:

18 miles / 20 minutes = 18 miles / 1/3 hour

18 ÷ 1/3 = 18 × 3 = 54 mph

The constant speed with given distance and time is 54 miles per hour.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Given that, you drove  18  miles in  20  minutes at a constant speed.

Here, 20 minutes =20/60 =1/3 hours

Now, Speed = Distance÷Time

Speed= 18÷1/3

Speed=54 miles per hour

Therefore, the constant speed is 54 miles per hour.

To learn more about the speed, distance, and time visit:

brainly.com/question/4978052.

#SPJ2

Based on the transformations that occurred, the preimage is most likely the topmost right image.

The transformations list shows that the first transformation was the reflection across the horizontal line drawn.

When a reflection is done, the shape looks like the inverse of itself. The only shape that looks like an inverse and is therefore a reflection is the bottom right shape which means the preimage must be the top right image.

Remaining part of question:

Which is the preimage?

Find out more on transformations at https://brainly.com/question/2063313.

#SPJ1

Answer:

i have no clue what this is

Step-by-step explanation:

The probability of an event not occurring refers to the probability of all other possible outcomes except for the event in question.

The odds for rolling a 6-sided die and getting a 2 are 1:5 or 1/5. This means that the probability of rolling a 2 is 1/6, and the probability of not rolling a 2 is 5/6. To find the odds against rolling a 6-sided die and getting a 2, we simply invert the odds for rolling a 2, which gives us the odds of rolling any number other than 2. The odds against rolling a 6-sided die and getting a 2 are therefore 5:1 or 5/1. This means that the probability of not rolling a 2 is 5/6, and the probability of rolling a 2 is 1/6. It's important to note that the odds against an event are not the same as the probability of that event not occurring. The odds against an event refer to the ratio of the number of unfavorable outcomes to the number of favorable outcomes, while the probability of an event not occurring refers to the probability of all other possible outcomes except for the event in question.

Learn more about probability here

https://brainly.com/question/13604758

#SPJ11

Answer:

5.66 feet

Step-by-step explanation:

a^2 + b^2 = c^2

2^2 +b^2 = 6^2

square root of (36-4) = b

b= 5.66 feet

Answer:

5.8 meters

Step-by-step explanation:

The formula to calculate this is given as:

Height/ Shadow

Shadow of the pole = 25.5 m

Height of the pole = x m

Tim's shadow = Height of the pole - Tim's distance

25.5 m - 15.4 m = 10.1 m

Tim's height = 2.3 m

Hence:

x/25.5 = 2.3/10.1

Cross Multiply

10.1x = 25.5 × 2.3

x = 25.5 × 2.3/10.1

x = 5.8069306931 m

Approximately = 5.8m

Hence, the height of the flagpole = 5.8m