Find the derivative of the following, using differentiation from first principles. f(x) = 2x²-1/x​

The Iength οf the diagοnaI οf the square exteriοr waII shοuId be 15 feet.

Accοrding tο the Pythagοrean theοrem, the square οf a right triangIe's hypοtenuse (the side οppοsite the right angIe) equaIs the sum οf its οther twο sides' squares.

Outside waII's Iength and width are equaI if it is a square. Let's caII this Iength "x"

Using the Pythagοrean theοrem, we can find the Iength οf the diagοnaI οf the square:

diagοnaI² = height² + width²

Since the height is 9 ft and οne side οf the square is 12 ft, we can write:

diagοnaI² = 9² + 12²

diagοnaI² = 81 + 144

diagοnaI² = 225

Taking the square rοοt οf bοth sides, we get:

diagοnaI = √(225)

diagοnaI = 15 ft

Therefοre, the Iength οf the diagοnaI οf the square exteriοr waII shοuId be 15 feet.

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The probability that the mean weight for 100 boys in the 5th grade will be between 60 and 70 pounds is approximately 0.674.

According to the central limit theorem, a statistical theory, regardless of the population distribution's form, the distribution of sample means tends to resemble a normal distribution as sample size grows. This implies that the distribution of the sample means will be about normal if we take several random samples from a population.

Given that, mean weight for 100 boys in the 5th grade will be between 60 and 70 pound.

The z-score is given as:

z = (x - μ) / (s / √(n))

Substituting the values:

z = (70 - 64.9) / (17.5 / √(100)) = 1.143 = 0.674

z = (60 - 64.9) / (17.5 / √(100)) = -1.143 =0.674

Hence, the probability that the mean weight for 100 boys in the 5th grade will be between 60 and 70 pounds is approximately 0.674.

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Answer:

i have solved it step by step

Answer:

C)  2, 7, 6 can form a triangle.

Step-by-step explanation:

The triangle inequality theorem states that the sum of any two sides of a triangle is greater than the length of the third side.

To determine which group of given side measures will form a triangle, sum each pair of sides and compare to the third side. If all three inequalities are true, the group will form a triangle.

Given side lengths: 9, 4, 3

  ⇒ 9 + 4 > 3

  ⇒ 9 + 3 > 4

  ⇒ 4 + 3 [tex]\ngtr[/tex] 9

Therefore, this group cannot form a triangle.

Given side lengths: 8, 1, 7

  ⇒ 8 + 1 > 7

  ⇒ 8 + 7 > 1

  ⇒ 1 + 7 [tex]\ngtr[/tex] 8

Therefore, this group cannot form a triangle.

Given side lengths: 2, 7, 6

  ⇒ 2 + 7 > 6

  ⇒ 2 + 6 > 7

  ⇒ 7 + 6 > 2

Therefore, this group can form a triangle.

Given side lengths: 12, 10, 22

  ⇒ 12 + 10  [tex]\ngtr[/tex] 22

  ⇒ 12 + 22 > 10

  ⇒ 10 + 22 > 12

Therefore, this group cannot form a triangle.

The value of x in the figure such that Ray YU is an angle bisector is 18 degrees

Given

The figure

Such that Ray YU is an angle bisector

An angle bisector is a line or a ray that divides an angle into two equal parts or halves.

In other words, an angle bisector divides an angle into two smaller angles with equal measures.

The point where the angle bisector intersects the opposite side is the angle bisector point

This means that

2x = 36

So, we have

x = 18

Hence, the value of x in the figure is 18

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Answer:

D. A triangle with sides measuring 5 inches, 7 inches, and 9 inches. This is because the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In option A, the side lengths satisfy this condition since 50 + 35 > 25. In option B, the side lengths do not satisfy this condition since 5 + 10 < 15. In option C, the side lengths satisfy this condition since 8 + 12 > 85. In option D, the side lengths do not satisfy this condition since 5 + 7 < 9, 7 + 9 > 5, and 5 + 9 > 7.

Statement B is true: The population will increase by 9%.

Various Functions:

A single function (Injective function) Many – one function. From onto function (Surjective Function) Function is into. polynomial operation.

P(t)=18,751(1.09)t is the population function, where t is the time in years.

The function's growth factor or multiplier, which is bigger than 1, is represented by the expression (1.09t). In other words, the population is growing over time.

Finding the difference between the final and starting values, dividing by the initial value, and then multiplying by 100% will give us the percentage growth in the population.

Let's contrast the population at t=0 and t=1 to see how they differ:

P(0) = 18,751(1.09)^0 = 18,751

P(1) = 18,751(1.09)^1 = 20,436.59

In the last year, the population has grown from 18,751 to 20,436.59.

The population has grown by the following amount:

[(20,436.59 - 18,751)/18,751] × 100% ≈ 9.0%

Thus, the population will grow by 9%, as stated in statement B.

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The formula for the future value of an annuity is FV = Pmt * (((1 + r)n - 1) / r) to calculate the balance of the IRA at age 65. To compare this amount to the total deposits made over the time period, Total Deposits = Pmt * n = $45,600.

To calculate the balance of the IRA at age 65, we need to use the formula for the future value of an annuity:

FV = Pmt * (([tex](1 + r)^n[/tex] - 1) / r)

Where:

Pmt = $95 (the monthly deposit amount)

r = 4% / 12 = 0.003333 (the monthly interest rate)

n = (65 - 25) * 12 = 480 (the total number of months, assuming retirement at age 65)

Plugging in these values, we get:

FV = 95 * (([tex](1 + 0.003333)^480[/tex] - 1) / 0.003333)

FV = $98,052.52

Therefore, the IRA will contain $98,052.52 at age 65.

Part 2

To compare this amount to the total deposits made over the time period, we can calculate the total deposits as:

Total Deposits = Pmt * n

Plugging in the values, we get:

Total Deposits = 95 * 480

Total Deposits = $45,600

Therefore, the IRA will contain significantly more than the total deposits made over the time period, due to the power of compounding interest.

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The equation given is A(t) = 10,250(1 + r 0.04/12)^120. To solve for the value of the account, we need to calculate the right side of the equation. First, we need to calculate the exponent of 1+r 0.04/12. This is equal to 120, so the exponent is 120. Next, we need to multiply 10,250 by the exponent of 1+r 0.04/12. This will give us the value of the account. The answer is 1,895,167.50.

The correct answer is true

Answer:

True hope this helps!

We can be 90% confident that the true proportion of all students who saw a film at the movie theater in the last 30 days is between 0.277 and 0.473.

What is proportion?

Proportion is a mathematical term that represents a relationship between two quantities or numbers. It refers to the comparison of one part of a whole to the whole itself.

To find a confidence interval for the proportion p of all students who saw a film at the movie theater, we can use the formula:

CI = p ± z * √(p(1-p)/n)

where p is the sample proportion, n is the sample size, z is the z-score corresponding to the desired level of confidence (90% in this case), and √(p(1-p)/n) is the standard error of the proportion.

First, we need to find the sample proportion p:

p = 37.5% = 0.375

Next, we need to find the z-score corresponding to a 90% confidence level. We can use a z-table or a calculator to find this value. The z-score for a 90% confidence level is 1.645.

Now we can plug in the values into the formula:

CI = 0.375 ± 1.645*√(0.375(1-0.375)/64)

Simplifying:

CI = 0.375 ± 0.098

Therefore, the 90% confidence interval for the proportion of all students who saw a film at the movie theater in the last 30 days is:

CI = (0.277, 0.473)

Hence, we can be 90% confident that the true proportion of all students who saw a film at the movie theater in the last 30 days is between 0.277 and 0.473.

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Parabola intersects x-axis at two points: (-5,0) and (-4,0)

What does a parabola actually mean?

Each point on a parabola with a U-shape is equally spaced from both the focus, a fixed point, and the directrix, a fixed line. As the topic of conic sections depends heavily on the parabola, all of the parabola-related concepts are covered here.

The x-intercepts of a parabola are where the parabola intersects the x-axis on its graph. There are a number of ways to find the x-intercepts of a parabola, and each one is usually specific to each situation.

In the case, when you are given the graph, the easiest way to find x-intercepts is to identify points at which parabola intersects the x-axis.

From your graph, parabola intersects x-axis at two points: (-5,0) and (-4,0)

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Answer:

8x - 58 ≤ 500

8x ≤ 500 + 58

8x ≤ 558

x ≤ 69.74

Answer:

Step-by-step explanation:

The surface area of a sphere is given by the formula:

S = 4πr^2

where S is the surface area and r is the radius of the sphere.

We are given that the surface area of the sphere is 60 square feet. Using the formula above, we can solve for the radius:

60 = 4πr^2

Dividing both sides by 4π, we get:

15/π = r^2

Taking the square root of both sides, we get:

r = sqrt(15/π)

Using 3.14 as an approximation for π, we can evaluate this expression:

r ≈ sqrt(15/3.14)

r ≈ 2.20

Therefore, the best approximation for the radius of the sphere is 2.20 feet.

Answer:

Radius is 2.18

Step-by-step explanation:

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Answer: James' age now is 12 years old.

Answer:2

Step-by-step explanation:Because the 2 is closest to the middle line

Answer:

relationship describes angles 1 and 2 is supplementary angles. From the given figure

it is concluded that

the relation ship between angle 1 and 2 is supplementary angles

because its is  linear pair

and forms a line

therefore , the angles are supplementary angles

hence , relationship describes angles 1 and 2 is supplementary angle

Step-by-step explanation: Hope this helps !! Mark me brainliest!! :))

4 number was not used in the statement. we can use -3 as the other value.

A simple statement is a single assertion that can be classified as true or false, while a compound statement is formed by combining two or more simple statements using logical operators such as "and", "or", and "not".

To explain the statement mathematically:

First, we evaluate N/N:

N/N = 1

Next, we simplify the inequality using this value:

1•N < N - 1 < N - N

Simplifying further, we get:

N < N - 1 < 0

We can then substitute the values of -4 to 4 for N and see which value(s) satisfy the inequality.

If N = -4, then we have:

-4 < -5 < 0

This is true, so we can use -4 as one of the values.

If N = -3, then we have:

-3 < -4 < 0

This is also true, so we can use -3 as the other value.

Therefore, the completed statement is:

-4/-4 • -4 < -4 - (-4/-4) < -4 + 4/-4 <br>

which simplifies to:

1 < -3 < 5/2

Note that one number, 4, was not used in the statement.

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Answer:7

Step-by-step explanation:

6.7 to the 10 is 7

Answer:

Step-by-step explanation:

To simplify the expression, we can use the distributive property of multiplication:

(x−3)(2x^2 −5x−5) = 2x^3 −5x^2 −5x −6x^2 +15x +15

Next, we can combine like terms:

2x^3 −5x^2 −6x^2 −5x +15x +15 = 2x^3 −11x^2 +10x +15

Therefore, the simplified polynomial in standard form is 2x^3 −11x^2 +10x +15.

1) the correct check register balance is $166.90.

2)
a) After 3 months, balance = $510.08

b) after 6 months, balance, = $520.40

c) After 9 months , balance = $531.07

d) After 1 year, balance = $542.50

3)
the interest earned in year 1 is $80,

the total balance at the end of year 1 is $1080,

the interest earned in year 2 is $86.40,

the total balance at the end of year 2 is $1166.40, and t

he interest earned in year 3 is $93.31, and

the total balance at the end of year 3 is $1259.71.

4)
the interest earned by the $100 savings account is $28, and the total balance at the end of 4 years is $128.
The interest earned by the $500 savings account is $120, and the total balance at the end of 3 years is $620.
The interest earned by the $300 savings account is $90, and the total balance at the end of 5 years is $390.

A check register balance is the amount of money in a bank account, as recorded by the account holder in their check register, after accounting for deposits, withdrawals, and fees.

1)

The check register balance is not correct. To find the correct balance, we need to adjust the statement ending balance for the outstanding deposits, subtract the outstanding check and service charge, and add any other transactions that may have been missed.

Adjusted balance for outstanding deposits: $41.27 + $27.70 + $12.30 + $102.43 = $183.70

Adjusted balance for outstanding deposits minus the outstanding check: $183.70 - $10.98 = $172.72

Adjusted balance for outstanding deposits minus the outstanding check minus the service charge: $172.72 - $5.82 = $166.90

Therefore, the correct check register balance is $166.90.

2)
To find the balance of the savings account after various time periods, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the balance after time t

P = the principal (initial deposit)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time period (in years)

For this problem, we have:

P = $500

r = 0.04

n = 4 (compounded quarterly)

t = 0.25 (3 months), 0.5 (6 months), 0.75 (9 months), 1 (1 year)

After 3 months:

A = $500(1 + 0.04/4)^(4*0.25) = $510.08

After 6 months:

A = $500(1 + 0.04/4)^(4*0.5) = $520.40

After 9 months:

A = $500(1 + 0.04/4)^(4*0.75) = $531.07

After 1 year:

A = $500(1 + 0.04/4)^(4*1) = $542.50

Therefore, the balance of the savings account after 3 months is $510.08, after 6 months is $520.40, after 9 months is $531.07, and after 1 year is $542.50.


3)
To find the interest earned and total balance at the end of each year, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the balance after time t

P = the principal (initial deposit)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time period (in years)

For this problem, we have:

P = $1000

r = 0.08

n = 1 (compounded annually)

t = 1 (year)

After year 1:

Interest earned = $1000 x 0.08 = $80

Total balance = $1000 + $80 = $1080

After year 2:

Interest earned = $1080 x 0.08 = $86.40

Total balance = $1080 + $86.40 = $1166.40

After year 3:

Interest earned = $1166.40 x 0.08 = $93.31

Total balance = $1166.40 + $93.31 = $1259.71

Therefore, the interest earned in year 1 is $80, the total balance at the end of year 1 is $1080, the interest earned in year 2 is $86.40, the total balance at the end of year 2 is $1166.40, and the interest earned in year 3 is $93.31, and the total balance at the end of year 3 is $1259.71.

4)

We can use the formula for compound interest to calculate the interest earned and total balance at the end of each year for each savings account:

$100 at 7% for 4 years:

P = $100, r = 0.07, n = 1 (compounded annually), t = 4

Interest earned = $100 x 0.07 x 4 = $28

Total balance = $100 + $28 = $128 after 4 years

$500 at 8% for 3 years:

P = $500, r = 0.08, n = 1 (compounded annually), t = 3

Interest earned = $500 x 0.08 x 3 = $120

Total balance = $500 + $120 = $620 after 3 years

$300 at 6% for 5 years:

P = $300, r = 0.06, n = 1 (compounded annually), t = 5

Interest earned = $300 x 0.06 x 5 = $90

Total balance = $300 + $90 = $390 after 5 years

Therefore, the interest earned by the $100 savings account is $28, and the total balance at the end of 4 years is $128.
The interest earned by the $500 savings account is $120, and the total balance at the end of 3 years is $620.
The interest earned by the $300 savings account is $90, and the total balance at the end of 5 years is $390.

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Answer: I'm not really sure what the question is but the volume is 224

Step-by-step explanation:

The answer to the crossnumber is 25.

Number is a mathematical object used to count, measure, and label. It is a fundamental concept in mathematics and is used to describe sets, groups, and other mathematical objects. Numbers are used to measure quantities, such as length, area, time, and weight. They are also used to represent relationships between objects, and to describe the properties of those objects. Numbers can be represented in various forms, such as integers, fractions, and decimals.

This can be determined by examining the clues and their corresponding digits. Across, the clue is "A square", so the digit in the corresponding cell must be a perfect square, in this case 1. The next clue is "An odd square", so the digit must be an odd perfect square, which is 3. Down, the first clue is "A square", so the digit must be a perfect square, which is 5. The last clue is "A square", so the digit must be a perfect square, which is 7. When all the digits are put together, the resulting two-digit number is 25.

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Answer:

9 minutes and 25 seconds to 9 in the evening in analogue time is represented as:

8:50:35 PM

Using a trigonometric relation, we can see that the values of x and y are:

y = 25.98

x = 15

Here we can see a right triangle, where we know the interior angles and the length of the hypotenuse.

To get the lengths of the legs, we can use trigonometric relations, like:

cos(a) =(adjacent cathetus)/hypotenuse.

For example, if we want to find y, then the angle at which this side is adjacent is the 30° one, now replacing the known values in the formula we will get:

cos(30°) = y/30

cos(30°)*30 = y = 25.98

And to get the value of x, we should use the 60°angle, so:

cos(60°) = x/30

30*cos(60°) = x =  15

These are the two lengths we wanted to get.

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Answer:Convert from English to metric.

a. 1 foot = 304.8 millimeters

b. 40 lb-ft = 54.24 Newton/meters

Convert from metric to English.

a. 30 lb = 13.61 kilograms

b. 90.8 qt = 96.25 liters

26 m = 26,000,000 µm (micrometer)

60,000 cm = 600 m

8.275 L = 0.008275 kL

0.00349 km = 349 cm

Name the metric system unit that measures each of the following:

a. Light intensity - Candela

b. Mass - Gram

c. Pressure - Pascal

d. Electric current - Ampere

e. Distance - Meter

1,200 Ω = 1.2 kΩ (kilohm)

120 kΩ = 120,000 Ω (ohm)

3,500,000 Ω = 3.5 MΩ

6.03 MΩ = 6,030,000 Ω

0.000355 A = 355 µA (microampere)

0.000355 A = 0.355 mA (milliampere)

863 mV = 0.863 V (volt)

657 Ω = 0.657 kΩ (kilohm)

35 µA = 0.000035 A (ampere)

2.2 kΩ = 2200 Ω

500 kV = 500,000 MV (megavolt)

7,500,000 µA = 7.5 A (ampere)

What’s 30 percent of 150? = 45

What’s 25 percent of 2,300? = 575

Historically, the _______ was used as the basis for all measurements. = Human body

The number below the line in a fraction indicating the number of equal parts into which the unit is divided is the _______. = Denominator

In the English system, _______ is the traditional unit of pressure. = PSI (pounds per square inch)

The metric system is based on powers of _______. = 10

What unit is used for time in the metric system? = Second

20°C equals _______°F. = 68°F

45°F equals _______°C. = 7.2°C

The basic volume unit in the English measuring system is the _______. = Gallon

One ounce equals approximately _______ grams. = 28.35 grams

Answer:

20.8

Step-by-step explanation:

Let h be the height of the ladder. We know that the distance BC is 8 ft, and the angle of elevation BAC is 69 degrees. Therefore, we have:

tan(69) = h/8

Multiplying both sides by 8, we get:

8*tan(69) = h

Using a calculator, we get:

h ≈ 20.8 ft

Therefore, the height of the top of the ladder from the ground is approximately 20.8 feet.

The statement which best describe the correct null and alternative hypotheses, the test statistic, and conclusion at a significance level of 0.05 is:

D. H₀: μ₁ = μ₂ H₁: μ₁ < μ₂.

test statistic, t = -1.5625.

conclusion: fail to reject the null hypothesis μ₁ = μ₂.

Based on the information provided, the appropriate null hypothesis and alternative hypothesis would be represented by the following mathematical expression:

H₀: μ₁ - μ₂ ≤ 0; μ₁ = μ₂

H₁: μ₁ - μ₂ < 0; μ₁ < μ₂.

For the critical value, we have:

Critical probability (p*) = 1 - α

Critical probability (p*) = 1 - 0.05

Critical probability (p*) = 0.9500.

Based on the distribution table for probabilities, a value that corresponds to 0.9500 can be calculated as follows;

Zα = 1.6 + 0.05 = 1.65.

For an upper-tailed test, the critical value is given by;

Z_{critical} = 1.65.

Therefore, if Z_{test} > 1.65; reject null hypothesis (H₀) and if Z_{test} < 1.65; fail to reject null hypothesis (H₀).

Next, we would determine the test statistic:

[tex]Z_{test} = \frac{116 -121 -0}{\sqrt{\frac{16^2}{50} +\frac{16^2}{50} } } \\\\Z_{test} = \frac{-5}{\sqrt{\frac{256}{50} +\frac{256}{50} } }\\\\Z_{test} = \frac{-5}{\sqrt{10.24} }[/tex]

Z_{test} = -5/3.2

Z_{test} = -1.5625

In conclusion, we would fail to reject null hypothesis (H₀) since a Z_{test} of -1.5625 is less than a Z_{critical} of 1.65.

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23/200

Hope it helped

In the above proportions problem, note that the distance of PR is 155.17ft.

To solve for PR, note that

OC/RE = PR/OR

That is:

225/145 = PR/100

To solve for PR, we can cross-multiply the fractions:

225 * 100 = 145 * PR

22,500 = 145PR

Dividing both sides by 145:

PR = 155.17

Therefore, PR is approximately 155.17ft

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