write a function that returns the digital root of an integer n. [note: there is a shortcut, where the digital root is equal to n mod 9, but do not use that here.]

Part A: Calcitonin hormone is currently thought to decrease plasma calcium levels

Part B: PTH (parathyroid hormone) promotes the formation of Calcitriol hormone

Part C: Parathyroid hormone (PTH) directly acts on calcitriol, which is produced in the kidney and acts on the intestines

Let's dive deeper into the details below.

Part A: Calcitonin hormone is currently thought to decrease plasma calcium levels in pregnant women and children.

Part B: PTH (parathyroid hormone) promotes the formation of Calcitriol hormone, which helps to increase the amount of calcium absorbed in the small intestine.

Not only does it increase the amount of calcium reabsorbed in the kidneys, but it also stimulates osteoclasts to break down bone and free calcium into the bloodstream. Hence, there is no need for an increase in osteoblasts, which is the false statement.

Part C: Parathyroid hormone (PTH) directly acts on calcitriol, which is produced in the kidney and acts on the intestines, causing them to absorb more calcium from the diet.

Therefore, Calcitriol hormone works directly in the intestine to increase plasma calcium levels in the body.

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Answer:

its 9.33 reapetting or just 9.33

Step-by-step explanation:

Answer:

The answer is reflection on the y-axis

Step-by-step explanation:

Reflection on the x-axis will change the y-intercept

Horizontal shrink will change the slope but not to the point of making the 3 negative

Horizontal stretch is the same concept

Thus Reflection on the y-axis on the y-axisis the answer

Hope this helps!

The number of combinations of 6 boys and 20 girls that can exist among 26 children born in a hospital on a given day is 230,230.

]To calculate the number of combinations, we can use the concept of binomial coefficients. The formula for calculating the number of combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of objects and k is the number of objects we want to select.

In this case, we have 26 children in total, and we want to select 6 boys and 20 girls. Plugging these values into the formula, we get C(26, 6) = 26! / (6!(26-6)!) = 230,230. Therefore, there are 230,230 different combinations of 6 boys and 20 girls that can exist among the 26 children born in the hospital on that given day.

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Answer:

c = 5

Step-by-step explanation:

b^2 is a 4x4 square and so we know that the side of "b" is 4. a^2 is a 3x3 square so we know that side "a" is 3. Now, we can use the Pythagorean theory and do 4^2+3^2=c^2 and get c = 5. Or we could just count the squares and see that there are 5 squares on side "c".

Answer:

i think 18

Step-by-step explanation:

Answer:

y11_maths_foundation_mock_apr18_paper1_answers.pdf

Step-by-step explanation:

use it to get answer

Answer:

77π/15 or 16.13

Step-by-step explanation:

Arc length = 2πr (θ/360)

= 2π(14)(66/360)

= 77π/15 or 16.13

Answer:

16.12 inches

Step-by-step explanation:

To find the arc length of a circle, you can use the formula 2\(\pi\)r(θ/360)

θ is the central angle

Substitute Pi for 3.14

Substituting the numbers in the equation, we have 2 × 3.14 × 14 × \(\frac{66}{360}\)

Put this equation into a calculator and you will get 16.118667, which can be simplified to 16.12 inches.

Answer:

7.75

Step-by-step explanation:

By Geometric mean property:

\( GH = \sqrt {a \times b} \)

\( GH = \sqrt {3 \times 20} \)

\( GH = \sqrt {60} \)

\( GH = 7.74596669\)

\( GH \approx 7.75\)

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

Explanation:

There are 7 numbers in the set {1,2,...,6,7}. Then we add on 0 to get to the 8th number. So there are 8 numbers overall listed in bold above.

Since the sample space is {0,1,2,...,8,9}, we have 10 digits listed here. So the probability of success is 8/10 = 0.80 = 80%

Side note: The values 8 and 9 would represent a failure. We have 2 failures out of 10 so we get 2/10 = 0.20 = 20%

The groups of numbers could represent a success 80 percent is {0, 1, 2, 3, 4, 5, 6, 7}. Therefore, option C is the correct answer.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

Here, the sample space is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

To simulate an event that has a probability of success of 80%.

Now, 8/10 ×100

= 8×10

= 80%

Therefore, option C is the correct answer.

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The interval (461.7, 598.1) is estimating the parameter of expected lead content when traffic flow is 15, denoted as Lead Content|Traffic flow = 15. This interval represents the range of values where we can be 95% confident that the true population parameter lies, based on the sample data collected.

To calculate a 99% confidence interval for Lead Content|Traffic flow = 15, we would need to use the same sample data and formula as for the 95% confidence interval but using a higher level of significance. Assuming the underlying assumptions of normality, independence, and constant variance are met, a 99% confidence interval would be wider than the 95% interval. Therefore, we would expect the 99% confidence interval for Lead Content|Traffic flow = 15 to be (430.7, 629.1), which represents a larger range of values where we can be more confident that the true population parameter lies.

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The range of the exponential function y based on its equation and the context of the problem is a set of positive real numbers less than the initial value of 62,150, representing the decreasing value of the car over time.

The given function represents the depreciation of Morgan's car over time, where x represents the number of months since the car was purchased. The function is y = 62,150 * (0.9999)^x.

To determine the range of the exponential function y, we need to consider the context of the problem. In this case, the range represents the possible values for the car's depreciation, or the value of y.

The base of the exponential function is 0.9999, which is less than 1. When a value between 0 and 1 is raised to a positive power, it decreases exponentially as the power increases. Therefore, as x (the number of months) increases, the value of y (the car's depreciation) decreases.

Since the base is less than 1, the range of the exponential function y is also less than the initial value of 62,150. As x approaches infinity, the value of y approaches 0, but it will never actually reach 0.

In practical terms, the range of the exponential function represents the decreasing value of the car over time. It indicates that the car's depreciation is continuous and will approach zero but will never completely reach zero.

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Answer:

I got 9/20

Hope that helps!

A statement which best describe the transformation from Figure 1 to Figure 2 is: C. reflection over the y-axis.

In Mathematics, a reflection can be defined as a type of transformation which moves every point of the geometric figure by producing a flipped, but mirror image of the geometric figure.

In Geometry, a reflection over the y-axis (y = x) is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By applying a reflection over the y-axis to the coordinates of figure 1, the coordinates of figure 2 include the following:

(x, y)                               →              (-x, y)

Coordinate A = (-6, 5)   →  Coordinate A' = (-(-6), 5) = (6, 5).

Coordinate B = (-4, 5)   →  Coordinate B' = (-(-4), 5) = (4, 5).

Coordinate C = (-3, 5)   →  Coordinate C' = (-(-3), 5) = (3, 5).

Coordinate D = (-5, 4)   →  Coordinate D' = (-(-5), 4) = (5, 4).

Coordinate E = (-5, 3)   →  Coordinate E' = (-(-5), 3) = (5, 3).

Coordinate F = (-7, 3)   →  Coordinate F' = (-(-7), 3) = (7, 3).

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The point on the shore will be 3 km from the restaurant.

To minimize her total travel time, the woman should row the boat directly to the shore at a point that is 3 km away from the restaurant, making the distance between the point on the shore and the restaurant 3 km.

Let's denote the distance from the boat's starting point to the point on the shore as \($x$\) km. Since the woman rows at 5 km/h, the time it takes to row to the shore is \($\frac{x}{5}$\) hours. After reaching the shore, she walks to the restaurant at a speed of 5 km/h, which takes \($\frac{2-x}{5}$\) hours.

To minimize the total travel time, she needs to find the value of \($x$\) that minimizes the sum of the rowing and walking times. The total travel time is given by

\($T(x) = \frac{x}{5} + \frac{2-x}{5} = \frac{2}{5} + \frac{x}{5} - \frac{x}{5} = \frac{2}{5}$\) hours, which is a constant value.

Since the total travel time is constant and does not depend on the distance X on the shore, it means that the point on the shore can be anywhere along the shoreline.

However, to minimize the walking distance, the woman should row the boat directly to a point on the shore that is closest to the restaurant, which is 3 km away.

Therefore, the point on the shore will be 3 km from the restaurant.

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Answer:

the 3 is in the hundred thousands

Step-by-step explanation:

Answer:6

Step-by-step explanation: each corner is a start for each angle so if you count each corner you have 6=6 angles

The Maclaurin series for f(x) converges absolutely for x within the interval (-2/3, 2/3).

To find the Maclaurin series for the function f(x) = (3cos(x))ln(1+x), we can use the standard formulas for the Maclaurin series expansion of elementary functions.

First, let's find the derivatives of f(x) up to the third order:

f(x) = (3cos(x))ln(1+x)

f'(x) = -3sin(x)ln(1+x) + (3cos(x))/(1+x)

f''(x) = -3cos(x)ln(1+x) - (6sin(x))/(1+x) + (3sin(x))/(1+x)² - (3cos(x))/(1+x)²

f'''(x) = 3sin(x)ln(1+x) - (9cos(x))/(1+x) + (18sin(x))/(1+x)² - (12sin(x))/(1+x)³ + (12cos(x))/(1+x)² - (3cos(x))/(1+x)³

Next, we evaluate these derivatives at x = 0 to find the coefficients of the Maclaurin series:

f(0) = (3cos(0))ln(1+0) = 0

f'(0) = -3sin(0)ln(1+0) + (3cos(0))/(1+0) = 3

f''(0) = -3cos(0)ln(1+0) - (6sin(0))/(1+0) + (3sin(0))/(1+0)² - (3cos(0))/(1+0)² = -3

f'''(0) = 3sin(0)ln(1+0) - (9cos(0))/(1+0) + (18sin(0))/(1+0)² - (12sin(0))/(1+0)³ + (12cos(0))/(1+0)² - (3cos(0))/(1+0)³ = -9

Now we can write the first three nonzero terms of the Maclaurin series:

f(x) = f(0) + f'(0)x + (f''(0)/2!)x² + (f'''(0)/3!)x³ + ...

f(x) = 0 + 3x - (3/2)x² - (9/6)x³ + ...

Simplifying, we have:

f(x) = 3x - (3/2)x² - (3/2)x³ + ...

To determine the values of x for which the series converges absolutely, we need to find the interval of convergence. In this case, we can use the ratio test:

Let aₙ be the nth term of the series.

|r| = lim(n->infinity) |a_(n+1)/aₙ|

= lim(n->infinity) |(3/2)(xⁿ+1)/(xⁿ)|

= lim(n->infinity) |(3/2)x|

For the series to converge absolutely, we need |r| < 1:

|(3/2)x| < 1

|x| < 2/3

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Answer:

\(195\)

Step-by-step explanation:

Let \(a\) represent the number of math problems Matthew solved on Sunday. From the problem, we know he solved \(5a\) problems on Saturday.

Therefore, we have:

\(5a+a=234,\\6a=234,\\a=39\)

Substitute \(a=39\) into \(5a\):

\(5(39)=\boxed{195}\)

Answer:

The probability is 1/4

Step-by-step explanation:

In this question, we are interested in calculating the probability of obtaining even numbers which are less than 7, when two fair six-sided dice are rolled.

Now, mathematically the probability will be;

number of even numbers less than 7/total number of outcomes

Firstly, the total number of outcomes is 36. Now to get the number of even numbers less than 7, we need to construct tables that could show our sample space.

Please check attachment for this.

Now from the constructed table, we can find the number of even numbers less than 7.

By counting, we can see that the we have 9 even numbers which are less than 7

Thus, the probability of selecting an even number which is less than 7 is;

9/36 = 1/4

The area of the polygon is approximately 497.41 square centimeters.

A polygon is a two-dimensional geometric shape that is made up of straight lines connected end to end to form a closed shape. A polygon must have at least three sides, and each side must intersect with exactly two other sides.

The exterior angle of a regular polygon is equal to 360 degrees divided by the number of sides. So, if the exterior angle is 20 degrees, the number of sides can be found by dividing 360 by 20, which gives us 18.

Each interior angle of a regular polygon can be found using the formula:

Interior angle = (n - 2) x 180 / n

where n is the number of sides. For an 18-sided polygon, the interior angle is:

(18 - 2) x 180 / 18 = 160 degrees

Apothem = (Side length) / (2 x tan(π/n))

where n is the number of sides. Plugging in the values, we get:

Apothem = (6) / (2 x tan(π/18)) = 6 / (2 x 0.32492) ≈ 9.2367 cm

Finally, we can use the formula for the area of a regular polygon:

Area = (1/2) x Apothem x Perimeter

where Perimeter is just the side length multiplied by the number of sides. Plugging in the values, we get:

Perimeter = Side length x Number of sides = 6 x 18 = 108 cm

Area = (1/2) x 9.2367 x 108 ≈ 497.41 cm²

Therefore, the area of the polygon is approximately 497.41 square centimeters.

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Answer:

1221.2 factor increase

Step-by-step explanation:

It is difficult interpreting the numbers.  I'll assume:

2.25x10^2 and 2.75x10^5

----

225

275000

The difference(increase) is 274775, or 2.75 x 10^5 to 3 sig figs

There is a (2.75 x 10^5)/(2.25x10^2) or 1221.2 factor increase in bacteria between the two weeks.

Answer:

Puede ser Asi:

\( {10}^{6} = 1000000\)

Tambien puede ser:

\(1000000 \div 10 = 100000\)

he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

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Answer: ten dollars an hour that seems simple

Step-by-step explanation:

pls mark brainlist

Answer:

10.00

Step-by-step explanation:

Keep the first fraction the same

Change the division symbol into a multiplication symbol

Swap the numerator and the denominator of the second fraction

Example:

\(\frac{1}{2} \div \frac{1}{4}\) will turn into \(\frac{1}{2} \times \frac{4}{1}\) giving you an answer of \(\frac{4}{2}\) which is 2

- Kan Academy Advance

Answer

5

Explanation

Twenty divided by the difference of seven and three

In mathematical terms,

20 ÷ (7 - 3)

= 20 ÷ 4

= 5

Hope this Helps!!!