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To the nearest tenth, the quantity of the amount after \(7\) weeks is around \(1804.74\).

Quantity simply refers to how much or how many of anything there are. A quantity can also be an amount, a number, or a measurement. It responds to the "how much?" query. Numbers may also be used to understand quantities, such as this book has 55 pages, this container has 'x' quantities of black pens, etc.

Numbers can be used to express quantities, such as 55 pages or reading. Entire numbers, fractions, fractions, percentages, or units of measurement like space, money, length, or weight can all be used to express these values. Quantities may also be stated using uncommon units.

\(A_{0} = 3600\)

\(r = 0.01\) (since the rate of decay is \(1\)%)

\(t = 7\) weeks \(= 56\) days (since there are \(7\) days in a week)

We can first find the value of \(e^{-rt}\) as follows:

\(e^{-rt} = e^{-0.0187} = 0.5013\)

Substituting into the formula, we have:

\(A = 3600 * 0.5013 ≈ 1804.74\)

Therefore, the value of the quantity after \(7\) weeks, to the nearest hundredth, is approximately \(1804.74\).

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Hannah's debt-to-equity ratio when her liabilities was $30,000 (excluding her mortgage of $100,000 ) and her net worth is $45,000 is 0.75.

Debt-to-equity ratio is a financial ratio that measures the proportion of total liabilities to shareholders' equity. To calculate the debt-to-equity ratio for Hannah, we need to first calculate her total liabilities and shareholders' equity.

We are given that Hannah has liabilities of $30,000 excluding her mortgage of $100,000. Therefore, her total liabilities are $30,000 + $100,000 = $130,000.

We are also given that her net worth is $45,000. The net worth is calculated by subtracting the total liabilities from the total assets. Therefore, the shareholders' equity is $45,000 + $130,000 = $175,000.

Now we can calculate the debt-to-equity ratio by dividing the total liabilities by the shareholders' equity.

Debt-to-equity ratio = Total liabilities / Shareholders' equity = $130,000 / $175,000 = 0.74 (rounded to two decimal places)

Therefore, Hannah's debt-to-equity ratio is 0.74, which is closest to option 0.75.

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Answer:

The slope of a linear model can be calculated using the formula:

m = Δy / Δx

where:

Δy = change in y (the dependent variable, in this case, total cost)

Δx = change in x (the independent variable, in this case, number of candy bars)

This is essentially the "rise over run" concept from geometry, applied to data points on a graph.

In this case, we can take two points from the table (for instance, the first and last) and calculate the slope.

Let's take the first point (3 candy bars, $6.65) and the last point (25 candy bars, $48.45).

Δy = $48.45 - $6.65 = $41.8

Δx = 25 - 3 = 22

So the slope m would be:

m = Δy / Δx = $41.8 / 22 = $1.9 per candy bar

This suggests that the cost of each candy bar is $1.9 according to this linear model.

Please note that this assumes the relationship between the number of candy bars and the total cost is perfectly linear, which might not be the case in reality.

Answer:

0 ,1cyvkdcbdfiiihh7v6ctc6e5a5ise5aasusti

Answer:

Step-by-step explanation:

10% = 15.30

40%=61.20

1% = 1.53

2%=3.06

61.20+3.06=64.26

153+ 64.26=217.26

The given data is used to obtain the equation as y = x - 2 and the table and graph has been drawn clearly.

A straight line can be written in the slope-intercept form as, y = mx + c.

In order to obtain the slope, the ratio of the difference of the coordinates are taken and c is the y-intercept which can be found by substituting x = 0 in the equation.

The data is given as below,

slope = 1 and y-intercept = -2.

The equation, graph and table for the given data can be formed as follows,

(a) The slope-intercept equation is y = mx + c, where m is the slope and c is the y-intercept.

Substitute the corresponding values to obtain,

y = 1 × x + (-2)

  = x - 2

(b) The graph for the given equation is plotted below as,

(c) The table for the given equation can be formed with different values of x and y as below,

y = x - 2

Substitute x = 0 to get y = -2, x = 1, y = -1 and x = 2, y= 0.

Now, the table can be formed as below,

Hence, the equation is given as y = x - 2 and the graph and table for the equation is drawn properly.

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The measure of angle M in triangle KLM is approximately 47.3 degrees, to the nearest 10th of a degree.

Solving for nearest 10th of degree:

To find the measure of angle M in triangle KLM, we can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles. The Law of Cosines states that:

\(c^2 = a^2 + b^2 - 2ab cos(C)\)

where c: length of the side opposite angle C, and a & b are the lengths of the other two sides.

In this case, we wish to find the measure of angle M, which will be opposite the side of length m. We are aware that the lengths of the other two sides, k and l, and measure of angle L. To find l, we use the Law of Cosines:

\(l^2 = k^2 + m^2 - 2km cos(L)\)

Substituting:

\(l^2 = 8.3^2 + 5.2^2 - 2(8.3)(5.2) cos(162 degree)\)

Solve for the l, we get:

l = 10.038 cm

We will use Law of Cosines again to find the measure of angle M:

cos(M) = \((k^2 + l^2 - m^2) / (2kl)\)

Substituting:

cos(M) = \((\)\(8.3^2 + 10.038^2 - 5.2^2)\) \(/ (2(8.3)(10.038))\)

Simplifying:

cos(M) = 0.665

To get the measure of angle M, we take the inverse cosine:

M = 47.3°

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The height after the 18th month is 69 cm

The function definition is given as

H(m) = 51 + m

Where m represents the number of months

In this case;

m = 18

So, we have

H(18) = 51 + 18

Evaluate the sum

H(18) = 69

Hence, the height after the 18th month is 69 cm

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The value of given expression is :

\(3 - \sqrt{5} \)

Solution is in attachment ~

Answer:

Step-by-step explanation:

ion

Answer:

The circumcenter of a triangle is defined as the point where the perpendicular bisectors of the sides of that particular triangle intersect. In other words, the point of concurrency of the bisector of the sides of a triangle is called the circumcenter. It is denoted by P(X, Y). The circumcenter is also the centre of the circumcircle of that triangle and it can be either inside or outside the triangle.

Step-by-step explanation:

Steps to find the circumcenter of a triangle with vertices are:

Calculate the midpoint of given coordinates, i.e. midpoints of AB, AC, and BC

Calculate the slope of the particular line

By using the midpoint and the slope, find out the equation of the line (y-y1) = m (x-x1)

Find out the equation of the other line in a similar manner

Solve two bisector equations by finding out the intersection point

Calculated intersection point will be the circumcenter of the given triangle

Answer:i think it is 7/3

Step-by-step explanation:

ANSWER:

The attendance before the increase is 4714

STEP-BY-STEP EXPLANATION:

From the statement we can propose the following equation

solving for x:

The required equation of the circle whose endpoint of the diameter  (-2, -1) and (4,7) is  (x - 1)² + (y - 3)² = 25 ​. Option D is correct.

Given that,

The endpoints of the circle's diameter (-2, -1) and (4,7).
The equation of the circle is to be determined.

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r².

where h, k is the coordinate of the circle's center on the coordinate plane and r is the circle's radius.

Center of the circle(h, k) = (-2 + 4)/2 ,(-1+7)/2
                                  = 1  , 3
Radius of the circle,
\(r^2 =\sqrt{(1+2)^2+(3+1)^2}\\r^2 =\sqrt{9+16} \\r^2 = 25\)

Equation of the circle with center (1, 3)
\(r^2 = (x - 1)^2 + (y-3)^2\)
\(25 = (x - 1)^2 + (y-3)^2\)

Thus, the required equation of the circle whose endpoint of the diameter  (-2, -1) and (4,7) is  (x - 1)² + (y - 3)² = 25 ​. Option D is correct.

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The measure of arc BC is 720 times the measure of angle BAC.

Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).

To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:

AB * BC = AC * CE

16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)

Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:

Area = π * r^2

289 = π * r^2

r^2 = 289 / π

r = √(289 / π)

Now, we can substitute the known values into the equation for the product of the segments:

16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8

To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.

mBC = 0.5 * m(arc BC)

To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:

arc BC = (mBC / 0.5) * 360

arc BC = 720 * mBC

Therefore, the length of the arc BC equals 720 times the length of the angle BAC.

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Answer:

Step-by-step explanation:

From the figure

x+159=180°

(linear pair)

x=180-159

x=21°

hope it helps...

have a great day!!

Answer:

The answer is:

\(2480 {cm}^{2} \)

Answer:

0.111 hope that helps you

F(Y) = (1/2) [ 1 + erf(Y/(√2√n))] We can see that, as n → ∞, the above expression F(Y) approaches the distribution function of N(0,1) distribution which is given by, G(Y) = (1/2) [ 1 + erf(Y/(√2))]

Given a sequence of random variables {Xn} where Xn has N(0,1/n) distribution.

To determine if {Xn} have a limit in distribution and what is it, let us find the distribution function of the sequence.

Suppose F(x) be the distribution function of {Xn} and Y be any real number.

Then, we have,

F(Y) = P({Xn} ≤ Y)

Here,{Xn} ≤ Y

Xn ≤ Y for all n∈N

And we know that Xn has N(0,1/n) distribution, so we can write,

P({Xn} ≤ Y) = \(\int_{-\infty}^{Y}f_{X_n}(x) dx\)

where, \(f_{X_n}(x)\) is the probability density function of Xn which is given by

f_{X_n}(x) = (1/√(2π/n)) e^((-x^2)/(2/n))

Next, we integrate \(f_{X_n}(x)\) with limits -∞ and Y, we get,

\(\int_{-\infty}^{Y}f_{X_n}(x) dx\)

= \(\int_{-\infty}^{Y} (1/\sqrt2\pi/n)) e^{((-x^2)/(2/n))} dx\)

= (1/2) [ 1 + erf(Y/(√2√n))]

where, erf(z) = (2/√π) ∫_{0}^{z} e^(-t^2) dt is the error function.

Now, we have, F(Y) = (1/2) [ 1 + erf(Y/(√2√n))]We can see that, as n → ∞, the above expression F(Y) approaches the distribution function of N(0,1) distribution which is given by,G(Y) = (1/2) [ 1 + erf(Y/(√2))]

Thus, {Xn} has a limit in distribution and it is N(0,1) distribution.

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Answer:

so is actually bidmas of bodmas however you want to call it but what's in the brackets you always have to do first so what you would do is because as for subtraction comes last you 1st to -8+10 which is to then you do 2-5 which is -3 so then you do -7 times -3 which because if two minuses or times or multiplied like everyone say it would be a positive so that

It's the answer is 21

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

Answer:

m∠A = 60°

Step-by-step explanation:

Complementary Angles add up to 90°

Step 1: Set up equation

8x + 20 + 7x - 5 = 90

Step 2: Solve for x

15x + 15 = 90

15x = 75

x = 5

Step 3: Find m∠A

m∠A = 8x + 20

m∠A = 8(5) + 20

m∠A = 40 + 20

m∠A = 60°

Answer:

Step-by-step explanation:

\(c^{2}+b^{2} = (4+a)^2 \\c = \sqrt{6^2+4^2}\\ c = \sqrt{36+16}\\ c = \sqrt{52} \\c^2 = 52\\a^2 + 6^2 = b^2\\\\52 + a^2 + 36 = 16 + a^2 + 8a\\ 8a = 72\\a = 9\)

Please mark my answer as brainliest .

Answer:

5,2

Step-by-step explanation:

since you're moving down the y-axis you will subtract 4 from 6 because 6 is on the y-axis

5 stays the same since you're not moving on the x-axis

(5,2)

Answer:

The watered area is approximately 3783 square feet.

Step-by-step explanation:

The area that is watered due to the rotation of the spankler is a circular section area (\(A\)), whose formula is:

\(A = \frac{\theta }{2}\times \frac{1}{360^{\circ}}\times 2\pi \times d^{2}\)

Where:

\(d\) - Water distance, measured in feet.

\(\theta\) - Rotation angle, measured in sexagesimal degrees.

Given that \(d = 85\,ft\) and \(\theta = 60^{\circ}\), the watered area is:

\(A = \frac{60^{\circ}}{2} \times \frac{1}{360^{\circ}}\times 2\pi \times (85\,ft)^{2}\)

\(A \approx 3783\,ft^{2}\)

The watered area is approximately 3783 square feet.

Answer:176

Step-by-step explanation:

6 times 29.33333333333333

^answer:^

~10 cubic feet~

^step by step explanation:^

first, calculate the volume of the front “panel” of the shape. (5 cubic centimeters because 5 times 3 is 15 and 15 times 1/3 is 5. 5 times 2 is 10.

Given:

The function is

\(f(x)=-x^2+4\)

It defined on the interval -8 ≤ x ≤ 8.

To find:

The intervals on which the function is increasing and the interval on which decreasing.

Step-by-step explanation:

We have,

\(f(x)=-x^2+4\)

Differentiate with respect to x.

\(f'(x)=-(2x)+(0)\)

\(f'(x)=-2x\)

For turning point f'(x)=0.

\(-2x=0\)

\(x=0\)

Now, 0 divides the interval -8 ≤ x ≤ 8 in two parts [-8,0] and [0,8]

For interval [-8,0], f'(x)>0, it means increasing.

For interval [0,8], f'(x)<0, it means decreasing.

Therefore, the function is increasing on the interval [-8,0] and decreasing on the interval [0,8].

Answer:

3n

Step-by-step explanation:

n is the middle integer of 3 consecutive even integers.

The difference between 2 consecutive even integers is 2.

The smallest of the 3 integers is n - 2. The greatest of the 3 integers is n + 2.

The sum of the 3 integers is:

n - 2 + n + n + 2 = 3n

Answer:

2 nonreal solutions

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 (a ≠ 0 )

then the nature of the roots are determined by the discriminant

b² - 4ac

• if b² - 4ac > 0 then 2 real and irrational solutions

• if b² - 4ac > 0 and a perfect square then 2 real and rational solutions

• if b² - 4ac = 0 then 2 real and equal solutions

• if b² - 4ac < 0 then no real solutions

5x² - 2x + 6 = 0 ← in standard form

with a = 5 , b = - 2 , c = 6

b² - 4ac

= (- 2)² - (4 × 5 × 6)

= 4 - 120

= - 116

since b² - 4ac < 0

then there are 2 nonreal solutions to the equation