Use Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05.
Find an explicit solution for the initial-value problem and then fill in the following tables. (Round your answers to four decimal places. Percentages may be rounded to two decimal places.) y' = 2xy, y(1) = 1; y(1.5) y(x) = (explicit solution)
h = 0.1
xn yn Actual Value Absolute Error % Rel. Error
1.00 1.0000 1.0000 0.0000 0.00
1.10 1.2337 1.20 1.5527 1.30 1.9937
1.40 2.6117 1.50 3.4903
h = 0.05
xn yn Actual Value Absolute Error % Rel. Error
1.00 1.0000 1.0000 0.0000 0.00
1.05 1.1000 1.1079 0.0079 0.71
1.10 1.2155 1.2337 0.0182 1.48
1.15 1.3492 1.3806 0.0314 2.27
1.20 1.5044 1.5527 0.0483 3.11
1.25 1.6849 1.7551 0.0702 4.00
1.30 1.8955 1.9937 0.0982 4.93
1.35 2.1419 2.2762 0.1343 5.90
1.40 2.4311 2.6117 0.1806 6.92
1.45 2.7715 3.0117 0.2402 7.98

Answer:

Step-by-step explanation:

Here we have,

E(X) = 1, var(X) = 3, E(Y) = 0, var(Y) = 4

Since X and Y has normal distribution so W will also have normal distribution with mean

E(W) = E(05X-Y+6)

= 0.5E(X) - E(Y) +6

= 0.5* 1 -0+ 6

= 6.5

and variance

Var(W) = Var(0.5X-Y+6)

= 0.25Var(X)+Var(Y)

= 0.25 * 3 + 4

= 4.75

(b)

The z-score for W = 6 is

[tex]z=\frac{6-6.5}{\sqrt{4.75} } \\\\=-0.23[/tex]

The required probability is:

P(W>6) = P(z > -0.23)

= 0.5910

Answer: c

Step-by-step explanation: 4/1 x 1/3 = 4/3

Answer:

The experimental probability that the next contestant will qualify for the bonus round is [tex]\frac{7}{10}[/tex]

Step-by-step explanation:

The experimental probability of an outcome is the number of trials in which the desired outcome happened divided by the total number of trials.

What is the experimental probability that the next contestant will qualify for the bonus round?

14 contestants qualified out of 14+6 = 20 contestants. So

[tex]p = \frac{14}{20} = \frac{7}{10}[/tex]

The experimental probability that the next contestant will qualify for the bonus round is [tex]\frac{7}{10}[/tex]

Answer:

The graph crosses the x-axis at x = 0 and touches the x-axis at x = 3.

Step-by-step explanation:

When you graph this equation, you should see the zeros it passes and touches.

Answer:

A. The graph crosses the x-axis at x = 0 and touches the x-axis at x = 3.

Step-by-step explanation:

Answer:

64√2 or 64 StartRoot 2 EndRoot

Step-by-step explanation:

A 45-45-90 traingle is a special traingle.  Let's say one of the leg of the triangle is x. The other one is also x because of the isosocles triangle theorem.  Therefore, using the pytagorean theorem, you find that x^2+x^2=c^2.  2(x)^2=c^2.  You then square root both sides and get c= x√2.  

Therefore, the two legs are x and the hypotenuse is x√2.  x√2=128 because the question says that the hypotenuse is 128.  Solve for x by dividing both sides by √2.  X=128/√2.  You rationalize it by multiplying the numberator and denominator of the fraction by √2.  √2*√2= 2.

X=(128√2)/2= 64√2 cm.

Since X is the leg, the answer would be 64√2

Answer:

B.

Step-by-step explanation:

Answer:

Sarah has to invest $502,958.58 today.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

[tex]E = P*I*t[/tex]

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

[tex]T = E + P[/tex]

In this question:

[tex]t = 35, I = 0.07, T = 1700000[/tex]

She has to invest P today.

[tex]T = E + P[/tex]

[tex]1700000 = E + P[/tex]

[tex]E = 1700000 - P[/tex]

So

[tex]E = P*I*t[/tex]

[tex]1700000 - P = P*0.07*34[/tex]

[tex]3.38P = 1700000[/tex]

[tex]P = \frac{1700000}{3.38}[/tex]

[tex]P = 502958.58[/tex]

Sarah has to invest $502,958.58 today.

Answer:

3

Step-by-step explanation:

6/4 (divide numerator and denominator each by 2)

= 3/2

= 3 x (1/2)

hence there are 3  halves in 6/4

Answer:

3

Step-by-step explanation:

To find out, we need to divide.

[tex]\frac{6}{4}[/tex] ÷ [tex]\frac{1}{2}[/tex]

When dividing fractions, you multiply the 1st term by the second term's reciprocal.

so

[tex]\frac{6}{4}[/tex] x 2

If you simplify you get [tex]\frac{6}{2}[/tex] or 3.

Answer:

0.9 grams

Step-by-step explanation:

The point estimate for the average weight of Soap Bar A is:

[tex]A=\frac{121+122+124+ 123+ 120+ 124+ 121+ 121+ 121+ 123+ 120}{11}\\A=121.82\ grams[/tex]

The point estimate for the average weight of Soap Bar B is:

[tex]B=\frac{121+120+122+ 119+ 121+ 122+ 122+ 120+ 120 +121+ 122+123+119}{13}\\B=120.92\ grams[/tex]

Therefore, the point estimate for the true difference between the given population means is:

[tex]Dif = A-B\\Dif = 121.82-120.92\\Dif=0.9\ grams[/tex]

The point estimate for the difference is 0.9 grams.

Answer:

m>n

Step-by-step explanation:

The value of m

The sum of the angles of a triangle are 180

50+30 + m = 180

m = 180-50-30

m = 100

The value of n

The sum of the angles of a triangle are 180

28 + 58+n = 180

n = 180-58-28

n=94

m>n

Answer:

[225(pi)]/4

Step-by-step explanation:

circumference = pi(diameter)

area = pi (radius)^2

Diameter = 2(radius)

15pi cm = pi(diameter)

divide both sides by pi

diameter = 15

radius = 7.5

Area = pi (7.5)^2

A  = 56.25 pi

most teachers prefer fractions so

225pi/4

Answer:

The answer is D.

Step-by-step explanation:

First, you have to convert the mixed number into improper fraction :

[tex]6 \frac{2}{3} [/tex]

[tex] = \frac{3 \times 6 + 2}{3} [/tex]

[tex] = \frac{20}{3} [/tex]

Next, you can divide it by cutting out the common factor :

[tex]15 \div \frac{20}{3} [/tex]

[tex] = 15 \times \frac{3}{20} [/tex]

[tex] = 3 \times \frac{3}{4} [/tex]

[tex] = \frac{9}{4} [/tex]

[tex] = 2 \frac{1}{4} [/tex]

The value of the expression after divide is,

⇒ 2 1/4

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The expression is,

⇒ 15 divided by 6 2/3

Now,

We can divide as;

⇒ 15 divided by 6 2/3

⇒ 15 ÷ 6 2/3

⇒ 15 ÷ 20/3

⇒ 15 × 3/20

⇒ 45/20

⇒ 9/4

⇒ 2 1/4

Learn more about the divide visit:

https://brainly.com/question/28119824

#SPJ2

Answer:

The low tide, when it is 10 feet below the high tide would be at 7am and 7pm

Step-by-step explanation:

Answer:

ED = 26

Step-by-step explanation:

Using tangent-secant theorem

(12)²=(8)(x+10)

144=8x+80

144-80=8x

8x = 64

x=8

Now

ED = 8+8+10

ED = 26

Answer:

26

Step-by-step explanation:

Applying the tangent-secant theorem, we get:

12^2 = 8 * (x + 10)

144 = 8x + 80

= 8x = 144 - 80

8x = 64

x = 8

Putting x = 8 in ED, which is x + x + 10, we get:

= 8 + 8 + 10

= 26

Hope this helps!

Answer:

The mean and standard deviation of the corrected pH measurements are 6.63 and 3.8025 respectively.

Step-by-step explanation:

We can correct the values of the mean and standard deviation using the properties of the mean and the variance.

To the original value X we have to add 0.2 and multiply then by 1.3 to calculate the new and corrected value Y:

[tex]Y=1.3(X+0.2)[/tex]

The mean and standard deviation of the original value X are 4.9 and 1.5 respectively.

Then, we can apply the properties of the mean as:

[tex]E(Y)=E(1.3(X+0.2))=1.3E(X+0.2)=1.3E(X)+1.3*0.2\\\\E(Y)=1.3E(X)+0.26\\\\E(Y)=1.3*4.9+0.26=6.37+0.26=6.63[/tex]

For the standard deviation, we apply the properties of variance:

[tex]V(Y)=V(1.3(X+0.2))\\\\V(Y)=1.3^2\cdot V(X+0.2)\\\\V(Y)=1.69\cdot V(X)\\\\V(Y)=1.69\cdot 1.5^2=1.69\cdot 2.25=3.8025[/tex]

The properties that have been applied are:

[tex]1.\,E(aX)=aE(X)\\\\ 2.\,E(X+b)=E(X)+b\\\\3.\,V(aX)=a^2V(X)\\\\4.\,V(X+b)=V(X)+0[/tex]

Answer:

two to the thrid power is 8.

Step-by-step explanation:

2^3= 8

Answer:

I'm not sure what exactly the question is but it should be 8

Step-by-step explanation:

2^3

2×2×2=8

Answer:

Step-by-step explanation:

Find the exact frequency table in the diagram attached. x is the midpoint of the interval f is the frequency. Using the formula below to find the mean;

[tex]\overline x = \frac{\sum fx}{\sum f} \\[/tex]

[tex]\sum fx = (42*2)+(47*7)+(52*9)+(57*5)+(62*1)\\\sum fx = 84+329+468+285+62\\\sum fx = 1,228\\\sum f = 24\\\\\overline x = \frac{1,228}{24} \\\overline x = 51.17^{0} F[/tex]

The mean of the frequency distribution compare to the actual mean of 50.7°F is 51.2°F(to nearest tenth)

Answer:

2.555555

Step-by-step explanation: Nine times 2 is 18. When we subtract 18 from 23 we get 5. In the quotient we add a decimal point and add a zero to 5 which is 50. Nine times 5 is 45. When we subtract 45 from 50 we get 5 again and again and again . In decimal form it is 2.5555555.

Answer:

2.55 Hope this helps!

Answer:

c = ± 8.363277

Step-by-step explanation :

[tex]5.72^{2} = 32.49\\\\6.12^{2} = 37.4544\\3.49 + 37.4544 = 69.9444\\\\c^{2} = \sqrt{69.9444} \\= 8.363277[/tex]

Answer:

a) Null hypothesis: [tex] \mu \geq 863[/tex]

Alternative hypothesis: [tex] \mu >863[/tex]

b) For this case using the significance level of [tex]\alpha=0.05[/tex] we can use the normal standard distirbution in order to find a quantile who accumulates 0.05 of the area in the left and we got:

[tex] z_{\alpha}=-1.64[/tex]

And the rejection zone would be:

[tex] z<-1.64[/tex]

c) For this case since the statistic calculated is lower than the critical value we have enough evidence to reject the null hypothesis at 5% of significance

d) [tex] p_v = P(z<-2.17) =0.015[/tex]

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis at the significance level provided

Step-by-step explanation:

Part a

We want to test for this case if the true mean is significantly less than 863 calories so then the system of hypothesis are:

Null hypothesis: [tex] \mu \geq 863[/tex]

Alternative hypothesis: [tex] \mu >863[/tex]

Part b

For this case using the significance level of [tex]\alpha=0.05[/tex] we can use the normal standard distirbution in order to find a quantile who accumulates 0.05 of the area in the left and we got:

[tex] z_{\alpha}=-1.64[/tex]

And the rejection zone would be:

[tex] z<-1.64[/tex]

Part c

For this case since the statistic calculated is lower than the critical value we have enough evidence to reject the null hypothesis at 5% of significance

Part d

For this case the p value would be given by:

[tex] p_v = P(z<-2.17) =0.015[/tex]

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis at the significance level provided

Answer:

  D'(-2, 5), E'(3, 5), F'(3, 3), G'(-2, 3)

Step-by-step explanation:

Adding (-1, 2) to each of the coordinates gives ...

  D +(-1, 2) = (-1-1, 3+2) = D'(-2, 5)

  E +(-1, 2) = (4-1, 3+2) = E'(3, 5)

  F +(-1, 2) = (4-1, 1+2) = F'(3, 3)

  G +(-1, 2) = (-1-1, 1+2) = G'(-2, 3)

Answer:

The answer is B.

Step-by-step explanation:

I got it correct on Edge 2020

Answer:

(0,0)

Step-by-step explanation:

If a point satisfies both functions, they must be equal to each other. Thus, we have:

[tex]f(x)=g(x)[/tex]

[tex]2x=3x[/tex]  

The only x that satisfies this is 0.

Therefore, the y is also zero.

The point is (0,0).

Alternatively, you can also visualize the graphs. The only point where the graphs will touch is the origin point or (0,0).

｡☆✼★ ━━━━━━━━━━━━━━  ☾  

Tangents that meet at a point are equal in length so DB = CB

Let's form an equation:

10x + 16 = 5x + 20

- 16 from both sides

10x = 5x + 4

- 5x from both sides

5x = 4

/5 on both sides

x = 4/5

Sub this value into the expression for CB

5(4/5) + 20 = 24

Thus, the answer is option D. 24

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Answer:

4TH OPTION

Step-by-step explanation:

IN A CIRCLE , TANGENT DRAWN FROM AN EXTERNAL POINT TO THE CIRCLE ARE EQUAL.

ie BD = BC

ie 10x +16 = 5x+20

10x - 5x = 20 -16

5x = 4

x = 4/5

therfore BC = 5x+20 = 5*4/5 +20

BC= 4+20

BC = 24

HOPE IT HELPS...

Answer:

55.56  or  55 5/9

Step-by-step explanation:

To find the time it takes to type a report, you need to divide the number of words in the report by the words the typist can type in a minute.

2500/45 = 55.56

It takes 55.56 minutes or 55 5/9 minutes to type a 2500 word report.

Answer:

55 minutes and 33 seconds.

Step-by-step explanation:

To solve this we can set up a proportion.

1/45=x/2500

Cross multiply.

1*2500=45*x

45x=2500

Divide both sides by 45.

x=55.5*

.5* minutes is about 33 seconds. (0.55555*60)

So, it will take him around 55 minutes and 33 seconds.

Answer:

11

Step-by-step explanation:

I looked it up for you so no problem

Answer: 11 and 22

Step-by-step explanation:

We can start by making an equation. Since we know we have two numbers added to make 33. One number can be represented by x and the other is half of this x number so we can write this equation.

33 = 1/2x + x

Now we can combine like terms.

33 = 3/2x

Then either multiply by the reciprocal or divide by 1.5 on both sides.

x = 22

And the other number is half this number so divide by 2.

y = 11

Answer:

84

Step-by-step explanation:

Basically the ratio was multiplied by 12 to get the number of boys so you do the same to the other one.

Answer:

number of boys+number of girls=48boys+36girls=84members

Step-by-step explanation:

FIRST WE FIND THE NUMBER OF GIRLS BY STATISTICAL METHOD

4:3=48:x

4/3=48/x

By cross multiplication

4×x=48×3

4x=144

Dividing 4 on both sides

4x/4=144/4

x=36=number of girls

Answer:

The answer is x ≤ 2.

Step-by-step explanation:

Firstly, you have to move the unrelated term to the other side :

[tex] - 9 \leqslant 7 - 8x[/tex]

[tex] - 9 - 7 \leqslant - 8x[/tex]

[tex] - 16 \leqslant - 8x[/tex]

Next you can solve it :

[tex] - 8x \geqslant - 16[/tex]

[tex]x \leqslant - 16 \div - 8[/tex]

[tex]x \leqslant 2[/tex]

*Remember to change the symbol, when it is dividing by a negative value

Answer:

63 miles       x miles

----------- = -------------

3 gallons    7 gallons

Step-by-step explanation:

We will use proportions.  the number of miles over the gallons of gas

63 miles       x miles

----------- = -------------

3 gallons    7 gallons

Answer: 147 miles

Step-by-step explanation:

On 3 gallons, he travelled 63 miles

On 7 gallons, he travels

7/3 x 63 = 147 miles

Answer:

2.5 pounds

Step-by-step explanation:

Answer:

[tex] P(X=3)[/tex]

And using the probability mass function we got:

[tex] P(X=3)= (12C3)(\frac{1}{6})^3 (1-\frac{1}{6})^{12-3}=0.1974[/tex]

Step-by-step explanation:

Let X the random variable of interest "number of times that 6 appears", on this case we now that:

[tex]X \sim Binom(n=12, p=1/6)[/tex]

The probability mass function for the Binomial distribution is given as:

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]

Where (nCx) means combinatory and it's given by this formula:

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]

And we want to find this probability:

[tex] P(X=3)[/tex]

And using the probability mass function we got:

[tex] P(X=3)= (12C3)(\frac{1}{6})^3 (1-\frac{1}{6})^{12-3}=0.1974[/tex]

Answer:

Total chocolates= 48

Each friend get 3 chocolates

Step-by-step explanation:

Ray has 3 boxes of chocolates = 3

Each box has 4 layers of chocolates

= 4

Each layer has 4 rows of 4 chocolates each= 4

Total number of chocolates = 3*4*4

Total number of chocolates

= 48 chocolates

He shares 48 chocolates among 16 friends.

They Will all obtain 48/16= 3 chocolates each

Answer: the correct answer is 12