Bob reads 72 chapters of a book in 8 hours.
What is his rate in chapters per hour

Formula of simple interest rate:

Where,

For Monica interest rate is:

For Paul interest rate is:

No, Paul interest rate higher then Monic.

The limit of (f(x) + 1) / sin(x) as x approaches 0 is 0, the approximation for f(1/2) using Euler's method with two steps is 19/32 and the particular solution to the differential equation with the initial condition f(0) = -1 is: y(x) = -1 / (x²  + 2x + 1) - 1.

(a) To find the limit of (f(x) + 1) / sin(x) as x approaches 0, we can first rewrite the given differential equation as:

dy / dx = y²  (2x + 2)

Separating variables, we get:

dy / y²  = (2x + 2) dx

Integrating both sides, we have:

∫(1 / y² ) dy = ∫(2x + 2) dx

Integrating the left side gives:

-1 / y = x²  + 2x + C1

where C1 is the constant of integration.

Since we have the initial condition f(0) = -1, we substitute x = 0 and y = -1 into the above equation:

-1 / (-1) = 0²  + 2(0) + C1

1 = C1

So the particular solution is:

-1 / y = x²  + 2x + 1

Multiplying through by y gives:

-1 = y(x²  + 2x + 1)

Simplifying further:

y(x²  + 2x + 1) + 1 = 0

Now, to find the limit (f(x) + 1) / sin(x) as x approaches 0, we substitute x = 0 into the particular solution equation:

f(0)(0²  + 2(0) + 1) + 1 = 0

-1(0) + 1 = 0

1 = 0

Therefore, the limit of (f(x) + 1) / sin(x) as x approaches 0 is 0.

(b) Using Euler's method, we approximate the value of f(1/2) starting at x = 0 with two steps of equal size. Let's choose the step size h = 1/4.

First step:

x0 = 0, y0 = f(0) = -1

Using the differential equation, we have:

dy / dx = y²  (2x + 2)

dy = y²  (2x + 2) dx

Approximating the derivative using the Euler's method:

Δy ≈ y²  (2x + 2) Δx

Δy ≈ (-1)²  (2(0) + 2) (1/4)

Δy ≈ 1/2

Next, we update the values:

x1 = x0 + Δx = 0 + 1/4 = 1/4

y1 = y0 + Δy = -1 + 1/2 = 1/2

Second step:

x0 = 1/4, y0 = 1/2

Using the differential equation again:

dy / dx = y^2 (2x + 2)

dy = y²  (2x + 2) dx

Approximating the derivative using the Euler's method:

Δy ≈ y²  (2x + 2) Δx

Δy ≈ (1/2)²  (2(1/4) + 2) (1/4)

Δy ≈ 3/32

Updating the values:

x2 = x1 + Δx = 1/4 + 1/4 = 1/2

y2 = y1 + Δy = 1/2 + 3/32 = 19/32

Therefore, the approximation for f(1/2) using Euler's method with two steps is 19/32.

c)To find the particular solution to the differential equation dy/dx = y^2 (2x + 2) with the initial condition f(0) = -1, we can solve the separable differential equation.

Separating variables, we have:

dy / y² = (2x + 2) dx

Integrating both sides:

∫(1 / y² ) dy = ∫(2x + 2) dx

Integrating the left side:

-1 / y = x²  + 2x + C

where C is the constant of integration.

To find the particular solution, we substitute the initial condition f(0) = -1:

-1 / (-1) = 0²  + 2(0) + C

1 = C

So the particular solution is:

-1 / y = x²  + 2x + 1

Multiplying through by y gives:

-1 = y(x²  + 2x + 1)

Simplifying further:

y(x²  + 2x + 1) + 1 = 0

Therefore, the particular solution to the differential equation with the initial condition f(0) = -1 is: y(x) = -1 / (x²  + 2x + 1) - 1

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Answer:

Step-by-step explanation:

You want the value of the piecewise function for various values of x.

The first step in evaluating a piecewise function is determining which domain is applicable to the value of x you have. Then you use the corresponding function, evaluating it in the usual way.

For x = -5, the applicable domain is x < -3, so the function is ...

  h(-5) = -4(-5) -18 = 20 -18

  h(-5) = 2

For x = 0, the applicable domain is -3 ≤ x < 1, so the function is ...

  h(0) = 1

For x = 1 or 4, the applicable domain is x ≥ 1, so the function is ...

  h(1) = 1 +2 = 3

  h(4) = 4 +2 = 6

<95141404393>

Answer:

$60

Step-by-step explanation:

19 times 15 = 285
1425-285=1140
1140 divided by 19 = 60

To check: Divide 1425 by 75 to get 19.

(a) The general solution of cos(6x)y' = y is y = Csec^(-6)(6x), where C is a constant.   (b) The other two roots of x³ + 22x - 52, given one complex root, are -1-5i and 0. The integral 34 dx / (x³ + 22x - 52) involves partial fractions.



(a) To find the general solution of the differential equation cos(6x) y' = y, we set v = y'. Differentiating both sides gives -6sin(6x) v + cos(6x) v' = v. Rearranging, we have v' - 6tan(6x) v = 0. This is a linear first-order differential equation, and its integrating factor is e^(-∫6tan(6x) dx) = e^(-ln|cos(6x)|^6) = sec^6(6x). Multiplying the equation by the integrating factor, we get (sec^6(6x) v)' = 0. Integrating, we have sec^6(6x) v = C, where C is a constant. Solving for v, we get v = Csec^(-6)(6x). Finally, integrating v with respect to x, we find y = ∫ Csec^(-6)(6x) dx.

(b) (i) If -1+5i is a complex root of x³ + 22x - 52, its conjugate -1-5i is also a root. By Vieta's formulas, the sum of the roots is zero, so the remaining root must be the negation of their sum, which is 0.

(ii) Using the result from (a), we can write x³ + 22x - 52 = (x - 0)(x - (-1+5i))(x - (-1-5i)) = (x)(x + 1 - 5i)(x + 1 + 5i). Applying partial fractions, we can express 34 dx / (x)(x + 1 - 5i)(x + 1 + 5i) and integrate each term separately. The final solution involves logarithmic and inverse tangent functions.

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Answer:

Price per pound of apple=$0.84

Price per pound of cherry=$2.52

Step-by-step explanation:

Let apple=a

Let cherry =c

Fredrick

4a+14c=38.64. (1)

Wilhelmina

12a+7c=27.72. (2)

Multiply (1) by 1 and (2) by 2

4a+14c=38.64. (3)

24a+14c=55.44 (4)

Subtract (3) from (4)

20a= 16.8

a=16.8/20

a=0.84

Substitute a=0.84 into equ (1)

4a+14c=38.64

4(0.84)+14c=38.64

3.36+14c=38.64

14c=38.64-3.36

14c=35.28

c=35.28/14

c=2.52

Price per pound of apple=$0.84

Price per pound of cherry=$2.52

Check

4(0.84)+14(2.52)

3.36+35.28=38.64

12a+7c=27.72

12(0.84)+7(2.52)

=10.08+17.64

=27.72

Answer:

12

Step-by-step explanation:

bc it is

Answer:

see explanation

Step-by-step explanation:

Given

f(x) = \(3^{x}\) , then

f(x + 1) = \(3^{x+1}\) = \(3^{x}\) × 3

Then

f(x) + f(x + 1)

= \(3^{x}\) + 3. \(3^{x}\) ← factor out \(3^{x}\) from each term

= \(3^{x}\) (1 + 3)

= 4. \(3^{x}\)

= 4f(x)

Answer:

(6a-4)°=(2a+68)°

6a-2a=68+4

4a=72

a=72/4

a=18

Answer:

The answer is 18. (A)

Step-by-step explanation:

Let me know if this helps

Based on the information, the area of the figure would be: 86.13 units ²

To find the area of the figure we must perform the following procedure:

1. Find the area of the triangle with the following formula:

height * base / 2 = area of the triangle

6 * 6 / 2 = area of the triangle

18 = area of the triangle

2. Find the area of the rectangle with the following formula:

height * base = area of rectangle

6 * 9 = area of the rectangle

54 = area of rectangle

3. Find the area of the semicircle with the following formula:

\(\pi\)  * r² / 2 = area of the semicircle

\(\pi\)  * 3² / 2 = area of the semicircle

\(\pi\)  * 9 / 2 = area of the semicircle

28.27 / 2 = area of the semicircle

14.13 = area of the semicircle

4. We must add the area of all the figures to find the total area.

14.13 + 54 + 18 = 86.13 units ²

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Answer:

2 (-3 - 1) = 6 (-1)?? If thats the equation you were trying to type then the answer is: -8 = -6

Step-by-step explanation:

Answer:

1320ft

Step-by-step explanation:

1 mile is equal to 5280 feet, divide 5280/4

this will result in a quarter mile, being 1320ft. So for the question "1/4 mile or less" the Answer is the horse excels in 1320ft mile races

The probability, P(not green) when choosing one marble from the bag is 88%.

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

Given is that Joseph has a bag filled with 3 red, 3 green, 9 yellow, and 10 purple marbles

We can write -

P(not green) = 1 - P(green)

So, we can write -

P(green) = n{g}/n{s}

P(green) = 3/25

So, we can write -

P(not green) = 1 - P(green)

P(not green) = 1 - 3/25

P(not green) = 22/25

Now -

Let -

22 is x% of 25

22 = x/100 x 25

x/4 = 22

x = 88%

Therefore, the probability, P(not green) when choosing one marble from the bag is 88%.

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Answer:

\(\frac{29}{3}\)

Step-by-step explanation:

9*3+2

Answer:

Two sets of dimensions are possible:

              L(m)   W(m)   Area(m^2)   Fence (m) Perimeter

Set 1         19        16       304              51

Set 2         32      9.5      304              51

Step-by-step explanation:

Let's set L and W for the Length and Width of the perimeter.  We know that:

Area = L*W

Area = 304 m^2

Perimeter = 51 m

Let's say that the side bounded by the river is the length side.   No fence is required for that portion, so the fencing for the perimeter is given by:

Perimeter, P = L + 2W

P = 51 m

We can write:   L+2W=51 m

Rearrange to isolate one of the two variables.  Lets pick L:

 L+2W=51

 L=51-2W

L = (51-2W)

Now use this in the area equation:

304 m^2 = L*W

304 m^2 = (51-2W)*W

304 m^2 = (51-2W)*W

304 m^2 = 51W-2W^2

Arrange this in the standard form of a quadratice equation and solve:

-2W^2+51W-304 m^2 = 0

W = 16 and 9.5 meters

W = 16 m

Since L=51-2W

 L=51-2*(16)

L = 51-32

L = 19 m

Area = L*W

L*W = 304 m^2

(19m)W = 304 m^2

W =  16 m

Check:

Does a length (L) of 19 m and a width (W) of 16 m give an area of 304 m^2 and a fencing perimeter of 51 m if one of the L sides is the river?

Area = (19 m)*(16 m) = 304 m^2  YES

Per.  = 2*(16)+ 19 = 51 m  YES

W = 9.5 m

Ding the same calculation for a width of 9.5 m also satisfies all the equations, as per above.  

Both values of W are valid, so the twos sets of possible dimensions are:

                   L(m)    W(m)   Area(m^2)   Fence (m) Perimeter

Set 1          19      16       304              51

Set 2          32      9.5      304              51

Answer:

7 2/4 or 7 1/2

Step-by-step explanation: You can add the 3 3/4 to 3 3/4 or mutlipy 3 3/4 by 2 because you need to find the number of 2 batches.

The equation has a value less than 2,175 is- one half x 2,175

0.5 x 2,175 = 1087.5

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

The equation has a value less than 2175, let us simplify each option:

A) 1 x 2175 = 2175

B) 2 x 2175 = 4350

C) 2/2 x 2175 = 1 x 2175 = 2175

D) 1/2 x 2175 = 1087.5

From the simplified forms, we see that the equation that has a value less than 2175 is:

The correct answer is Option D

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We are 99% confident that the true average stance duration among elderly individuals lies within the range of 744.56 ms to 857.44 ms.

To test whether the true average stance duration is larger among elderly individuals than among younger individuals, we can perform a one-tailed independent samples t-test. The null hypothesis (H0)

Using the t-test, we compare the means and standard deviations of the two samples and calculate the test statistic

a) To calculate a 99% confidence interval for the true average stance duration among elderly individuals, we can use the sample mean, sample standard deviation, and the t-distribution.

Given:

Older adults: n = 28, sample mean = 801, sample standard deviation = 117

Using the formula for a confidence interval for the mean, we have:

Margin of error = t * (sample standard deviation / √n)

Since the sample size is relatively large (n > 30), we can use the z-score instead of the t-score for a 99% confidence interval. The critical z-value for a 99% confidence level is approximately 2.576.

Calculating the margin of error:

Margin of error = 2.576 * (117 / √28) ≈ 56.44

The confidence interval is then calculated as:

Confidence interval = (sample mean - margin of error, sample mean + margin of error)

Confidence interval = (801 - 56.44, 801 + 56.44) ≈ (744.56, 857.44)

b) To test whether the true average stance duration is larger among elderly individuals than among younger individuals, we can perform a one-tailed independent samples t-test.

The null hypothesis (H0): The true average stance duration among elderly individuals is equal to or less than the true average stance duration among younger individuals.

The alternative hypothesis (Ha): The true average stance duration among elderly individuals is larger than the true average stance duration among younger individuals.

. With the given data, perform the t-test and obtain the p-value.

c) To construct a 95% confidence interval for the difference in means between older and younger adults, we can use the formula for the confidence interval of the difference in means.

Given:

Older adults: n1 = 28, sample mean1 = 801, sample standard deviation1 = 117

Younger adults: n2 = 16, sample mean2 = 780, sample standard deviation2 = 72

Calculating the standard error of the difference in means:

Standard error = √((s1^2 / n1) + (s2^2 / n2))

Standard error = √((117^2 / 28) + (72^2 / 16)) ≈ 33.89

Using the t-distribution and a 95% confidence level, the critical t-value (with degrees of freedom = n1 + n2 - 2) is approximately 2.048.

Calculating the margin of error:

Margin of error = t * standard error

Margin of error = 2.048 * 33.89 ≈ 69.29

The confidence interval is then calculated as:

Confidence interval = (mean1 - mean2 - margin of error, mean1 - mean2 + margin of error)

Confidence interval = (801 - 780 - 69.29, 801 - 780 + 69.29) ≈ (-48.29, 38.29)

Comparison with part (b): In part (b), we performed a one-tailed test to determine if the true average stance duration among elderly individuals is larger than among younger individuals. In part (c), the 95% confidence interval for the difference in means (-48.29, 38.29) includes zero. This suggests that we do not have sufficient evidence to conclude that the true average stance duration is significantly larger among elderly individuals compared to younger individuals at the 95% confidence level.

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Answer:

17% i think

Step-by-step explanation:

The equation of linear equation is y = -5x +3.

What is equation of linear equation?

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named as a 'linear equation'.

The standard form or the general form of linear equations in one variable is written as, Ax + B = 0; where A and B are real numbers, and x is the single variable. The standard form of linear equations in two variables is expressed as, Ax + By = C; where A, B and C are any real numbers, and x and y are the variables.

The slope intercept form of linear equation is

y = mx + b

where m is the slope.

Given,

The slope = -5

and the points are (4, -17)

y = -17, x = 4, m = -5

-17 = -5(4) + b

-17 = -20 + b

-17 + 20 = b

b =3

The equation of linear equation is y = -5x + b

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Answer:

its got 6

Step-by-step explanation:

I REALLY DONT KNOW

Answer:

Step-by-step explanation:

Let t be the unit cost of the tomatoes:  e. g., t = $1.25/lb.

If Keith spent $8 on tomatoes, the number he bought would then be

   $8

------------- = 6.4 lb of tomatoes

$1.25/lb

Of course he couldn't buy 0.4 tomato, but this method of calculating how many tomatoes he could buy theoreticallyl is correct.

The general formula would be

   $8

------------   and the end result would be the number of pounds Keith could

  $t / lb                               buy for $8.

Answer:

d

Step-by-step explanation:

we won't know because there is not enough info

No.1

Set those two equations equal to each other.

-7/4 x - 4 = -1/4 x + 2

x on one side, constant on other side.

-6/4 x = 6

x = -4

now put x value into any of the two equations given

y = -7/4 * -4 - 4 = 7 - 4 = 3

(-4,3)

No.2

Set those two equations equal to each other.

x + 2 = -1/5 x - 4

x on one side, constant on other side.

6/5 x = -6

x = -5

now put x value into any of the two equations given

y = -5 + 2 = -3

(-5,-3)

To determine the value of x, you have to apply the Thales theorem. Which states that the line segments determined by the parallel lines are at the same ratio, so that:

From this expression, you can determine the value of x. Multiply both sides f the equal sign by 28 to calculate the value of x:

The value of x is equal to 14

the cosine of the angle between the planes is:

cos(theta) = (n1 . n2) / (|n1| |n2|) = 10 / (sqrt(3) * sqrt(42)) = 10 / (sqrt(126)) = (10/6) * sqrt(14) = (5/3) * sqrt(14)

To find the cosine of the angle between the planes, we need to find the normal vectors of both planes, and then use the dot product formula:

cos(theta) = (n1 . n2) / (|n1| |n2|)

where n1 and n2 are the normal vectors of the planes.

For the first plane x + y + z = 0, the coefficients of x, y, and z give us the normal vector <1, 1, 1>.

For the second plane x + 5y + 4z = 8, the coefficients of x, y, and z give us the normal vector <1, 5, 4>.

Taking the dot product of these vectors, we get:

<1, 1, 1> . <1, 5, 4> = 11 + 15 + 1*4 = 10

To find the magnitudes of the normal vectors, we can use the Pythagorean theorem:

|<1, 1, 1>| = sqrt(1^2 + 1^2 + 1^2) = sqrt(3)

|<1, 5, 4>| = sqrt(1^2 + 5^2 + 4^2) = sqrt(42)

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