Store A's profit is modeled by f(x) =2x, and Store B's profit is modeled by g(x) = 83x. Over what interval is Store A's profit greater than Store B's?

Step-by-step explanation:

22×(t + 18) - 7

t = 13

so,

22×(13 + 18) - 7 = 22×31 - 7 = 682 - 7 = 675

the directional derivative of f(x, y) = xe³ - y² at the point (5, 0) in the direction of the vector 47 - 3j is (141e³) / sqrt(2218).

To find the directional derivative of the function f(x, y) = xe³ - y² at the point (5, 0) in the direction of the vector 47 - 3j, we need to compute the dot product of the gradient of f with the unit vector in the given direction.

First, let's find the gradient of f(x, y):

∇f(x, y) = (∂f/∂x, ∂f/∂y)

Taking partial derivatives:

∂f/∂x = (3e³)x

∂f/∂y = -2y

The gradient of f(x, y) is: ∇f(x, y) = (3e³)x - 2y

To calculate the directional derivative, we need the unit vector in the direction of 47 - 3j. The magnitude of the vector 47 - 3j is:

|47 - 3j| = sqrt(47² + (-3)²) = sqrt(2209 + 9) = sqrt(2218)

The unit vector in the direction of 47 - 3j is obtained by dividing the vector by its magnitude:

u = (47 - 3j) / |47 - 3j|

u = (47 - 3j) / sqrt(2218)

Now, we can compute the directional derivative by taking the dot product of the gradient with the unit vector:

Directional derivative = ∇f(x, y) · u

= [(3e³)x - 2y] · [(47 - 3j) / sqrt(2218)]

= (3e³)(47) / sqrt(2218) - (2)(0) / sqrt(2218)  [since we are evaluating at (5, 0)]

= (141e³) / sqrt(2218)

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Answer:

Set two equations:

\(\left \{ {{x+y=50} \atop {\frac{x}{y}=\frac{7}{11} }} \right.\)

Rearrange one of the equations to find the value of a variable:

\(x+y=50\\x=50-y\)

Substitute in that value into the other equation:

\(\frac{50-y}{y}=\frac{7}{11}\)

Cross-multiply & solve for y:

\(7y=11(50-y) \\7y=550-11y\\7y+11y=550\\18y=550\\y=\frac{550}{18}=\frac{275}{9}\)

Substitute in the value to the original equation to find x:

\(\frac{x}{\frac{275}{9}}=\frac{7}{11} \\\frac{9x}{275}=\frac{7}{11} \\9(11)x=275(7)\\99x=1925\\x=\frac{1925}{99} =\frac{175}{9}\)

Therefore, the answer will be:

You can check your answers by:

\(\frac{175}{9} +\frac{275}{9} =\frac{450}{9} =50\)

\(\frac{\frac{175}{9} }{\frac{275}{9} } =\frac{175}{9} *\frac{9}{275} =\frac{175}{275}=\frac{7}{11}\)

Answer:

x = 175/9

y = 275/9

Step-by-step explanation:

Let the larger number be 'x' and smaller number be 'y'

sum of two numbers is 50.

x +y = 50 --------(I)

      x = 50 - y   -------------(II)

The larger number is divided by the smaller number we get 7/11.

\(\frac{x}{y}=\frac{7}{11}\\\\\)

Cross multiply,

11x = 7y

11x - 7y = 0 ------------(III)

Substitute x = 50 -y in equation (III)

11*(50-y) - 7y = 0  

11*50 - 11*y - 7y  = 0             {Distributive property}

550 - 11y - 7y = 0  

550 - 18 y = 0        {Combine like terms}

Subtract 550 from both sides

- 18y = -550

Divide both sides by (-18)

y = -550/-18

y = 275/9

substitute y = 275/9 in equation (III)

\(11x - 7*(\frac{275}{9})=0\\\\11x-\frac{1925}{9}=0\\\\11x =\frac{1925}{9}\\\\x=\frac{1925}{9*11}\\\\x=\frac{175}{9}\)

Answer:

x = -3

y = 2

Step-by-step explanation:

Let the two integers be x and y

sum is -1

x + y = -1 •••(i)

x-y = -5 •••••(ii)

From ii, x = -5 + y

substitute into i

-5 + y+ y = -1

-5 + 2y = -1

2y = -1 + 5

2y = 4

y = 4/2

y = 2

Recall;

x = -5 + y

x = -5 + 2

x = -3

The probability that the number of heads obtained from flipping the two fair coins is the same is 35/128.

Probability:

Probability means the fraction of favorable outcome and the total number of outcomes.

So it can be written as,

Probability = Favorable outcomes / Total outcomes

Given,

The coin a is flipped three times and coin b is flipped four times.

Here we need to find the probability that the number of heads obtained from flipping the two fair coins is the same.

We know that,

There are 4 ways that the same number of heads will be obtained;

0, 1, 2, or 3 heads.

The probability of both getting 0 heads is

\($\left(\frac12\right)^3{3\choose0}\left(\frac12\right)^4{4\choose0}=\frac1{128}$\)

Probability of getting 1 head,

\($\left(\frac12\right)^3{3\choose1}\left(\frac12\right)^4{4\choose1}=\frac{12}{128}$\)

Probability of getting 2 heads is,

\($\left(\frac12\right)^3{3\choose2}\left(\frac12\right)^4{4\choose2}=\frac{18}{128}$\)

And the probability of getting 3 heads is,

\($\left(\frac12\right)^3{3\choose3}\left(\frac12\right)^4{4\choose3}=\frac{4}{128}$\)

Therefore, the probability that the number of heads obtained from flipping the two fair coins is the same is,

=> (1/128) + (12/128) + (18/128) + (4/128)

=> 35/128.

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Some information that someone might use to solve problems related to a circle design is the Tangent Arc theorem.

The tangent arc theorem states that if an angle is formed by two secants, one secant, one tangent, or two tangents, and also intersects in a space outside of the circle, then the value obtained will be equal to the difference of the values of the intercepted arcs divided by one and a half.

Also, note that angles outside a circle are those whose vertex or arc is pointed outwards and their sides are either secants or tangents. With this information, it will be possible to solve problems related to tangent lines and arc measures.

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9514 1404 393

Answer:

  $1320

Step-by-step explanation:

The amount of commission is the product of the commission rate on sales and the amount of sales:

  Job A commission = 0.12 × $11,000 = $1320

_____

It may help you to realize that the percent symbol (%) is fully equivalent to /100. That is 12% = 12/100 = 0.12.

Eli will take 12 hours alone to complete the task.

Acc to our question-

Hence,Eli will take 4 hrs.

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a) Using the Euclidean algorithm, we can find gcd (707,413) as follows:707 = 1 · 413 + 294413 = 1 · 294 + 119294 = 2 · 119 + 562119 = 2 · 56 + 71356 = 4 · 71 + 12 71 = 5 · 12 + 11 12 = 1 · 11 + 1

Thus, gcd (707,413) = 1.

We can find the coefficients s and t that solve the equation 707s + 413t

= 1 as follows:1 = 12 - 11 = 12 - (71 - 5 · 12) = 6 · 12 - 71 = 6 · (119 - 2 · 56) - 71

= - 12 · 56 + 6 · 119 - 71

= - 12 · 56 + 6 · (294 - 2 · 119) - 71 = 18 · 119 - 12 · 294 - 71

= 18 · 119 - 12 · (413 - 294) - 71 = 30 · 119 - 12 · 413 - 71

= 30 · (707 - 1 · 413) - 12 · 413 - 71 = 30 · 707 - 42 · 413 - 71

Thus, s = 30, t = -42. So we have found that 707(30) + 413(−42) = 1.

b) Since 707s + 413t = 1 and 9 does not divide 1, the equation 707x + 413y = 9 has no integer solutions. Therefore, we can conclude that there are no such integers x and y.

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We have been given that in ΔRST, s = 93 inches, ∠S=123° and ∠T=28°. We are asked to find the length of r to the nearest 10th of an inch.

We will use law of sines to solve for side r.

\(\frac{a}{\text{Sin}(a)}=\frac{b}{\text{Sin}(B)}=\frac{c}{\text{Sin}(C)}\), where a, b and c are corresponding sides to angles A, B and C respectively.

Let us find measure of angle S using angle sum property of triangles.

\(\angle R+\angle S+\angle T=180^{\circ}\)

\(\angle R+123^{\circ}+28^{\circ}=180^{\circ}\)

\(\angle R+151^{\circ}=180^{\circ}\)

\(\angle R+151^{\circ}-151^{\circ}=180^{\circ}-151^{\circ}\)

\(\angle R=29^{\circ}\)

\(\frac{r}{\text{sin}(R)}=\frac{s}{\text{sin}(S)}\)

\(\frac{r}{\text{sin}(29^{\circ})}=\frac{93}{\text{sin}(123^{\circ})}\)

\(\frac{r}{\text{sin}(29^{\circ})}\cdot \text{sin}(29^{\circ})=\frac{93}{\text{sin}(123^{\circ})}\cdot \text{sin}(29^{\circ})\)

\(r=\frac{93}{0.838670567945}\cdot (0.484809620246)\)

\(r=110.889786233799179\cdot (0.484809620246)\)

\(r=53.7604351\)

Upon rounding to nearest tenth, we will get:

\(r\approx 53.8\)

Therefore, the length of r is approximately 53.8 inches.

There are average 360 ways to seat 6 people around a circular table since any arrangement with the same immediate left and right neighbor is considered the same.

For seating 6 people around a circular table, there are many possible arrangements. However, two arrangements are considered the same if everyone has the same immediate left and right neighbor. This means that, for any given seating arrangement, there are six possible rotations, so the total number of different arrangements is 6 times the number of arrangements that can be made with the initial seating. Since there are 6! (6 factorial, or 6x5x4x3x2x1) arrangements that can be made with the initial seating, the total number of different seating arrangements is 6! x 6, or 360. In other words, there are 360 ways to seat 6 people around a circular table where two sections are considered the same when everyone has the same immediate left and immediate right neighbor.

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a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

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The combined mean weight of all Indian and German students is 57.81 kg. The combined standard deviation of weight for the group is 3.59 kg.

The combined mean weight is calculated by adding the mean weights of the two groups and dividing by the total number of students. In this case, the mean weight of the Indian students is 55 kg and the mean weight of the German students is 60 kg. There are a total of 350 Indian students and 450 German students, so the combined mean weight is (350 * 55 + 450 * 60) / (350 + 450) = 57.81 kg.

The combined standard deviation is calculated using a formula that takes into account the standard deviations of the two groups and the number of students in each group. In this case, the standard deviation of the Indian students is 3 kg and the standard deviation of the German students is 4 kg. The combined standard deviation is sqrt((350 * 3^2 + 450 * 4^2) / (350 + 450)) = 3.59 kg.

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Answer:

\( Area = 112.1 m^2 \)

Step-by-step Explanation:

Given:

∆WXY

m < X = 130°

WY = x = 31 mm

m < Y = 26°

Required:

Area of ∆WXY

Solution:

Find the length of XY using Law of Sines

\( \frac{w}{sin(W)} = \frac{x}{sin(X)} \)

X = 130°

x = WY = 31 mm

W = 180 - (130 + 26) = 24°

w = XY = ?

\( \frac{w}{sin(24)} = \frac{31}{sin(130)} \)

Multiply both sides by sin(24) to solve for x

\( \frac{w}{sin(24)}*sin(24) = \frac{31}{sin(130)}*sin(24) \)

\( w = \frac{31*sin(24)}{sin(130)} \)

\( w = 16.5 mm \) (approximated)

\( XY = w = 16.5 mm \)

Find the area of ∆WXY

\( area = \frac{1}{2}*w*x*sin(Y) \)

\( = \frac{1}{2}*16.5*31*sin(26) \)

\( = \frac{16.5*31*sin(26)}{2} \)

\( Area = 112.1 m^2 \) (to nearest tenth).

The area of the given trapezoid is 27280 cm².

There are different quadrilaterals, for example square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example,  in a square, all angles are 90° and all sides present the same value.

The sum of the interior angles of a quadrilateral is equal to 360°.

This question requires your knowledge about the area of compound shapes. For solving this, you should:

       The trapezoid is composed for:

          - 2 triangles whose sides are equal to 34 cm and 110 cm/ 22 cm and 110cm.

          - 1 rectangle whose sides are 220 cm and 110 cm.

 Therefore, you should sum the area of these geometric figures for finding the total area.

Area of each triangle = \(\frac{bh}{2}\), where b=the length of the side and h= the height of the triangle.  Then,

              A_triangle1= \(\frac{bh}{2}=\frac{34*110}{2}\)=1870 cm²

              A_triangle2= \(\frac{bh}{2}=\frac{22*110}{2}\)=1210cm²

Area of the rectangle=bh, where b=the length of the side and h= the height of the rectangle.  Then,

              A_rectangle= bh=110*220=24200

A_trapezoid= A_rectangle+A_triangle1+A_triangle2

A_trapezoid= 24200+1870+1210

A_trapezoid= 27280 cm²

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Answer:

D. 9 + 4√5

Step-by-step explanation:

What we're essentially doing here is squaring 2 + √5. (2 + √5 and 2 + 1√5 are essentially the same)

(2 + √5)(2 + √5) (I didn't put the one on the conjugate for a reason; look above)

Step 1: Apply the distributive property by multiplying each term of 2 + √5 by 2 + √5

4 + 2√5 + 2√5 + (√5)²

Step 2: Combine 2√5 and 2√5 to get 4√5.

4 + 4√5 + (√5)²

Step 3: The square of √5 is 5.

4 + 4√5 + 5

Step 4: Add 4 and 5 to get 9.

9 + 4√5 is the final answer to this question.

A discrete variable is a variable whose value is obtained by counting while a continuous variable is a variable whose value is obtained by measuring.

From the question,

The number of cars a car dealer sells in a day is a discrete variable.

The time it takes to have a medical physical exam is a continuous variable.

Using the formula of volume of rectangular prism;

1. The volume of the rectangular prism is 3672cm³

2. The volume of the rectangular prism is 630in³

3. The volume of the rectangular prism is  3744ft³

The volume of a rectangular prism can be calculated by multiplying its length (l), width (w), and height (h). The formula for the volume of a rectangular prism is:

Volume = length × width × height

V = l × w × h

By substituting the given values for the length, width, and height into the formula, you can calculate the volume of the rectangular prism.

1. To find the volume of the rectangular prism, we have to substitute the value into the formula;

v = 9 * 24 * 17

v = 3672cm³

2. The volume of the rectangular prism is given as;

v = 4.5 * 14 * 10

v = 630in³

3. The volume of the rectangular prism is given as;

v = 8 * 12 * 39

v = 3744ft³

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Therefore, the sum of the first 1234 terms of this sequence is 1234.

To find the sum of the first 1234 terms of the sequence consisting of 1's separated by blocks of 2's with n 2's in the nth block, we need to determine the number of blocks and the number of 1's in each block.

Let's examine the pattern of the sequence:

Block 1: 2's

= 1's

= 1 (1 2)

Block 2: 2's

= 2's

= 22 (1 22 1)

Block 3: 2's

= 3's

= 222 (1 222 1)

Block 4: 2's

= 4's

= 2222 (1 2222 1)

...

We observe that the number of 2's in each block is equal to the number of the block itself. So, in the nth block, there are n 2's.

Now, let's calculate the number of blocks required to reach the 1234th term:

To find the number of blocks, we need to determine the maximum block number before the 1234th term. We can calculate this by finding the sum of the series 1 + 2 + 3 + ... + n until the sum is greater than or equal to 1234.

The formula for the sum of the series 1 + 2 + 3 + ... + n is given by: S = (n/2)(n+1).

Let's solve this equation:

(n/2)(n+1) = 1234

\(n^2 + n - 2468 = 0\)

Using the quadratic formula:

n = (-1 + √(1 + 4*2468)) / 2

n ≈ 61.76

Since n must be a whole number, we take the ceiling of n, which gives us 62.

Therefore, there are 62 blocks in the sequence.

Next, let's calculate the number of 1's in each block:

In the nth block, there are n 2's. Since each 2 is separated by a 1, there are n + 1 terms in each block.

So, the number of 1's in each block is (n + 1) - n = 1.

Since there is always one 1 between two consecutive blocks, the total number of 1's in the sequence is equal to the number of blocks, which is 62.

Finally, let's calculate the sum of the first 1234 terms:

Each block has n + 1 terms, which gives us (n + 1) + (n + 1) + ... + (n + 1) (62 times).

Sum of (n + 1) repeated 62 times = 62(n + 1)

= 62 * 2

= 124.

In addition to the blocks, we have 1234 - 62 = 1172 remaining terms, which are all 1's.

So, the sum of the first 1234 terms is 62 + 1172 = 1234.

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The figure contains a triangle and a semicircle

The area of the figure is 49.12 square feet

The dimension of the triangle is:

Base = 8 ft

Height = 6ft

So, the area is:

Area = 0.5 * Base * Height

This gives

Area = 0.5 * 8ft * 6ft

Evaluate

Area = 24 square feet

The radius of the semicircle is:

r = 4 ft.

So, the area is:

\(Area = 0.5\pi r^2\)

This gives:

Area = 0.5*3.14 * 4^2

Area = 25.12 square feet

Add the calculated  areas.

Total = 24 square feet + 25.12 square feet

Total = 49.12 square feet

Hence, the area of the figure is 49.12 square feet

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The expected number of left-handed students in a typical class of 188 students can be estimated using the prevalence rate of left-handedness in the general population.

According to studies, approximately 10% of the population is left-handed. Therefore, we can expect around 18.8 left-handed students in a class of 188 students.

To calculate the standard deviation, we need additional information. The standard deviation depends on the variability of left-handedness in the population. Without this data, it is not possible to provide an accurate estimation of the standard deviation.

Similarly, the expected number of right-handed students can be estimated by subtracting the expected number of left-handed students (18.8) from the total number of students (188). This gives us an expected number of around 169.2 right-handed students.

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The width of the previous image was 9.5 millimeters.

If the new image is an enlargement of the previous image with a scale factor of 2, it means that the width of the new image is twice the width of the previous image.

Let's denote the width of the previous image as "x" millimeters.

According to the information given, the width of the new image is 19 millimeters.

Since the new image is an enlargement with a scale factor of 2, we can set up the following equation:

\(2x = 19\)

To find the width of the previous image, we need to solve this equation for "x."

Dividing both sides of the equation by 2, we get:

\(x=\frac{19}{2}\)

\(x = 9.5\)

Therefore, the width of the previous image was 9.5 millimeters.

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This new circle is the dilated image of circle A, and we can see that it is similar to circle X, with a scale factor of XY/AB. Therefore, the two circles are similar.

What is circle?

The eccentricity is 0 and the two foci are coincident in a circle, which is a special type of ellipse. A circle is also known as the location of points that are evenly spaced apart from the centre. The radius of a circle is measured from the centre to the edge.

To prove that the circles are similar, we have to translate the center of circle A onto point X and then dilate the image of circle A about its center by a scale factor of XY/AB. The complete statements below describe how to prove that the circles are similar.

Translation:

First, we will translate the center of circle A to the point X. To do this, we will use a straightedge and draw a line from the center of circle A to point X. Then we will measure the length of this line, and with the same length, we will draw a new line from point X parallel to the original line. This new line intersects the circle A at a new point B′.

Dilation:

Next, we will dilate the image of circle A about its center by a scale factor of XY/AB. To do this, we will use a compass to draw a circle with radius XY centered at point X. Then we will draw a line from the center of circle A to point B′.

This line intersects the circle with radius XY at a new point Y. We will then draw a new circle with center A and radius AY. This new circle is the dilated image of circle A, and we can see that it is similar to circle X, with a scale factor of XY/AB. Therefore, the two circles are similar.

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The unit step response, y(t), for the given LTI system with transfer function H(s) = (s+4)(s+5)′(s+2), and input X(s) = 1/s, is a function of time that can be represented as \(y(t) = (4/3)e^(-2t) - (4/3)e^(-5t) - (1/3)e^(-4t) + (1/3)e^(-2t)\).

The unit step response of a linear time-invariant (LTI) system represents the output of the system when the input is a unit step function. In this case, the transfer function H(s) is given as (s+4)(s+5)′(s+2), where s is the Laplace variable. The prime symbol (') denotes differentiation with respect to s.

To find the unit step response, we first need to determine the inverse Laplace transform of the transfer function H(s). By applying partial fraction decomposition, the transfer function can be expressed as H(s) = A/s + B/(s+2) + C/(s+4) + D/(s+5), where A, B, C, and D are constants.

Taking the inverse Laplace transform of each term using known transforms, we obtain the time-domain representation of H(s) as \(y(t) = (4/3)e^(-2t) - (4/3)e^(-5t) - (1/3)e^(-4t) + (1/3)e^(-2t)\).

In summary, the unit step response y(t) for the given LTI system is a function of time that includes exponential terms with different coefficients and time constants. This response represents the system's output when the input is a unit step function.

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Answer:

864

Step-by-step explanation:

Question:

Nadia is a stockbroker. She earns 12​% commission each week. Last​ week, she sold ​$7,200 worth of stocks. How much did she make last week in​ commission?

What were trying to find:

How much did she make last week in​ commission?

Answer:

Nadia made $44,928 last week.

Step-by-step explanation:

7,200 x 12% = $864 (0.12)

$864 x 52 = $44,928

Therefore, $44,928 is your answer.

Hope this helped! :^)

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Submitted on 4/18/2022 at 12:06 PM

(To avoid plagarism, by users whom decide to copy.)

The probability of a premature baby girl being born at this hospital is 5%.

Let's break down the problem step by step. We are given that 56% of the babies born are not girls. This implies that the remaining 100% - 56% = 44% of the babies born are girls.

Next, we are given that out of the baby girls born, 12% are premature. To find the probability of a premature baby girl being born, we need to multiply the probability of being a girl (44%) by the probability of being premature (12%).

Probability = 44% * 12% = 0.44 * 0.12 = 0.0528

Now, we need to round this probability to the nearest percent. Since the decimal portion is 0.0528, which is closer to 0.05 than 0.06, we round down.

Therefore, the probability of a premature baby girl being born at this hospital is approximately 5%.

In conclusion, based on the given information, the probability of a premature baby girl being born at this hospital is approximately 5%.

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Answer:

y = -3x

Step-by-step explanation:

The definition of an equation with a proportional relationship with another is that they need to intersect at a 90° angle.

To do this you just have to multiply the slope of the line by its negative reciprocal. So you have to flip the fraction (reciprocal) and then multiply it by -1.

Find the equation of the line:

The line starts at the origion so the y-intercept (b value) is equal to 0.

Looking at slope we can tell that the line has a point at (0, 0) and (3, 1).

The slope between these points is as follows

\(\frac{1 - 0}{3 - 0}\)

So the equation for the first line is y = 1/3x

We then flip the fraction and multiply by -1 to get its proportional line.

y = 1/3x

y = 3x

y = -3x