Find the derivative of the function y=x^(x+8)

The bracket should be placed 40 inches away from the vertex (0,0) looking at the equation y=1/160x^2 models a solar cooker.

The equation with a vertex is : y = ax²

We know that the focus of a parabola is normally at the point (h, k + p), where (h, k) is the vertex of the  parabola  and 'p' is the distance between the vertex and the focus.  

Since the vertex at the origin is  (0,0), the parabolic equation then becomes;

y = (1/4p)x²

1/4p = 1/160

4p = 160

p = 160 ÷ 4

p = 40

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At the start of 2014 lucys house was worth $250,000.

Step-by-step explanation:

We can use the formula for continuously compounded interest to find the balance in Amadou's account after 20 years:

A = Pe^(rt)

where A is the balance, P is the initial investment, e is Euler's number (approximately 2.718), r is the interest rate, and t is the time in years. Plugging in the values given, we get:

A = 760e^(0.81*20)

A ≈ $91,012.43

Now we can use the formula for annually compounded interest to find the balance in Mia's account after 20 years:

A = P(1 + r)^t

Plugging in the values given, we get:

A = 760(1 + 0.83)^20

A ≈ $33,883.24

Finally, we can subtract Mia's balance from Amadou's balance to find the difference:

$91,012.43 - $33,883.24 ≈ $57,129.19

So Amadou would have about $57,129 more in his account than Mia after 20 years.

The account balance is b) $3,796.

To calculate the account balance after two years, we need to use the formula for the future value of an annuity due:

FV = Pmt x [[tex](1+r/n)^{nt}[/tex] - 1] x (1 + r/n)

where:

Pmt is the monthly payment ($150 in this case)

r is the annual interest rate (5.5%)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years (2 in this case)

Plugging in the numbers, we get:

FV = $150 x [[tex](1+0.055/12)^{(12*2)}[/tex] - 1] x (1 + 0.055/12)

FV = $150 x [1.1247 - 1] x 1.004583

FV = $150 x 0.1247 x 1.004583

FV = $18.69 x 1.004583 x 24

FV = $449.56

So the account balance after two years, rounded to the nearest dollar, is $450. Therefore, the closest answer is option B: $3,796.

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Answer: Is a plane figure with at least 3 straight sides and angles, and typically five or more sides.

Step-by-step explanation:

Lines AC and RS are skew lines

Skew lines are lines that exist in different planes and are does not intersect each other directly.

The following are properties of skew lines;

1. They continue in two directions

2. They are in different planes

3. They are never parallel

4. They never intersect

5. They are never perpendicular

As we can see from the diagram, line AC and RS are not on thesame place and they are not parallel lines. They do not intersect each other.

This means that line AC and RS has shown skew lines property and they are therefore skew lines.

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The correct equation which represents the number of meters, M, swam to the number of laps, L is,

⇒ M = 25L

We have to given that;

The table shows the number of meters swam by a swimmer after a given number of laps.

Now, Take two points from table as;

⇒ (L, M) = (1, 25) and (2, 50)

Hence, We can find the rate of change as;

⇒ m = (50 - 25) / (2 - 1)

⇒ m = 25

Thus, The correct equation which represents the number of meters, M, swam to the number of laps, L is,

⇒ M - 25 = 25 (L - 1)

⇒ M - 25 = 25L - 25

⇒ M = 25L

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The molarity of acetic acid in the vinegar is 0.561 M and the mass percent of acetic acid in the vinegar is 33.6%.

In this problem, we are given the volume and concentration of the base (NaOH) used to titrate a sample of vinegar, and we need to find the molarity of acetic acid in the vinegar and the mass percent of acetic acid.

To start, we can use the balanced chemical equation for the reaction between acetic acid and NaOH to find the moles of NaOH used in the titration:

CH₃COOH + NaOH → CH₃COONa + H₂O

From the equation, we can see that the ratio of moles of acetic acid to moles of NaOH is 1:1. Therefore, the number of moles of NaOH used is the same as the number of moles of acetic acid in the original vinegar sample.

Molarity of acetic acid in the vinegar:

moles of NaOH = concentration of NaOH × volume of NaOH used

moles of acetic acid = moles of NaOH

molarity of acetic acid = moles of acetic acid / volume of vinegar sample

Substituting the given values, we get:

moles of NaOH = 0.231 M × 0.02430 L = 0.00561 moles

moles of acetic acid = 0.00561 moles

molarity of acetic acid = 0.00561 moles / 0.0100 L = 0.561 M

Mass percent of acetic acid in the vinegar:

mass of acetic acid = density × volume × molarity × molecular weight

mass percent = (mass of acetic acid / mass of vinegar sample) × 100%

Substituting the given values and the molecular weight of acetic acid (60.05 g/mol), we get:

mass of acetic acid = 1.01 g/mL × 0.0100 L × 0.561 mol/L × 60.05 g/mol = 3.39 g

mass percent = (3.39 g / (1.01 g/mL × 0.0100 L)) × 100% = 33.6%

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Answer:

63 more women than men.

Step-by-step explanation:

Let's start by finding out how many women and men on average buy tickets per day:

For women: (356 tickets) / (3 days) = 118.67 tickets per day

For men: (329 tickets) / (3 days) = 109.67 tickets per day

So on average, 9 more women than men buy tickets per day.

To find out how many more women than men will buy tickets during the first 7 days, we need to multiply the difference per day by the number of days:

9 (more women per day) x 7 (days) = 63

Since the circle is divided into 12 equal sections by radii, the measure of any one of the 12 equal central angles would be:

360 degrees (total angle measure of a circle) ÷ 12 (number of sections) = 30 degrees

Therefore, any one of the 12 equal central angles would have a measure of 30 degrees.

The perimeter of the tiles is 53 inches.

The perimeter of the two dimensional figure is the sum of the whole sides of the figure,

Therefore, let's find the base of the other triangle and the height of the other as follows:

using trigonometric ratios,

cos 35  = adjacent / hypotenuse

cos 35 = x / 12

cross multiply

x = 12 cos 35

x = 9.82982453147 inches

sin 35 = opposite / hypotenuse

sin 35° = y / 12

cross multiply

y = 12 sin 35

y = 6.88291723621

Therefore, lets use Pythagoras's theorem to find the height of the other triangle.

9 + 6.88 = 15.88

Therefore,

15.88² - 8² = h²

252.267059932 - 64 = h²

h = √188.267059932

h = 13.7210422345

Therefore,

perimeter of the figure = 8 + 9 + 13.72 + 12 + 9.83

perimeter of the figure = 52.55

perimeter of the tiles = 53 inches

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Statement b) 'The spread of the data is the same for both towns' and c) 'The interquartile range is less for Town A than Town B' are true.

a) The median is greater for town A:

To find the median, we need to arrange the data in order:

Town A: 0, 0, 0, 1, 2, 2, 3, 4, 5, 10

Town B: 2, 2, 4, 4, 5, 6, 8, 9, 12

The median for town A is 2 and the median for town B is 5. Therefore, statement (a) is false.

b) The spread of the data is the same for both towns:

To compare the spread of the data, we can look at the range, which is the difference between the largest and smallest values.

Town A: Range = 10 - 0 = 10

Town B: Range = 12 - 2 = 10

Both towns have the same range, so statement (b) is true.

c) The interquartile range is less for Town A than Town B:

The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). To find the quartiles, we need to arrange the data in order:

Town A: 0, 0, 0, 1, 2, 2, 3, 4, 5, 10

Q1 = 0.5, Q3 = 4

Town B: 2, 2, 4, 4, 5, 6, 8, 9, 12

Q1 = 2.5, Q3 = 9

The IQR for town A is 3.5 (4 - 0.5) and the IQR for town B is 6.5 (9 - 2.5). Therefore, statement (c) is true.

d) The modes are the best representation of the data for both towns:

The mode is the value that occurs most frequently in the data.

Town A: The mode is 0, which occurs three times.

Town B: There are two modes, 2 and 4, which each occur twice.

While the modes are a useful summary of the data, they may not be the best representation in this case since there are only ten data points for each town. Therefore, statement (d) is false.

e) The mean number of inches of snow per day was twice as much as in Town B as in Town A:

To compare the means, we need to calculate them for each town:

Town A: Mean = (2+0+5+4+2+10+1+3+0+0)/10 = 2.7

Town B: Mean = (4+4+9+8+12+2+2+2+6+5)/10 = 5.2

The mean for town B is approximately 1.9 times greater than the mean for town A, but not twice as much. Therefore, statement (e) is false.

Correct Question :

Two friends both claim that their towns received more snow during January. They picked ten random days in the month and listed the number of inches of snow that fell on those days in each of their towns.

Town A: 2, 0, 5, 4, 2, 10, 1, 3, 0, 0

Town B: 4, 4, 9, 8, 12, 2, 2, 2, 6, 5

Choose all true statements :-

a) The median is greater for town A

b) The spread of the data is the same for both towns

c) The interquartile range is less for Town A than Town B

d) The modes are the best representation of the data for both town

e) The mean number of inches of snow per day was twice as much as in Town B as in Town A

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3 + 6 + 1 + 4 or 2 + 3 + 4 + 5

Step-by-step explanation:

3 + 6 + 1 + 4 or 2 + 3 + 4 + 5

For two vectors u and v, the magnitude and direction of the sum of vectors, u +v, are equal to the 1.75 and 35.14°.

The formula to determine the magnitude of a vector (in two dimensional space) v = (x, y) is [tex]|v| =\sqrt {(x² + y²)}[/tex]. We have two vectors say v and u.

Magnitude of vector u = 5

direction of vector u = 265°

Magnitude of vector v = 8

direction of vector v = 105°

[tex]\vec u = ( 5cos(265°), 5sin(265°)) [/tex]

[tex]= (−0.436 , −4.981) [/tex]

[tex]\vec v = ( 8cos(105°), 8sin(105°)) [/tex]

[tex]= (−1.294 ,4.829 ) [/tex]

We have to determine the magnitude and direction of the sum, [tex] \vec u + \vec v[/tex]. Vector addition means putting two or more vectors together. Two vectors, a and b, can be added together using vector addition, and the resultant vector can be written as : a + b.

[tex] \vec u + \vec v = (-0.436 + (-1.294), -4.981 +4.829) [/tex]

[tex]= (- 1.730, -0.251) [/tex]

Now, the magnitude of the sum of two vectors is [tex]| \vec u + \vec v | = \sqrt{ {(u + v)_x}^{2} + {(u+v)_y}^{2} } [/tex]

[tex]= \sqrt{ 1.730² + 0.251²} [/tex]

[tex]= 1.74811355466 [/tex] ~ 1.75

Now, direction of vector which is sum of vectors : Let x be angle between componets of vector ( u + v) then direction is [tex]tan ( \theta) = \frac{-0.251}{-1.730} [/tex]

[tex]\theta = tan^{-1}(0.1451)[/tex]

= 35.14°

Hence, required value is 35.14°.

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The probability that he has exactly 7 hits in his next 7 at bats is  0.0106%.

To find the probability that a baseball player with a batting average of 0.31 gets exactly 7 hits in his next 7 at-bats, we can use the binomial distribution formula:

P(X=k) = (n choose k) * [tex]p^{k}[/tex] * [tex](1-p)^{n-k}[/tex]

where:

P(X=k) is the probability of getting k hits in 7 at-bats

n is the number of trials (in this case, 7 at-bats)

k is the number of successes (in this case, 7 hits)

p is the probability of success on a single trial (in this case, the batting average of 0.31)

(n choose k) is the binomial coefficient, which represents the number of ways to choose k successes from n trials.

Using this formula, we can calculate the probability as follows:

P(X=7) = (7 choose 7) * [tex]0.31^{7}[/tex] * [tex](1-0.31)^{7-7}[/tex]

P(X=7) = 1 * [tex]0.31^{7}[/tex]* [tex]0.69^{0}[/tex]

P(X=7) = 0.000106288

Therefore, the probability that the baseball player with a batting average of 0.31 gets exactly 7 hits in his next 7 at-bats is approximately 0.000106 or 0.0106%.

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The probabilities are given as follows:

The Poisson distribution was used, as we have only the mean of the distribution, and the Poisson distribution was then approximated to the normal.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For the Poisson distribution, the standard deviation is the square root of the mean, hence the mean and the standard deviation for the normal distribution are given as follows:

[tex]\mu = 150, \sigma = \sqrt{150} = 12.15[/tex]

The probability of less than 100 customers per day, using continuity correction, is one subtracted by the p-value of Z when X = 99.5, hence:

Z = (99.5 - 150)/12.15

Z = -4.16

Z = -4.16 has a p-value of 0.

The probability of more than 185 customers is one subtracted by the p-value of Z when X = 184.5, hence:

Z = (184.5 - 150)/12.15

Z = 2.84

Z = 2.84 has a p-value of 0.9977.

Hence:

1 - 0.9977 = 0.0023 = 0.23%.

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Answer: x=25/3 or 8[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Since they are similar triangles the sides inc/dec by proportion

the longest sides of the triangle went from 48 to 16  which is 48/16=3

The larger triangle is 3 times bigger so each of the sides are 3 times bigger or you can look at it like the smaller triangle is 1/3 smaller than bigger.

so short side is 25 on bigger triangle and went down to x or 25/3=x

The baby's weight at birth is

The linear model's y-intercept (b) is required to ascertain the infant's birth weight.

We can determine the slope (m) of the line from given coordinates (1, 8) and (11, 12):

slope(m) = (y2 - y1)/(x2 - x1) = (12 - 8)/(11 - 1) = 0.4

To find the y-intercept, we then apply the previously computed slope with one point (1, 8):

y = mx + b

8 = 0.4(1) + b

b = 7.6

Therefore, it can be deduced that the baby weighed 7.6 pounds at its time of birth when x=0.

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Answer:

225°/360° = 5/8

Length of arc = (5/8)(2π)(1) = 5π/4 units, or about 3.927 units

The wellbeing of a community can be significantly harmed by poor service delivery. It may result in dangers to one's health and safety, a decline in quality of life, negative economic effects, and social unrest.

The quality of service that is rendered to the members of a community contributes to the level of development and self actualization of the members of the community.

As such, the community may suffer economically as a result of poor service delivery. Poor transportation infrastructure, for instance, can drive up the cost of goods and services, and bad water supply can have an impact on the local economy's agricultural and industry.

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Answer:  

a

Step-by-step explanation:

reflection acrossv y=-3

The percentage daily value for protein for a serving of miso soup is around 16%.

The percentage daily value will be calculated by the formula -

Percentage daily value = mass of protein in miso soup/ amount of daily requirement of protein × 100

Assuming the daily value of protein to be 50 gram based on the question. Keep the values in formula -

Percentage daily value = [tex] \frac{8}{50} \times 100[/tex]

Cancelling zero and performing multiplication and division

Percentage daily value is 16%.

Hence, the daily value of protein in miso soup is 16%.

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Answer:

The answer is

1)0.96 to 2d.p

2)0.28 to 2d.p

3)3.49 to 2d.p

Step-by-step explanation:

tan0=3/4

0=tan‐¹[3/4]

0=36.9°

0≈37°

1) sin2(0)

sin (2×37)=sin 74=0.96 to 2.dp

2)cos 2(37)

sin(2×37)=cos 74=0.28 to 2d.p

3) tan20

=tan(2×37)=tan74=3.49 to 2d.p

The area of the circle is 452.38 square inches.

An area in geometry is a measurement of how much space a two-dimensional form or surface takes up. Usually, it is expressed in square units like square meters or square feet.

The volume of space encircled by a circle's perimeter, or circumference, is its area.

The area of the circle is calculated by the formula,

Area = πr²

Here, r is the radius of the circle.

The given radius of the circle is 12 inches. The area of the circle is calculated as,

Area = πr²

Area = π x ( 12 )²

Area = 452.38 square inches

Therefore, the circle will have an area of 452.38 square inches.

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To determine which account would be a better investment for Phoebe, we need to calculate the future value of each account after one year and compare them.

Account A earns simple interest, which means that the interest is calculated only on the initial investment. After one year, the investment in Account A would be worth:

$10,000 + ($10,000 x 0.09) = $10,900

Account B earns interest that is compounded annually, which means that the interest is calculated on the initial investment plus any previously earned interest. After one year, the investment in Account B would be worth:

$10,000 x (1 + 0.09)^1 = $10,900

As we can see, both accounts would have the same value of $10,900 after one year. Therefore, the choice between the two accounts depends on Phoebe's investment goals and preferences.

If Phoebe wants a simple and straightforward investment that provides a guaranteed return, Account A would be the better choice.

If Phoebe is willing to take on some risk and wants the potential for higher returns, Account B would be the better choice as the compounding of interest can lead to a higher return over a longer period of time.

Answer: 336in^3

Step-by-step explanation: In order to find the volume of a trapezoidal prism, you'll need to go by the formula of 1/2 (base 1 + base 2) x height x length.

In this case, you'll need to do 1/2 ( 10 + 4) x 6 x 8 and you should receive the answer of 336.

Answer:

0.25

Step-by-step explanation:

Concept testing is the test done before product launch, clients try a sample product and are then surveyed about whether they would buy the product again. So, option D is correct.

In concept testing, the companies will give newly launched products or new ideas or prototype products to the potential customers, to take reactions from them. This feedback is collected and assisted and analyze the feedbacks in order to improve their products sale.

The main aim of this concept testing is to collect information, patron needs, and assertions and can take powerful good decisions. This can gauge the market price and sale of the products through advertising.

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The complete question is:

type of test before product launch, customers try a sample product and are then surveyed about whether they would buy/use the product again. this process is known as:

a. premarket testing

b. alpha testing

c. prelaunch testing

d. concept testing

e. market testing.

95% confidence that the sample mean for the bio/total carbon ratio of blended fuels will fall within the interval is 0.9390 ± 0.002696, which is (0.9364, 0.9416).

We can use the formula for the margin of error for a 95% confidence interval for the population mean, given by:

the margin of error = 1.96 × standard deviation / √(sample size)

where the standard deviation of the sampling distribution of the sample mean is given by:

standard deviation = population standard deviation / sqrt(sample size)

Substituting the given values, we have:

standard deviation = 0.0080 / √(34) = 0.001375

margin of error = 1.96 × 0.001375 = 0.002696

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The question is -

Concerns about climate change and CO2 reduction have initiated the commercial production of blends of biodiesel (e.g., from renewable sources) and petrodiesel (from fossil fuel). Random samples of 34 blended fuels are tested in a lab to ascertain the bio/total carbon ratio.

If the true mean is .9390 with a standard deviation of .0080, within what interval will 95 percent of the sample mean to fall? (Round your answers to 4 decimal places.)