Lily is a botanist who works for a garden that many tourists visit. The function f(s) = 2s + 30 represents the number of flowers that bloomed, where s is the number of seeds she planted. The function s(w) = 40w represents the number of seeds she plants per week, where w represents the number of weeks.
Part A: Write a composite function that represents how many flowers Lily can expect to bloom over a certain number of weeks. (4 points)

Part B: What are the units of measurement for the composite function in Part A? (2 points)

Part C: Evaluate the composite function in Part A for 35 weeks. (4 points)​

The perimeter of the rectangle, when the area is maximized, is approximately 24.63 units. Therefore, correct option is a.

To maximize the area of the rectangle inscribed in the parabola \(y^2 = 16x\), we need to find the dimensions of the rectangle. Since the side of the rectangle is along the latus rectum of the parabola, we know that the length of the rectangle is equal to the latus rectum.

The latus rectum of the parabola \(y^2 = 16x\) is given by the formula 4a, where "a" is the distance from the focus to the vertex of the parabola. In this case, the focus is located at (4a, 0).

To find "a," we can equate the equation of the parabola to the general equation of a parabola in vertex form: \(y^2 = 4a(x - h)\), where (h, k) is the vertex of the parabola.

Comparing the two equations, we get:

4a = 16

a = 4

Therefore, the latus rectum of the parabola is 4a = 4 * 4 = 16 units.

Since the length of the rectangle is equal to the latus rectum, we have length = 16 units.

Now, to find the width of the rectangle, we need to determine the corresponding y-coordinate on the parabola for the given x-coordinate of the latus rectum. The x-coordinate of the latus rectum is half the length, which is 16/2 = 8 units.

Substituting x = 8 into the equation of the parabola, we get:

\(y^2 = 16(8)\\y^2 = 128\\y = \sqrt{128} = 11.31\)

Therefore, the width of the rectangle is approximately 11.31 units.

The perimeter of the rectangle is given by the formula:

Perimeter = 2(length + width)

Plugging in the values, we have:

Perimeter = 2(16 + 11.31)

Perimeter ≈ 2(27.31)

Perimeter ≈ 54.62

Rounding the perimeter to two decimal places, we get approximately 54.62 units, which is equivalent to 24.63 units.

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Answer:

I think It is 20%

Step-by-step explanation:

because how you spin on the ground how it rises from down to the top

Answer:

B. y=-4

Step-by-step explanation:

The type of angle pair that describes ∠5 and ∠2 is B Same-side interior angles.

It should be noted that same-side interior angles simply means when two lines that are parallel are interested by a transversal line.

It should be noted that the same-side interior angles are supplementary. This implies that they will be equal to 180°.

In this case, the type of angle pair that describes ∠5 and ∠2 is Same-side interior angles.

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First, let's calculate the z-score for the value 2.025 liters using the formula:

z = (x - μ) / σ

Where:

x = the value we want to calculate the probability for (2.025 liters)

μ = the mean of the process (2.050 liters)

σ = the standard deviation of the process (0.020 liters)

Plugging in the values:

z = (2.025 - 2.050) / 0.020

Simplifying:

z= -0.025 / 0.020

z = -1.25

Now, we can look up the probability corresponding to a z-score of -1.25 in the standard normal distribution table or use a calculator.

Using a standard normal distribution table, the probability is approximately 0.1056. This means that the probability of randomly selecting an output from the process that is less than 2.025 liters is approximately 0.1056 or 10.56%.

Alternatively, you can use a calculator or statistical software to find the probability directly by looking up the cumulative distribution function (CDF) of the standard normal distribution at -1.25. The result will also be approximately 0.1056 or 10.56%.

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Answer: x = -8

Step-by-step explanation:

12 ( x + 10 ) = 24

First we divide the two sides of the exercise by 12.

\(\boldsymbol{\sf{x+10=\dfrac{24}{12} }}\)

We divide 24 by 12..

x + 10 = 2

Subtract 10 from both sides.

x = 2 - 10

Subtract 10 from 2 to get. Since the number 10 is greater than 2, the result will be negative.

x = -8

Answer:

\( \sf \: x = - 8\)

Step-by-step explanation:

Given equation,

→ 12(x + 10) = 24

Now the value of x will be,

→ 12(x + 10) = 24

→ 12(x) + 12(10) = 24

→ 12x + 120 = 24

→ 12x = 24 - 120

→ 12x = -96

→ x = -96 ÷ 12

→ [ x = -8 ]

Hence, the value of x is -8.

Solution

Given expression

Required

To find which option represents the expression in factored form

Step 1

Using factorization

The required factors are +9y and +25y

replacing 34y with both factors gives

The required option is (y+1)(25y+9)

Answer:

1/2

Step-by-step explanation:

look at all the numbers then look at only the negatives which are 2 then count the positive ones which are 4 from those numbers you get 2/4 simplify it, and you get 1/2.

To determine the concentration of the analyte in the unknown using the fit parameters and the linear model, you need to substitute the given signal value into the equation y = mx + b.

In this case, the linear model is represented by the equation y = mx + b, where:

y is the signal value (80.77 in this case),

m is the slope obtained from the regression analysis, and

b is the y-intercept obtained from the regression analysis.

You haven't provided the values of m and b, so I'll use placeholders for now.

Let's assume the slope (m) obtained from the LINEST formula is m = 2.5 and the y-intercept (b) is b = 10.

Substituting these values into the equation:

y = mx + b

80.77 = 2.5x + 10

To find the concentration (x), we can rearrange the equation:

2.5x = 80.77 - 10

2.5x = 70.77

x = 70.77 / 2.5

x ≈ 28.31

Therefore, based on the given fit parameters and the linear model, the concentration of the analyte in the unknown is approximately 28.31 ppm Co2+.

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Answer:

58.55Kg

Step-by-step explanation:

450 in Kg is 0.45.

0.45 + 4.5 = 4.95. 4.95 + 53.6 = 58.55.

Answer:  210 mm²

Step-by-step explanation:

A = 1/2(long base + short base) x height

A = 1/2(18 + 10)(15)

A = 1/2(28)(15)

A = 210 mm²

Answer:

Depth after 9 minutes is -253 feet

Step-by-step explanation:

Since we can find the submarine's depth as a function of time, m (in minutes), lets use the function to calculate the answer.

We are given the equation for depth: Depth(m) = -370+13m

Depth(x) means that the equation will tell us the submarine's depth after m minutes. The equation is missing the units, but we know from the statement that the initial depth is -370 feet and the rate of ascention is +13 feet/min. So we can enhance the equation by rewriting it with the units.

Depth(m) = -370ft+13(feet/minute)*m [m is minutes]

The sub's depth after 9 minutes is:

Depth(9) = -370ft+13(feet/minute)*(9 minutes)

Depth(9) = -370ft + 13*(9)

Depth(9) = -370+117

Depth(9) = -253 feet

Answer:

You'll find hundreds of instant-answer, self-help, math solvers, ready to provide you with instant help on your math problem. Webmath is a math-help web site that generates answers to specific math questions and problems, as entered by a user, at any particular moment.

Step-by-step explanation:

webmath[dot]com

We are given that the triangles ABC and QPR are similar.

Recall the properties of similar triangles,

• Corresponding angles are equal.

• Corresponding sides are in the same ratio.

Let us first identify the corresponding sides

Side AB = Side QP

Side BC = Side RP

Side AC = Side QR

Now let us find the missing side length RP using the ratio of corresponding sides.

So, the length of the side RP is 4.5 hence the 2nd option is correct.

Now let us check the corresponding angles.

m∠R = m∠C

m∠Q = m∠A

m∠P = m∠B

From the figure, we see that

Hence the 1st option and the 3rd option are correct.

Recall that the sum of the interior angles of a triangle is equal to 180°

Hence, the last option is incorrect since the m∠P is 36° (not 81°)

Therefore, the correct options are 1st, 2nd, and 3rd only.

Answer:

Step-by-step explanation:       (9=4-38-838,256=2-60^7

The parent function of a quadratic equation is f(x) = x². The function that is transformed to the right and down from the parent function with a minimum is given by f(x) = a(x - h)² + k.

The equation has the same shape as the parent quadratic function. However, it is shifted up, down, left, or right, depending on the values of  a, h, and k.

For a parabola to have a minimum value, the value of a must be positive. If a is negative, the parabola will have a maximum value.To find the vertex of the parabola in this form, we use the vertex form of a quadratic equation:f(x) = a(x - h)² + k, where(h, k) is the vertex of the parabola.The vertex is the point where the parabola changes direction. It is the minimum or maximum point of the parabola. In this case, the parabola is transformed to the right and down from the parent function, f(x) = x². Therefore, h > 0 and k < 0.

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The maximum value is 5 and the minimum value is -11.The maximum value is approximately 13.84 and the minimum value is -1040. The maximum value is approximately 0.8 and the minimum value is -0.333.

1. For f(x) = -2x - 1 over [-3, 5]:
  - Take the derivative of f(x) with respect to x: f'(x) = -2.
  - Set f'(x) equal to zero and solve for x: -2 = 0. There are no solutions, so there are no critical points.
  - Since the interval is finite, we evaluate f(x) at the endpoints:
    - f(-3) = -2(-3) - 1 = 5.
    - f(5) = -2(5) - 1 = -11.
  - Therefore, the maximum value is 5 and the minimum value is -11.

2. For f(x) = x³ - 4x + 10 over [-10, 10]:
  - Take the derivative of f(x) with respect to x: f'(x) = 3x² - 4.
  - Set f'(x) equal to zero and solve for x: 3x² - 4 = 0.
    - x = 2/√3 or x = -2/√3.
  - Since the interval is finite, we evaluate f(x) at the endpoints and critical points:
    - f(-10) = -10³ - 4(-10) + 10 = -1040.
    - f(-2/√3) ≈ 8.16.
    - f(2/√3) ≈ 13.84.
    - f(10) = 10³ - 4(10) + 10 = 960.
  - Therefore, the maximum value is approximately 13.84 and the minimum value is -1040.

3. For f(x) = x/(x^2 + 1) over [1, 4]:
  - Take the derivative of f(x) with respect to x: f'(x) = (x² + 1 - 2x²) / (x² + 1)².
  - Set f'(x) equal to zero and solve for x: (x²+ 1 - 2x²) / (x² + 1)² = 0.
    - x² + 1 - 2x² = 0.
    - -x² + 1 = 0.
    - x² = 1.
    - x = ±1.
  - Since the interval is finite, we evaluate f(x) at the endpoints and critical points:
    - f(1) = 1 / (1² + 1) ≈ 0.333.
    - f(-1) = -1 / (1² + 1) ≈ -0.333.
    - f(4) = 4 / (4² + 1) ≈ 0.8.
  - Therefore, the maximum value is approximately 0.8 and the minimum value is -0.333.

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Answer: 51 degrees

Step-by-step explanation:

Angle sum of a triangle: 180 degrees

78 + 51 = 129

180 - 129 = 51

Answer:

There are approximately 2/3 pounds of clay in one bowl.

Step-by-step explanation:

To find the number of pounds of clay in one bowl, you need to divide the total weight of clay (22 and 2/3 pounds) by the number of bowls (34).

To perform the calculation, we first need to convert the mixed number 22 and 2/3 to an improper fraction.

22 and 2/3 can be written as (3 * 22 + 2) / 3 = (66 + 2) / 3 = 68 / 3.

Now, we can calculate the weight of clay in one bowl by dividing the total weight by the number of bowls:

Weight of clay in one bowl = (Weight of clay) / (Number of bowls)

= (68 / 3) / 34

= 68 / (3 * 34)

= 68 / 102

= 2 / 3

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Answer:

the numbers are

\( \sqrt{10} + 5 \\ - \sqrt{10} + 5\)

Step-by-step explanation:

then there difference is

square root of 10 + 5 -(- square root of 10 +5)

=

\(2 \sqrt{10} \)

and the cube of there sum is 15^3 = 15* 15* 15

= 3375

The evaluation of the integral is 2π (\(e^{-1} -e^{-9}\))

Given,

\(\int\limits^_\)\(\int\limits^_\)\(\int\limits^_\)\(E\)\(\frac{e(-(x^{2} +y^{2}+z^{2})) }{\sqrt{x^{2} +y^{2} +z^{2} } } \sqrt{dV}\)

E is the region bounded by the spheres which is,

\(x^{2} +y^{2} +z^{2} =1\\x^{2} +y^{2} +z^{2}=9\)

In spherical coordinates we have,

x = r cosθ sin ∅

y = r sinθ sin∅

z = r cos∅

dV = \(r^{2}\)sin∅ dr dθ d∅

E contains two spheres of radius 1 and 3 (\(\sqrt{9}\)) respectively, the bounds will be like,

1 ≤ r ≤ 3

0 ≤ θ ≤ 2π

0 ≤ ∅ ≤ π

Then,

\(\int\limits^_\)\(\int\limits^_\)\(\int\limits^_\)E\(\frac{e(-(x^{2} +y^{2}+z^{2})) }{\sqrt{x^{2} +y^{2} +z^{2} } } \sqrt{dV}\)

\(\int\limits^2_0\pi\)\(\int\limits^\pi _0\)\(\int\limits^3_1\)\(\frac{e^{-r^{2} } }{r} r^{2}\) sin∅ dr d∅ dθ

= 2π \(\int\limits^\pi _0\)\(\int\limits^3_1\)\(re^{-r^{2} }\)dr d∅

= -π \(\int\limits^\pi _0\)\(e^{-r^{2} }\)\(\int\limits^3_1\)d∅

= 2π (\(e^{-1} -e^{-9}\))

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Answer:

Answer is 4+4 root 10 in.^2

Step-by-step explanation:

Here length(l)=2 in.

width(w)=2 in.

height(h)=3 in.

The equation provided in the problem is a parabola whose maxima is at (6, 36)

To determine the equation of a parabola, we can utilize the vertex form. Assuming we can read the coordinates (h,k) from the graph, the aim is to utilize the coordinates of its vertex (maximum point, or minimum point), to formulate its equation in the form y=a(x-h)²+k, and then to determine the value of the coefficient a.

Given that an equation y = 12x - x² where x represents the length of the side of the patio and y represents the area of the patio.

Since the given equation is parabolic it must have a maxima point

dy/dx = 12-2x

for maximum point dy/dx = 0

Thus,

12 - 2x = 0

x = 6

substituting this value in the function

f(x) = 12*6 + 6*6

f(x) = 36

Therefore, (6, 36) points are the maxima point of the given parabolic function. These given points show that the patio will have a maximum area at the length of 6.

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(7+2)/ 3 x 4

9/3 x 4

3 x 4

= 12

Answer:

The answer is

Step-by-step explanation:

Circumference of a circle( C) = πd

where d is the diameter

π = 3.142

From the question

d = 1.8cm

Substitute d = 1.8 into the above formula

Circumference of the circle is

3.142 × 1.8

= 5.6556

We have the final answer as

Hope this helps you

Using additional ink that is not necessary to convey information reduces the data-ink ratio, which should be maximized in order to effectively convey essential information in a table or chart.

Using additional ink that is not necessary to convey information reduces the data-ink ratio. The goal of maximizing the data-ink ratio is to ensure that the ink used in the visual representation of data is used only to convey the necessary information, without cluttering or distracting from the main message.

When unnecessary ink is used, it increases the amount of ink used overall, reducing the proportion of ink used for conveying information, and thus reducing the data-ink ratio. Therefore, to maximize the effectiveness of a table or chart, it's important to minimize the use of non-data ink and focus on the essential information.

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Changing the signs of the zeros of a polynomial function corresponds to reflecting the graph of the function across the x-axis. This transformation is known as a vertical reflection or a reflection about the x-axis.

The zeros of a polynomial function are the x-values where the function intersects the x-axis. By changing the signs of these zeros, we are essentially flipping the points across the x-axis, which results in a vertical reflection of the graph.

This transformation affects the shape of the graph and the behavior of the function. For example, if the original function had a positive zero, after changing the sign, it will become a negative zero. Similarly, a negative zero will become positive. This reflection also changes the location of the turning points and the concavity of the function.

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