for a fourth order runge-kutta approximation of a differential equation. if the time-step used in the approximate is reduced by a factor of 10, by what factor does the error of this approximate get reduced?

Answer:

106.8

Step-by-step explanation:

72 × 2 = 34

34 × 3.14 or

\(\pi\)

106.76 round to the nearest tenth

= 106.8

Answer:

To solve for x in this equation, we need to take the following steps:

Step 1: Add 5.3 to both sides of the equation to get 3 1/3x = 3.7.

Step 2: Divide both sides of the equation by 3 1/3 to get x = 1.1.

Therefore, x = 1.1 is the answer.

Answer:

x= 1.1

Step-by-step explanation:

Answer:

441.5

Step-by-step explanation:

Answer:

5.19

Step-by-step explanation:

Answer:

0.01167

Step-by-step explanation:

180 - 0.669 = 89.331

complementary angle = 89.331

cos(89.331) = 0.01167

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

carnival game:

spinner: 1 to 8

Step 02:

simple probability:

p = favorable outcomes / total outcomes

1. probability of an event:

a. p (odds):

p (odds) = 4 / 8 = 1 / 2

b. p (evens):

p (evens) = 4 / 8 = 1 / 2

c. p (3):

p (3) = 1 / 8

d. p (4 or 6):

p (4 or 6) = 2 / 8 = 1 / 4

e. p (7'):

p (7') = 7 / 8

f. p (1):

p (1) = 1 / 8

That is the full solution.

you just need to put the values of a and b where they have to be

.

hope I helped!

Answer:

126 in²

Step-by-step explanation:

C = πd when the diameter  is known.  If the diameter is 40 in, then the radius is half that, or 20 in.

Then the circumference of a circle with a diameter of 40 in is

C = (40 in)π.  This works out to approximately 126 in²

Answer:

55

Step-by-step explanation:

Make a proportion.

11/20=x/100

20*5=100, 11*5=55

The amount of interest that Rafa earns in one year, given the amount in the savings account and the interest is $ 238. 65 .

The amount earned by Rafa in one year can be found by the formula :

= Amount in savings account x Interest per year

Amount in savings account = $ 6, 450

Interest per year = 3. 7 %

The amount earned by Rafa for the year is therefore :

= 6, 450 x 3. 7 %

= $ 238. 65

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Answer:

Solution given;

total cost for of the beads and pendants

both necklaces;$10.20

1 necklaces=;$10.20/2=$5.1

beads =cost $1.80

now

each pendant cost =total cost of 1 necklaces-beast cost

=$5.10-1.80

=$3.3

each pendant cost$3.3

The water level of the cone is rising at the rate of  1/8π feet per minute.

Given:

Height of tank = h = 6 feet

Radius of tank, r = 4 feet

rate at which water is filled  =  2 ft³/min =dV/dt

We have to find the dh / dt when the water is 2 feet deep.

r/h = 4/5 = 2/3

or, r = 2h/3

Volume of the cone = 1/3πr²h

Now we substitute the value of r for h to get :

\(V=\frac{1}{3}\pi (\frac{2}{3}h)^2h\\\\V=\frac{4}{27}\pi h^3\)

No we will differentiate the volume with respect to t.

\(\frac{dV}{dt} = \frac{4}{3}\pi \times 3 \times h^2\times \frac{dh}{dt}\\\\\)

Now we will substitute the values to find the rate.

\(2 = \frac{4}{3}\pi \times 3 \times 2^2\times \frac{dh}{dt} \\\\or, \frac{dh}{dt} = \frac{1}{8\pi}\)

Hence the water level is rising at the rate of 1/8π cm per minute.

By using a series of line segments or lines to connect the points on a circular base to a single point, known as the apex or vertex, a cone is formed.

By calculating the distance between its vertex and base, one can measure the height of an object like a cone.

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Answer:

1/6

Step-by-step explanation:

Answer:

C=36

Step-by-step explanation:

Answer:

c = 36

Step-by-step explanation:

so our equation is 21 = 5/6c - 9

first we need to get rid of the 9. in order to do this, we have to do the opposite of the action shown. so in this case, we would add 9 to both sides. we add it to both sides to keep the equation balanced and equal.

adding 9 to 21 gives us 30. so our equation would then be 30 = 5/6c

now we need to get the c by itself. so we divide by 5/6 because in the original equation the 5/6 and the c are being multiplied to each other.

when we devide 5/6c by 5/6, it cancels out. leaving us with c. 30 divided by 5/6 will in turn gives 36. and there is your answer.

the expression "tangent (a)" represents the tangent of an angle "a" measured in radians. Without knowing the value of "a", we cannot determine the value of "tangent (a)" or the correct answer among the given options.

How to solve the question?

The tangent function is a mathematical function that relates the angle of a right triangle to the ratio of the length of its opposite side to the length of its adjacent side. The notation for the tangent function is "tan".

The expression "tan(a)" or "tangent (a)" represents the tangent of the angle "a" measured in radians. The value of tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side, where the angle is formed by the hypotenuse and adjacent side of a right-angled triangle.

So, "tan(a)" is given by the formula:

tan(a) = opposite/adjacent

Now, in the given expression "tangent (a)", the value of "a" is not specified. Therefore, we cannot determine the exact value of "tangent (a)" without knowing the value of "a".

In the answer options provided, all the options are in the form of "start fraction x over y end fraction". These are known as fractional expressions or fractions. The numerator "x" represents the top part of the fraction, while the denominator "y" represents the bottom part of the fraction.

To find the value of "tangent (a)", we need to know the value of "a". Without knowing the value of "a", we cannot determine which of the given options is the correct answer.

In summary, the expression "tangent (a)" represents the tangent of an angle "a" measured in radians. Without knowing the value of "a", we cannot determine the value of "tangent (a)" or the correct answer among the given options.

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The value of the given expression using PEDMAS is -19.

A set of guidelines called the order of operations establishes the sequence in which mathematical operations must be carried out. The following is the order: The acronym PEMDAS or PEDMAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). In order to guarantee that numerical methods are examined correctly and consistently, it is crucial to adhere to the sequence of operations. Even without order of operations, mathematical expressions could be unclear and confusing, which could result in various outcomes depending on how the statement is understood.

The given expression is:

x/y + x - (y + 3)²

Substitute the value of x = 4 and y = 2.

4/2 + 4 - (2 + 3)²

First solve the calculations inside the parentheses:

4/2 + 4 - (5)²

Solve the exponents:

4/2 + 4 - 25

Solve the division:

2 + 4 - 25

Finally perform the addition and then subtraction:

6 - 25 = -19

Hence, the value of the given expression in simplified form is -19.

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Answer:

1099in²

Step-by-step explanation:

SA = \( \sf A=2\pi rh+2 \pi r² \)

⇒ SA=2πrh+2πr²

⇒ SA = 2((3.14)(5)(30)+(2)(3.14)(5²)

⇒ SA = 2((3.14)(5)(30)+(2)(3.14)(25)

⇒ SA = 1099

Surface Area = 1,099 in²

Answer:

1.

Step-by-step explanation:

Since the line segment FH bisects angle EFG, angle HFG = Half of Angle EFG.

Angle EFG = 177 - 9x. Angle HFG = 92 - 8x.

177 - 9x = 2(92 - 8x)

177 - 9x = 184 - 16x

7x = 7

x = 1.

Step-by-step explanation:

x=85 hope it helps you. mark as brilliant

Answer:

a = 6

Step-by-step explanation:

Equate the two angles because opposite angles in a parallelogram are equal.

20a+30=17a+48

20a-17a=48-30

3a=18 (divide both sides by 3)

a=6

Answer:

Step-by-step explanation:

An investment banker received a bonus and invested that money in two investments. He put a certain sum

of money in the first investment that returned 7% interest after one year. In the second investment he

Invested four times that of the first investment and got a 12% interest return after one year. If the total

interest from his investments after one year was $8,525.00, find the amount invested at each interest rate.

If you rent a car, you should choose Option 3 and accept the fixed price of $50 for gasoline if you expect to drive 150 miles.

1. Total gasoline consumed (gallons):

To calculate the total gasoline consumed, divide the expected distance by the car's fuel efficiency:

Total gasoline consumed = Distance / Fuel efficiency

Total gasoline consumed = 150 miles / 28 miles per gallon

Total gasoline consumed ≈ 5.36 gallons

2. Option 1 cost:

In Option 1, you need to return the car with a full gas tank. Since the car has a 16-gallon tank and you've consumed approximately 5.36 gallons, you need to fill up the remaining 16 - 5.36 = 10.64 gallons.

Option 1 cost = 10.64 gallons * $3.95 per gallon = $42.01

3. Option 2 cost:

In Option 2, you return the car without filling it up and pay $5.45 per gallon. As calculated before, you've consumed approximately 5.36 gallons.

Option 2 cost = 5.36 gallons * $5.45 per gallon = $29.20

4. Option 3 cost:

In Option 3, you accept the fixed price of $50 for gasoline. This fixed price is the most cost-effective option compared to the other two choices.

Therefore, the best choice is Option 3, accepting the fixed price of $50 for gasoline, as it offers a better value for the expected distance of 150 miles.

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The value of alpha is 0.025. The Z-value is 1.96. The P(z) is 0.5. The effect size is 0.05. The Sample size for the study is 384.

An area created using fixed-size samples of data from a population (sample space) that follows a certain probability distribution is known as a confidence interval. A selected population statistic is built into the interval with a specified probability. An estimate's level of uncertainty is described by a confidence interval, which is a range of numbers. The 68-95-99.7 Rule states that 95% of values lie within two standard deviations of the mean, hence to get the 95% confidence interval, you add and subtract two standard deviations from the mean.

Here,

All the calculations attached in image.

z= 1.96

p = 0.5

q = 1-p = 0.5

E = 0.05

sample size =

(z^2).(pq)=(1.96^2).(0.5)(.0.5)

384.16,

round up

n for study =385

Alpha has a value of 0.025. There is a 1.96 Z-value. P(z) equals 0.5. The impact factor is 0.05. The Sample size for the study is 384.

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Answer:

y = ± √ 7/2

Step-by-step explanation:

2*y^2-8-(6-2*y^2)=0

(2 • (y2)) - 8) - (6 - 2y2) = 0

(2y2 - 8) - (6 - 2y2) = 0

Pull out like factors :

4y2 - 14 = 2 • (2y2 - 7)

4.2 Factoring: 2y2 - 7

difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

2 • (2y2 - 7) = 0

5.1 Solve : 2 = 0

5.2 Solve : 2y2-7 = 0

Add 7 to both sides of the equation :

2y2 = 7

Divide both sides of the equation by 2:

y2 = 7/2 = 3.500

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:

y = ± √ 7/2

The ∆ABC is an isosceles triangle and have the base angles m∠A and m∠C equal to 51° and the angle m∠B is equal to 78°.

An isosceles triangle have the measure of its base angles to be equal, and the sum of the interior angles sum up to 180°.

Given that sides AB ≅ BC, then the triangle ∆ABC has two sides with similar length and base angles so;

angles m∠A and m∠C are the base angles are both equal to 51°

m∠B = 180° - (51 + 51)° {sum of interior angles of a triangle}

m∠B = 180° - 102°

m∠B = 78°

Therefore, the isosceles triangle ∆ABC have the base angles m∠A and m∠C equal to 51° and the angle m∠B is equal to 78°.

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Answer: Let us assume that the number of months after which

the gym memberships will cost the same = x

Then

15 + 10x = 40 + 4x

10x - 4x = 40 - 15

6x = 25

x = 25/6

 = 4 1/6

So the membership fee of both the gyms will become same after 4 1/6 months. You can also consider that as after 5 months the membership fees of both the gyms will become same. I hope the procedure is not very complicated for you to understand.

Step-by-step explanation: Hope this helps!!

Answer:

0.25

Step-by-step explanation:

formula is y2-y1 / x2-x1

-1.5 - (-3) / 0 - (-6)

-1.5 - (-3) = 1.5

0 - (-6) = 6

1.5 / 6 = 0.25

Answer:

the slope is 1/4

Step-by-step explanation:

use the formula m= y2-y1/x2-x1

(6,-3) (0,-1.5)

-1.5 is y2 and -3 is y1 so the equation on the top will look like this:

-1.5-(-3)

Which is 1.5

0 is x2 and 6 is x1 so the equation on the bottom will look like this:

0-6 which is -6

Now the slope is -1.5/6

Multiply both sides by 10

-15/60

Divide both sides by 15

1/4

Hope this helps!

Answer:

42.39

Step-by-step explanation:

The formula for the volume of a cylinder:

V= πr^2h

Substitute values into the formula that was given:

π = 3.14

r = 3/2

h = 6

3.14(1.5^2)6=

3.14(13.5)=

42.39

I hoped this solved your problem <3

(I took the FLVS test too and got it right)

This statement is true, as the test statistic represents the number of standard deviations between the observed sample proportion and the claimed value (po) under the null hypothesis.

- The large value of the test statistic means that our observed data are not surprising when the null hypothesis is true. This statement is false. A large test statistic implies that the observed data is surprising when the null hypothesis is true, which means there is evidence against the null hypothesis.
- The researcher should fail to reject the null hypothesis. This statement is false. A large test statistic suggests evidence against the null hypothesis, so the researcher should reject the null hypothesis in favor of the alternative hypothesis.

- When the null hypothesis is true, the test statistic comes from a standard normal distribution. This statement is true, as the test statistic follows a standard normal distribution when the null hypothesis is true.
- There is a 4.318% chance that the alternative hypothesis is true. This statement is false. The test statistic does not directly provide the probability of the alternative hypothesis being true. Instead, we can use the test statistic to calculate the p-value, which represents the probability of obtaining a test statistic as extreme as the observed one, assuming the null hypothesis is true.

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