Work out the urface area of thi olid quarter-cylinder. Give your anwer in term of π

The rate is the water level decreasing when the radius of the water's surface is r = 2cm is 0.08 cm/sec or dh/dt = - 0.08 cm/sec.

We have given that,

Water is dripping from an inverted cone.

height , h = 12 cm

diameter , d = 12 cm

so, radius, r = 6 cm

rate , dV/dt = - 1 cm³/sec

At any point, the portion of the cone that is filled will have the ratio of radius/height = 6/12 = 1/2. Put another way, h = 2r.

we have to calculate the rate is the water level decreasing , dh/dt when radius of the water's surface is r = 2 cm .

Volume of cone , V = 1/3 π (r)²h = 1/3π (h/2)²h

plugging all known values,

V = 1/3 ( h³/4)π

differentiating with respect to h we get,

dV/dh = 1/3(3h²)π/4 , h = 12

= 1/12(3× 4r²)π ( from r = 2 cm)

= 4π cm²

but we have required, dh/dt = dV/dt × dh/dV

= - 1 cm³/sec × 1/4π cm²

= - 1/4π cm/sec

= - 0.0792 ~ 0.08 cm/sec

Hence, the required value is - 0.08 cm/sec.

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Complete question:

Water is dripping from an inverted cone with a diameter of 12 cm and a height of 12 cm at a rate of 1 cm3 /sec. At what rate is the water level decreasing when the radius of the water's surface is r = 2 cm?"

Both conditions must be met in order to ride: being at least five years old and being at least 36 inches tall. expression evaluates to true if a person can ride - (Age >= 5) && (Height > 36)

In order for a person to ride, two conditions must be true: they must be at least 5 years old and taller than 36 inches. In order to evaluate whether a person can ride, we can use the expression (Age >= 5) && (Height > 36). This expression evaluates to true if both conditions are true; if either one is false, then the expression will evaluate to false. For example, if a person is 4 years old and 40 inches tall, then the expression will evaluate to false because the first condition is false. On the other hand, if a person is 5 years old and 40 inches tall, then the expression will evaluate to true because both conditions are true.

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The probability that they all have different birthdays is 0.903 or 90.3%.

1. Calculate the number of days in a year.

There are 365 days in a year.

2. Calculate the number of possible combinations for 3 people.

There are 365 x 365 x 365 = 4,738,625 possible combinations for 3 people.

3. Calculate the number of combinations where all 3 people have different birthdays.

There are 365 x 364 x 363 = 4,324,320 combinations where all 3 people have different birthdays.

4. Calculate the probability.

The probability that they all have different birthdays is 4,324,320 / 4,738,625 = 0.903 or 90.3%.

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y=x/2 is equation for a tangent to the graph of y=arcsin(x/2) at the origin.

In order to fing the equation of tangent of any graph we need 2 things

 i . A point on the graph

 ii . Slope a line on that point

Given y=[tex]sin^-^1(\frac{x}{2} )[/tex]

put x=0

y = [tex]sin^-^1[/tex] (0)

=> y =0

so the graph passes through point (0,0)

now we have to find slope of the graph

slope = [tex]y^'[/tex] = [tex]\frac{d(y)}{dx}[/tex]

=> [tex]\frac{1}{\sqrt{4-x^2} }[/tex]

slope of line at point (0,0) is 1/2

so equation of line is y-0=1/2(x-0)

so the equation of tangent to the given graph is y=x/2

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Answer: -25y/216x

Step-by-step explanation: - 25y / 216x

Answer:

(-30x^2/y^2)^5

Step-by-step explanation:

First, we can simplify the exponent in the first term by using the property that (a^m)^n = a^(m⋅n). This property tells us that we can calculate the exponent of the first term by multiplying the exponent of the base by the exponent of the power, which gives us (-3)⋅(-3) = 9. This means that the first term can be rewritten as (2x ⋅ -3/y)^9.

Next, we can simplify the second term by calculating its exponent in the same way, which gives us (-2)⋅(2) = -4. This means that the second term can be rewritten as (-5x/y)^-4.

We can then combine the two terms by using the property that (a^m)⋅(b^n) = (a⋅b)^(m+n). This property tells us that we can calculate the exponent of the combined terms by adding the exponents of the individual terms, which gives us 9 + (-4) = 5. This means that the entire expression can be rewritten as (2x ⋅ -3/y)^9 ⋅ (-5x/y)^-4 = (2x⋅-3/y⋅-5x/y)^5.

Finally, we can simplify the base of the combined terms by multiplying the factors together, which gives us (2x⋅-3/y⋅-5x/y) = -30x^2/y^2. This means that the entire expression can be rewritten as (-30x^2/y^2)^5.

Answer:

b = - [tex]\frac{a}{a-1}[/tex]

Step-by-step explanation:

a = [tex]\frac{b}{1+b}[/tex] ( multiply both sides by 1 + b to clear the fraction )

a(1 + b) = b ← distribute parenthesis on left side

a + ab = b ( subtract b from both sides )

a + ab - b = 0 ( subtract a from both sides )

ab - b = - a ← factor out b from each term on left side

b(a - 1) = - a ( divide both sides by a - 1 )

b = - [tex]\frac{a}{a-1}[/tex]

To establish the given identity, we need to first multiply the left side of the equation and write it as the difference of two squares. This can be done by using the difference of squares formula, which states that the difference of two squares can be written as the product of the square of the sum and the square of the difference.

The left side of the given equation can be written as:

(csc0+1)(csc0-1)

We can then apply the difference of squares formula to this expression to get:

(csc0+1)(csc0-1) = (csc0+1)(csc0-1)

Now, we can see that this expression is equivalent to cot 0 using the Pythagorean Identity. This identity states that the sum of the squares of the cosecant and cotangent of an angle is equal to 1. In this case, since (csc0+1)(csc0-1) = cot 0, we can use the Pythagorean Identity to rewrite the left side of the equation as (csc0^2 + cot0^2) = 1, which is equivalent to cot 0.

Therefore, the given identity is established using the Pythagorean Identity. This means that the correct answer is C. Pythagorean Identity.

The correct option for given situation is,

⇒ To demonstrate your professionalism, you should arrive for the appointment ''Right on time''.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

You have a meeting with a potential client for your printing business.

And, To demonstrate your professionalism, you should arrive for the appointment.

Now, We know that;

The rule of business is,

To demonstrate your professionalism, you should arrive for the appointment on the right time.

Therefore, The correct option for given situation is,

⇒ Right on time

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Answer:

7 hours

every hour she makes $21

Step-by-step explanation:

378÷18=21

147÷21=7

7 hours

378÷18=21$/h in ONE hour Salma makes 21$ so you have to do 147÷21=7h

Answer:

B) If I do not make the team, then I do not get a uniform.

Step-by-step explanation:

The contrapositive of a conditional statement is formed by negating both the antecedent and the consequent of the statement and then swapping their order. In the case of the statement "If I do not get a uniform, then I do not make the team," the contrapositive is "If I do not make the team, then I do not get a uniform."

Answer:

Functions

Step-by-step explanation:

ok so you gotta substitute x into the original then expand simplify collect like terms then your done

Answer:

10

Step-by-step explanation:

[tex]x + 5 = 15 \\ x + 5 - 5 = 15 - 5 \\ x = 10 [/tex]

The number of remaining green and yellow pins is 14 pins and 21 pins.

A proportion is a mathematical calculation that compares two numbers. According to proportion, two sets of given numbers are said to be directly proportional to one another if they increase or decrease in the same ratio.

The fraction of green pins present in the bag is 3/7. Then, the fraction of yellow pins present in the bag is 4/7.

When Yaqub picks up the green pin and gives it to his sister, the new fraction of green and yellow pins are 2/5 and 3/5.

Let x be the number of pins remaining in the bag after 1 pin less. This is written as,

[tex]\begin{aligned}\frac{3}{7}x-1 &= \frac{2}{5}x\\\frac{3}{7}x-\frac{2}{5}x&=1\\x&=35\end{aligned}[/tex]

There are about 35 pins remaining in the bag.

Then, the number of green pins remaining is (2/5) × 35 = 14 pins.

The number of yellow pins remaining is (3/5) × 35 = 21 pins.

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As per the given confidence interval, the value of the mean is 1.96

The term confidence interval means a range of numbers constructed around a point estimate such as a sample mean or sample proportion.

Here we need to find at a 95% level of confidence we want to estimate the population mean for a quantitative variable that is normally distributed in the population there a 10 individuals in the random sample what is the value of mean.

While In the large-sample case, a 95% confidence interval estimate for the population mean is given by

=> x ± 1.96σ/√n.

Where the population standard deviation is denoted as σ, is unknown, And the the sample standard deviation is used to estimate σ in the confidence interval formula.

Here by the quantity 1.96σ/√n is often called the margin of error for the estimate.

Then the quantity σ/√n is the standard error, and 1.96 is the number of standard errors from the mean necessary to include 95% of the values in a normal distribution.

Therefore, the interpretation of a 95% confidence interval is that 95% of the intervals constructed in this manner will contain the population mean.

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Answer:1

Step-by-step explanation: 6x2= 12. 12/4=3. 3/3 is 1.

Answer:

1

Step-by-step explanation:

We can see only multiply and divide here so we go from left to right

6x2/4/3

= 12/4/3

= 3/3

= 1

Answer:

x = 0.5

Step-by-step explanation:

2 (x+1.25) = 3.5

Divide by 2 on both sides.

x + 1.25 = 1.75

Subtract 1.25 on both sides.

x = 0.5

Answer:

x = 0.5

Step-by-step explanation:

2(x+1.25) =3.5

Divide both sides by 2.

x+1.25 = 3.5/2

x + 1.25 = 1.75

Subtract 1.25 from both sides.

x = 0.5

Answer:

y = 2x + 7.

Step-by-step explanation:

An equation that passes through the point (-4,-1) and is parallel to the line y = 2x + 14 is of the form y = 2x + b, where b is the y-intercept of the line. Since the line passes through the point (-4,-1), we can use this point to solve for b:

-1 = 2 * (-4) + b

-1 = -8 + b

b = 7

Therefore, an equation that passes through (-4,-1) and is parallel to y = 2x + 14 is y = 2x + 7.

Answer:

y = 2x + 7

Step-by-step explanation:

parallel = same slope

y-(-1) = 2(x-(-4)

y+1 = 2(x+4)

y+1 = 2x + 8

y = 2x + 8 - 1

y = 2x + 7

Answer:

y= 4x + 0

Step-by-step explanation:

The perimeter y of a square with side length x can be described by the equation y = 4x + 0.

The perimeter of a square is equal to four times the length of one side. If the side length of a square is 1 centimeter, then the perimeter of the square is 4 centimeters. We can use this information to write an equation in point-slope form to describe the relationship between the side length of a square and its perimeter.

Point-slope form is a way of writing the equation of a line when we know the slope of the line and the coordinates of a point on the line. In this case, the slope of the line is 4, since the perimeter of a square is four times the length of one side. The coordinates of a point on the line are (1, 4), since the side length of a square is 1 centimeter and the perimeter of the square is 4 centimeters.

We can use this information to write the equation of the line in point-slope form. The equation of a line in point-slope form is given by the following equation:

y - y1 = m(x - x1)

where y is the y-coordinate of a point on the line, y1 is the y-coordinate of a known point on the line, m is the slope of the line, and x is the x-coordinate of a point on the line.

In this case, we can substitute the values we know into the equation above to get:

y - 4 = 4(x - 1)

This simplifies to:

y = 4x + 0

Therefore, the equation in point-slope form that describes the relationship between the side length x of a square and its perimeter y is y = 4x + 0.

This equation tells us that for any square, the perimeter is four times the side length plus zero. For example, if the side length of a square is 5 centimeters, then the perimeter is 4 x 5 + 0 = 20 centimeters. If the side length of a square is 10 centimeters, then the perimeter is 4 x 10 + 0 = 40 centimeters.

In summary, the perimeter y of a square with side length x can be described by the equation y = 4x + 0.

Answer:

19

Step-by-step explanation:

If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:

[tex]\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]

Given:

Therefore, if the heights of men are normally distributed:

[tex]\boxed{X \sim\text{N} \left(69.0, 2.8^2 \right)}[/tex]

where X is height in inches.

Given:

Find the probability that the heights of men is between 64 and 78 inches by calculating P(64 ≤ X ≤ 78).

Calculator input for "normal cumulative distribution function (cdf)":

⇒ P(64 ≤ X ≤ 78) = 0.9622733869...

To calculate how many men who want to enlist in the U.S. Marine Corps would not expect to meet the height requirements from a group of 500, multiply 500 by 1 less than the probability found above:

⇒ 500 × [1 - P(64 ≤ X ≤ 78)]

⇒ 500 × [1 - 0.9622733869...]

⇒ 500 × 0.03772661307...

⇒ 18.86330654...

Therefore, we would expect for 19 men to not meet the height requirements.

Answer:

The answer is 3 3/4

Step-by-step explanation:

2 7/4 = 15/4 = 3 3/4

Answer:

Below

Step-by-step explanation:

= sqt (45*10) = sqrt (450) = 15 sqrt 2

The expression √45 × √10 is simplified using the property of square roots to give an equivalent choice of 15√2

The product √45 × √10 can be simplified by using the property of square roots that states √(a × b) = √a × √b.

By application of this property, we have that:

√45 × √10 = √(45 × 10).

To simplify further, we find that 45 and 10 have a common factor of 5, and thus,

45 × 10 = 5 × (9 × 10)

45 × 10 = 5 × 90.

Now, we can rewrite √(45 × 10) as √(5 × 90).

Using the same property again, we obtain √5 × √90. Finally, we recognize that 90 can be factored into 9 × 10.

Thus;

√45 × √10 = √(2 × 9 × 25)

√45 × √10 = √2 × √225

√45 × √10 = √2 × 15

√45 × √10 = 15√2

Therefore, the expression√45 × √10 have an equivalent of 15√2

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Answer:

612.3 in.²

Step-by-step explanation:

Inner circle diameter = 34 in.

Inner circle radius = r = 17 in.

Outer circle diameter = 34 in. + 5 in. + 5 in. = 44 in.

Outer circle radius = R = 22 in.

The are of the ring is the area of the outer circle minus the area of the inner circle.

A = πR² - πr²

A = π(R² - r²)

A = 3.14[(22 in.)² - (17 in.)²]

A = 612.3 in.²

When jim cleaned out the fountain at the library, he found a total of 20 nickels and quarters , the collection of nickels and quarters totaled $2.60 then he find eight quarters.

Given that:

Let N be the number of nickels.

     Q be the number of quarters.

The value of one nickels N is 0.05N

The value of quarters Q = 0.25Q

Sum of total quarters is $ 2.60

  Total number of coins

N + Q = 20   , N = 20 - Q

0.05 N + 0.25 Q = 2.60

substitute n = 20 - Q , we get

0.05 (20 - Q) + 0.25 Q = 2.60

    1 - 0.05 Q + 0.25 Q = 2.60

                       1 + 0.2Q = 2.60

                           0.2 Q = 1.6

                                  Q = 1.6 / 0.2

                                  Q = 8

Therefore , Jim finds 8 quarters

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The graph has a horizontal intercept at (1, 0)

The line x = 0 (the y-axis) is a vertical asymptote; as x→0+,y→∞

The graph is decreasing if 0 < b < 1.

The domain of the function is x > 0, or (0, ∞)

The range of the function is all real numbers, or (−∞,∞)

What is function?

A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

The set of all positive real numbers serves as the function's domain. Assume that base 10 is written when no base is specified for the log. The equation y=logb(x+h)+k shifts the logarithmic function, y=logb(x), by k units vertically and h units horizontally. The graph would be moved upward if k>0.

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Answer:

0.65

Step-by-step explanation:

The probability that we would get tails is 0.35

so the probability we will get heads is

1 – 0.35 = 0.65

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True. the interpretation of the slope is different in a multiple linear regression model as compared to a simple linear regression model.

The slope and intercept of a line reveal the steepness of the line and the location in which it intersects an axis. The slope and intercept of the logistic relationship of the two variables can be utilized to get the average change rate. The ratio of a change in the variable y to the rise in the x component is known as the the line's slope.

Y = a + bX, where X seems to be the mediating variable and Y is the response variable, is the equation of a linear regression line. A is the intersection (the result of y for x = 0), and b is the line's slope.

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The number line to represent the given scenario is number line with close circle at point 12 and shaded to the right. The correct option is (D).

A number line is the pictorial representation of numbers on a graph. The reference point on the number line is known as origin and all the numbers right to the origin are taken as positive and those left to it are negative numbers.

The number of newspapers to be delivered is not less than 20.

Suppose the number of newspaper left at any time be x.

Then, the inequality for the given situation can be written as,

x ≥ 12

This implies all the whole numbers greater than and including 12 on the number line.

Hence, the solution can be represented as all numbers greater than and equal to 12.

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The observed value of student's t statistic rounded to the nearest hundredth is 1.72.

The stated data is-

Thus,

Degree of freedom = n -1

Df = 22-1

Df = 21

As, the significance level is 5% then test is right tailed.

So,

Alpha value = 0.05

Now,

For alpha value = 0.05 and degree of freedom = 21.

t- critical value = 1.721 (from the t-statiscts table).

Thus, the observed value of student's t statistic rounded to the nearest hundredth is 1.72.

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