Given the definitions of f(x) and g(x) below, find the value of f(g(-1)).
f(x) = x^2+ x + 10
g(x) -5x-3

To prove that the given series (sin x)2 x 2n +1 n=1 is uniformly convergent in R, we'll make use of the M-test for uniform convergence.

Let f(x,n) = (sin x)2 x 2n +1 n=1

Let Mn = sup[ f(x,n) ] ( x in R )

To find Mn, we differentiate f(x,n) w.r.t. x, set it to zero to get its critical points and find its maximum at these critical points.

Now,  f'(x,n) = 2 sin(x) cos(x) x 2n+1 - (sin(x))2 (2n + 1)x2n = sin(x)x2n[ 2 cos(x) - (2n+1)(sin(x)/x) ]= 0 either when sin(x) = 0, i.e. at x = nπ for any integer n, or when cos(x) = (2n+1)(sin(x)/x) / 2 (for non-zero values of x).

The values of x for which cos(x) = (2n+1)(sin(x)/x) / 2 are the critical points.

But since  | (2n+1)(sin(x)/x) / 2 | <= | 2n + 1 | / 2, we have | cos(x) | <= | 2n + 1 | / 2.

Hence, the critical values of cos(x) for any given value of n are between - (2n+1)/2 and (2n+1)/2 (note that these values depend on n).

Hence, we have:

Mn = sup[ f(x,n) ] ( x in R )<= sup[ f(x,n) ] ( x in [- (2n+1)/2, (2n+1)/2] )<= f((2n+1)/2,n) = [(2n+1)/2]2n+1 sin((2n+1)/2)

This last step uses the fact that sin(x) <= 1 for all x and (sin(x))2 <= 1 for all x, as well as the observation that f(x,n) is odd, so its maximum will occur at x = (2n+1)/2.

Hence, we have:

Mn <= [(2n+1)/2]2n+1 sin((2n+1)/2)

Now, we claim that this upper bound of Mn goes to zero as n goes to infinity.

To show this, we use the fact that sin(x)/x -> 1 as x -> 0. Hence, sin((2n+1)/2) / (2n+1)/2 -> 1 as n -> infinity. Thus, [(2n+1)/2]2n+1 sin((2n+1)/2) -> 0 as n -> infinity.

Therefore, by the M-test, the series (sin x)2 x 2n +1 n=1 is uniformly convergent in R.

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Answer:

8845 billion

Step-by-step explanation:

Since exponential growth is given by;

P = a( 1 + r)^t

Where;

P = amount spent after t years

r = exponential growth rate

t = time interval

2004 - 2014 is an interval of 10 years. If 5430 billion was spent in 2004 and the growth rate has been 5% each year, then;

P= 5430 * 10^9(1 + 5/100)^10

P = 8845 * 10^9

P = 8845 billion

We cannot claim that there is a correlation between the amount of money made and the maximum temperature at the ice cream store.

To test the claim that there is no correlation between the amount of money an ice cream store makes and the maximum temperature, we can perform a correlation test. Since the significance level is given as 0.05, we will conduct a hypothesis test with the null hypothesis stating that there is no correlation between the two variables.

H0: There is no correlation between the amount of money made and the maximum temperature.

Ha: There is a correlation between the amount of money made and the maximum temperature.

We will use the Pearson correlation coefficient as the test statistic. The correlation coefficient measures the strength and direction of the linear relationship between two variables. The test statistic follows a t-distribution.

Using statistical software or a calculator, we can find the correlation coefficient and perform the hypothesis test. The correlation coefficient is a value between -1 and 1, where 0 indicates no correlation, positive values indicate a positive correlation, and negative values indicate a negative correlation.

Performing the analysis on the given data, we find that the correlation coefficient is approximately 0.183.

Next, we calculate the degrees of freedom for the t-distribution, which is n - 2, where n is the number of data points. In this case, n = 45, so the degrees of freedom is 45 - 2 = 43.

Finally, we compare the obtained correlation coefficient to the critical value of the t-distribution at the 0.05 significance level with 43 degrees of freedom. If the obtained correlation coefficient falls within the critical region, we reject the null hypothesis and conclude that there is a correlation.

Looking up the critical value for a two-tailed test with a significance level of 0.05 and 43 degrees of freedom, we find it to be approximately 2.016.

Since the obtained correlation coefficient (0.183) is not greater than the critical value (2.016), we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that there is a correlation between the amount of money made and the maximum temperature at the 0.05 significance level.

In conclusion, based on the given data and the correlation test, we cannot claim that there is a correlation between the amount of money made and the maximum temperature at the ice cream store.

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Answer: 175 ft

Step-by-step explanation: Lateral surface area of a cube with dimensions a, b, c is 2ab+2ac+2bc, and then when you plug in the values and solve you get 175!

The indefinite integral ∫ 2dx evaluates to 2x + C, where C is the constant of integration.

The definite integral ∫ 2dx represents the area under the curve y = 2 from the lower limit to the upper limit. In this case, since there are no limits provided, the integral represents the indefinite integral, which evaluates to 2x + C, where C is the constant of integration.

The definite integral ∫ 2dx represents the area under the curve y = 2 with respect to x. Since there are no specific limits provided in the integral, it becomes an indefinite integral. To evaluate this indefinite integral, we integrate the function 2 with respect to x. The integral of a constant function is equal to the constant multiplied by x. Therefore, the result of the integral is 2x + C, where C is the constant of integration.

The indefinite integral 2x + C represents a family of functions that differ by a constant. This means that there are infinite functions that satisfy the derivative of 2x + C equals 2. The constant of integration, denoted by C, can take any real value, and it represents the arbitrary constant that accounts for all possible functions in the family. Hence, the indefinite integral ∫ 2dx evaluates to 2x + C, where C is the constant of integration.

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Using the Binomial distribution P(x=4) is 0.1804.

Given n=8 and p=0.3.

To find P(x=4) we use the Binomial distribution.

The formula for the Binomial distribution is as follows:

P(x) = nCx * px * (1 - p)n - x

Here, n = 8,

p = 0.3,

and x = 4.

Substitute the values in the formula to get:

P(4) = 8C4 * 0.3^4 * (1 - 0.3)8 - 4

= 0.1804

Therefore, P(x=4) is 0.1804.

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Answer:

=9c

Step-by-step explanation:

8c+c=9c

hope this is useful

Answer:

Sum = 4 + 5 = 9

Step-by-step explanation:

Equation

2*(x - 2)(x-2) = (x - 3)(x + 4)

Solution

2*(x^2 - 4x + 4) = x^2 + 4x - 3x - 12

2x^2 - 8x + 8  = x^2 +x - 12                     Subtract the right side from the left

x^2 - 9x + 20 = 0

(x - 4)(x - 5) = 0

The possible values for x are

x - 4 = 0

x = 4

x - 5 = 0

x = 5

Check

(4 - 2)^2 = (4) = 4

(x - 3)(x + 4) = (4 - 3)(8) = 8

This checks

(5 - 2)^2 = 3^2 = 9

(5 - 3)(5 + 4) = 2 * 9 = 18

Answer:

Just took the test, the answer is  14.7%

Step-by-step explanation:

If the stream narrows from 30 feet to 20 feet, the width of the stream has narrowed, and the velocity should increase. The correct answer is b.

According to the principle of conservation of mass, when the width of a stream narrows, the volume flow rate (the amount of water passing through a given point per unit time) must remain constant if there are no other factors involved.

The volume flow rate (Q) can be calculated as the product of the cross-sectional area (A) and the velocity (v): Q = A * v.

When the width of the stream narrows from 30 feet to 20 feet while the volume flow rate remains constant, the cross-sectional area decreases. To maintain a constant volume flow rate, the velocity must increase.

This is because the same amount of water is passing through a smaller cross-sectional area, requiring an increase in velocity to compensate for the reduced width.

Therefore, the correct statement is that the width of the stream has narrowed, and the velocity should increase.

The correct answer is b.

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Answer:

A=400, L=2W, L*W=A so, L*W=400, so, 400=2W*W or 200=W*W or 200=[tex]W^{2}[/tex], [tex]\sqrt{200\\[/tex] = W, L=2([tex]\sqrt{200\\[/tex]) and W=[tex]\sqrt{200\\[/tex], W=14.14 and L=28.28

Step-by-step explanation:

Forecast demand in summer 2013 using regression analysis on deseasonalized demand by using regression analysis is: The regression line equation is Y = 358.3 + 0.2407X.

After deseasonalizing the historical data and performing linear regression analysis, the forecasted demand for summer 2013 is 380 units.

To forecast demand in summer 2013 using regression analysis on deseasonalized demand, we need to first remove the seasonal component from the historical data. This can be achieved by calculating seasonal indices.

Step 1: Calculate the average demand for each season

Spring average = (210 + 465) / 2 = 337.5

Summer average = (136 + 274) / 2 = 205

Fall average = (375 + 695) / 2 = 535

Winter average = (582 + 972) / 2 = 777

Step 2: Calculate the seasonal indices

Spring index = Spring average / Overall average demand = 337.5 / 469.5 = 0.7189

Summer index = Summer average / Overall average demand = 205 / 469.5 = 0.4369

Fall index = Fall average / Overall average demand = 535 / 469.5 = 1.1397

Winter index = Winter average / Overall average demand = 777 / 469.5 = 1.6545

Step 3: Calculate deseasonalized demand for each observation

Deseasonalized demand = Actual demand / Seasonal index

For summer 2012: Deseasonalized demand = 274 / 0.4369 = 627.3

For summer 2011: Deseasonalized demand = 136 / 0.4369 = 311.4

Step 4: Use regression analysis to forecast demand in summer 2013

We can use a linear regression model to forecast demand based on deseasonalized demand.

Let's assign X as the independent variable (deseasonalized demand) and Y as the dependent variable (actual demand). Using the given historical data points (311.4, 627.3), we can calculate the regression line equation: Y = a + bX.

Step 5: Calculate the regression line equation

We can use the least squares method to find the coefficients a and b.

Sum of X = 311.4 + 627.3 = 938.7

Sum of Y = 136 + 274 + 375 + 582 + 465 + 695 + 972 = 3499

Sum of XY = (311.4 * 136) + (627.3 * 274) = 85316.4

Sum of X^2 = [tex](311.4^2) + (627.3^2) = 474405.61[/tex]

b = (n * Sum of XY - Sum of X * Sum of Y) / (n * Sum of [tex]X^2[/tex] - (Sum of [tex]X)^2)[/tex]

  = (2 * 85316.4 - 938.7 * 3499) / (2 * 474405.61 - (938.7)^2)

  = 0.2407

a = (Sum of Y - b * Sum of X) / n

  = (3499 - 0.2407 * 938.7) / 2

  = 358.3

Therefore, the regression line equation is Y = 358.3 + 0.2407X.

Finally, we can forecast demand in summer 2013 by substituting X with the deseasonalized demand value for summer 2013, which we calculate using the seasonal index:

Deseasonalized demand for summer 2013 = Summer average * Summer index  = 205 * 0.4369                                

 = 89.6065

Using the regression line equation: Y = 358.3 + 0.2407 * 89.

6065 = 380.3

Rounding to the nearest whole number, the forecasted demand in summer 2013 is approximately 380.

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The standard error is 0.5, (b) the error is 1.015, and (c) the 95% confidence interval is (33.985, 36.015).

A random sample of 36 cars of the same model has an average gas mileage of 35 miles/gallon with a sample standard deviation of 3 miles/gallon.

To find out the standard error, error, and the 95% confidence interval, we need to follow the following steps:

Step 1: Finding the Standard Error The formula for standard error is given as: Standard Error (SE) =

,[tex]\frac{s}{\sqrt{n}}[/tex]

where s is the sample standard deviation and n is the sample size.

Given, Sample standard deviation (s) =

3Sample size (n) = 36

The standard error (SE) is:

SE = [tex]$\frac{3}{\sqrt{36}}$\\SE = 0.5[/tex]

Thus, the standard error is 0.5.

Step 2: Finding the ErrorThe formula to calculate the error is given as:

Error (E) = t × SE

where t is the t-value of the distribution corresponding to the desired level of confidence.

For a 95% confidence interval with 35 degrees of freedom, the t-value is 2.030.The value of the error is:

Error (E) = 2.030 × 0.5E = 1.015

Thus, the error is 1.015.

Step 3: Finding the 95% confidence interval

The 95% confidence interval is given by the formula:

[tex]CI = $\overline{x}$ \pm t$_{\frac{\alpha}{2}, n-1}$ \times SE[/tex]

where [tex]$\overline{x}$[/tex]

is the sample mean,

[tex]t$_{\frac{\alpha}{2}, n-1}$[/tex]

is the t-value for the given confidence level and the degrees of freedom, and SE is the standard error. Given,

Sample mean

[tex]($\overline{x}$) = 35SE = 0.5t$_{\frac{\alpha}{2}, n-1}$ = t$_{\frac{0.05}{2}, 35}$ = t$_{0.025, 35}$[/tex]

The value of

[tex]t$_{0.025, 35}$[/tex]

can be found using the t-table or a calculator and is approximately equal to 2.030.

Substituting these values in the formula, we get:

CI = 35 ± 2.030 × 0.5CI = 35 ± 1.015

The 95% confidence interval is (33.985, 36.015).

Thus, (a) the standard error is 0.5, (b) the error is 1.015, and (c) the 95% confidence interval is (33.985, 36.015).

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Answer: W=12m

Step-by-step explanation:

Answer:

hello i posted the answer onto 345.tly.com

Step-by-step explanation:

Answer:

1000g

Step-by-step explanation:

2/5 =400g

3/5 = 600g

1/2(3/5) = 300g

400 + 600 = 1000

Answer: 60% would like another color

Step-by-step explanation:

The solution to the differential equation dy/dx = (x + y + 1)^2 using the method of linear substitution is given by the equation arctan(x + y + 1) = x + C, where C is an arbitrary constant.

To solve the differential equation dy/dx = (x + y + 1)^2 using the method of linear substitution, we can make a substitution to transform it into a separable equation.

Let u = x + y + 1. Differentiating both sides with respect to x, we have du/dx = 1 + dy/dx.

Rearranging the equation, we get dy/dx = du/dx - 1.

Substituting this expression back into the original differential equation, we have du/dx - 1 = u^2.

This is now a separable equation. We can rearrange it as du/(u^2 + 1) = dx.

Now, we integrate both sides with respect to their respective variables:

∫du/(u^2 + 1) = ∫dx

The integral of 1/(u^2 + 1) can be evaluated using the inverse tangent function:

arctan(u) = x + C

Substituting back the value of u = x + y + 1, we have:

arctan(x + y + 1) = x + C

This is the general solution to the given differential equation using the method of linear substitution. The constant C represents the arbitrary constant of integration.

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Answer:

50 years

Step-by-step explanation:

Given data

Principal= $500

Rate= 6%

Amount = $2000

The simple interest expression is given as

A=P(1+rt)

Substitute

2000= 500(1+0.06*t)

open bracket

2000=500+ 30t

2000-500=30t

1500=30t

t= 1500/30

t= 50 years

Hence the time is 50 years

Answer:

50 years

Step-by-step explanation:

Formula for simple interest:

I = Prt

where

I = interest earned

P = principal amount deposited

r = annual interest rate

t = number of years

When the account reaches $2000, $500 is from the principal and

$2000 - $500 = $1500 is from the interest.

We use the simple interest formula to find the number of years needed to earn $1500 in interest from $500 principal at 6% interest rate.

1500 = 500 * 0.06 * t

t = 50

Answer: 50 years

The probability of the Plinko chip landing on slot 4 when dropped from slot 3 is 0.25 or 25%.

To determine the probability of a Plinko chip landing on a specific slot, we need to know the number of possible outcomes and the number of favorable outcomes.

In the case of a Plinko game, each chip has two possible outcomes at each slot: it can either move to the left or to the right. Therefore, at each slot, there are two possible paths the chip can take.

Since the chip starts at slot 3, it has to go through one slot at a time to reach slot 4. Each slot has two possible paths, so for the chip to reach slot 4, it has to go through two slots. Therefore, there are a total of 2^2 = 4 possible paths for the chip to reach slot 4.

Now, we need to determine the number of favorable outcomes, which is the number of paths that lead to slot 4. In this case, there is only one path that leads directly to slot 4, which is by moving to the right at both slots.

Therefore, the probability of the chip landing on slot 4 when starting at slot 3 is 1 out of 4 possible paths, which simplifies to 1/4 or 0.25.

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Sold 80 plain bagels, 40 onion bagels, and 180 pumpernickel bagels that day.

How about we relegate factors to address the quantity of bagels sold for each kind. Let's say that P denotes the quantity of plain bagels, O the quantity of onion bagels, and Pu the quantity of pumpernickel bagels.

We realize that the absolute number of bagels sold is 300, so we have the condition P + O + Pu = 300.

Given that you sold 100 more pumpernickel bagels than plain bagels and that you sold twice as many plain bagels as onion bagels, the equation P = 2O can be written. Additionally, the equation Pu = P + 100 can be written.

Subbing the second and third conditions into the primary condition, we get 2O + O + (2O + 100) = 300.

We can reduce this equation to 5O = 200.

Partitioning the two sides by 5, we track down O = 40.

Pu = P + 100 = 80 + 100 = 180 and P = 2O = 2 * 40 = 80, respectively.

Accordingly, you sold 80 plain bagels, 40 onion bagels, and 180 pumpernickel bagels that day.

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============================================================

Explanation:

Refer to the diagram below. I've added the variables b, c and d to the drawing you posted.

The variable b is an inscribed angle, while variables c and d are arc measures.

For any inscribed quadrilateral, the opposite angles always add to 180. They are supplementary angles. This means the 110 degree angle and the angle b add to 180, so,

110+b = 180

b = 180-110

b = 70

Inscribed angle b is 70 degrees.

Next, we apply the inscribed angle theorem. This theorem says that the inscribed angle doubles in value to get its corresponding central angle measure (and therefore it's arc measure as well).

In other words, inscribed angle b = 70 doubles to 2*70 = 140 degrees. This represents the combination of arcs c and d. Therefore, c+d = 140. Note how inscribed angle b cuts off this longer arc.

We don't need to find the measure of arc c or arc d individually. We just need to find the measure of arc 'a'.

The four arc measures (161, a, c and d) all combine to a full 360 degree circle. Let's add those four parts, and set that equal to 360. We'll keep in mind that c+d = 140 as well.

So...

a+c+d+161 = 360

a = 360-161 - (c+d)

a = 360-161 - (140) ..... replaced "c+d" with "140"

a = 59

Arc 'a' is 59 degrees

Answer:

C i think

Step-by-step explanation:

Answer:

In the first box: 24a

In the second box: +12

In the third box: 24a + 12

Step-by-step explanation:

For the first box, you're multiplying 3 times 8a. Since we don't know a, we leave it alone and just multiply the number next to it. So 3 x 8 = 24...3 x 8a = 24a

3 times a positive 4 is a positive 12 (this is kind of a weird way to write it, but area models are weird, imo.

It's just trying to show that you multiply the 3 by every part of what's inside the parentheses.

Answer:

(x-5, y+7)

Step-by-step explanation:

If you start from one of the points on A, then you can see that A' moves 5 units to the left (x-5), and 7 units up (y+7).

hope this helped :)

howdy!!

the answer for yr question is B!!!!

goodluck<3

The inverse of the given function as required to be determined from the task content is; f-¹(x) = 2 / (x-3) + 4.

It follows from the task content that the inverse of the given function is to be determined.

Given; f(x) = 2 / (x-4) +3

y = 2 / (x-4) + 3

y - 3 = 2 / (x-4)

x - 4 = 2 / (y-3)

x = 2 / (y-3) + 4.

f-¹(x) = 2 / (x-3) + 4.

Hence, the inverse of the given function as required is; f-¹(x) = 2 / (x-3) + 4.

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