a biologist collected 326 fern and moss samples. there were 66 fewer ferns than moss samples. how many fern samples did the biologist collect?

Answer: 175,000

Step-by-step explanation:

Net Profit before Taxes = Gross Sales - Sales Returns - Cost of Goods Sold - Operating Expenses

= $300,000 - $5,000 - $40,000 - $80,000 = $175,000

Pre-Tax Profit = Net Profit before Taxes = $175,000.

Answer:Third optionoption

Step-by-step explanation:

Answer:

\(for \: quadrilaeral \: \: sum \: of \: angles \: is \: equal \: 180 \times 2 = 360 \\ 80 + 70 + x + 2x = 360 \\ 3x = 360 - 70 - 80 = 210 \\ x = 210 \div 3 = 70 \\ q = 70 \\ r = 140\)

In multivariable calculus, the tangent plane is a plane that "touches" a surface at a given point and has the same slope or gradient as the surface at that point.

To find the equation for the tangent plane at the point P0(2, 1, 2) on the surface 2x^2 + 4y^2 +3z^2 = 24, we need to find the gradient vector of the surface at P0, which gives us the normal vector of the plane. Then, we can use the point-normal form of the equation for a plane to find the equation of the tangent plane.

The gradient vector of the surface is given by:

grad(2x^2 + 4y^2 +3z^2) = (4x, 8y, 6z)

At P0(2, 1, 2), the gradient vector is (8, 8, 12), which is the normal vector of the tangent plane.

Using the point-normal form of the equation for a plane, we have:

8(x - 2) + 8(y - 1) + 12(z - 2) = 0

Simplifying, we get:

4x + 4y + 3z = 20

Therefore, the correct equation for the tangent plane is D. 5x + 4y + 3z = 20.

To find the equations for the normal line, we need to use the direction vector of the line, which is the same as the normal vector of the tangent plane. Thus, the direction vector of the line is (8, 8, 12).

The equations for the normal line can be expressed as:

x = 2 + 8t

y = 1 + 8t

z = 2 + 12t

where t is a parameter that can take any real value.

To learn more about  equation visit:

brainly.com/question/10413253

#SPJ11

The surface area of the pyramid is approximately 138.528 square feet.

The surface area of a solid is the sum of the areas of all faces of the solid. In this case, we find that the surface area is the sum of the areas of four triangles and the area of the square base. Then, we proceed to determine the surface area of the solid:

A = 4 · (1 / 2) · √[(3 ft)² + (8 ft)²] · (6 ft) + (6 ft)²

A ≈ 138.528 ft²

The surface area of the pyramid is approximately 138.528 square feet.

To learn more on surface areas: https://brainly.com/question/2835293

#SPJ1

Answer:

The answer equals -8

Step-by-step explanation:

Order of Operations: BPEMDAS

FOIL - First, Outside, Inside, Last

Step 1: Write out expression

\((\sqrt{4-3i} -\sqrt{4+3i})^6\)

Step 2: Expand

\((\sqrt{4-3i} -\sqrt{4+3i})(\sqrt{4-3i} -\sqrt{4+3i})(\sqrt{4-3i} -\sqrt{4+3i})(\sqrt{4-3i} -\sqrt{4+3i})(\sqrt{4-3i} -\sqrt{4+3i})(\sqrt{4-3i} -\sqrt{4+3i})\)

Step 3: FOIL first 2

\((\sqrt{4-3i} -\sqrt{4+3i})^2 = -2\)

Step 4: Replace square roots with -2

-2(-2)(-2) = (-2)³ = 8

Answer:

the correct answer is d. x^3

Answer:

There's no A so I'm going to assume you meant X

X = 23

Step-by-step explanation:

X is equal to 23, because 23 - 18 = 5

or 5 + 18 = 23

Answer:

$2.92

Step-by-step explanation:

Divde $11.67 by the 4 gallons that Dennis bought.

11.67/4=2.9175

round to the nearst cent (or hundreths place)

since 7 is greater than 5, it rounds up

$2.92

The directional derivative of the function at the given point in the direction of the vector v are as follows :

\(\[D_{\mathbf{u}} f(\mathbf{a}) = \nabla f(\mathbf{a}) \cdot \mathbf{u}\]\)

Where:

- \(\(D_{\mathbf{u}} f(\mathbf{a})\) represents the directional derivative of the function \(f\) at the point \(\mathbf{a}\) in the direction of the vector \(\mathbf{u}\).\)

- \(\(\nabla f(\mathbf{a})\) represents the gradient of \(f\) at the point \(\mathbf{a}\).\)

- \(\(\cdot\) represents the dot product between the gradient and the vector \(\mathbf{u}\).\)

Now, let's substitute the values into the formula:

Given function: \(\(f(x, y) = 7e^x \sin y\)\)

Point: \(\((0, \frac{\pi}{3})\)\)

Vector: \(\(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Gradient of \(\(f\)\) at the point  \(\((0, \frac{\pi}{3})\):\)

\(\(\nabla f(0, \frac{\pi}{3}) = \begin{bmatrix} \frac{\partial f}{\partial x} (0, \frac{\pi}{3}) \\ \frac{\partial f}{\partial y} (0, \frac{\pi}{3}) \end{bmatrix}\)\)

To find the partial derivatives, we differentiate \(\(f\)\) with respect to \(\(x\)\) and \(\(y\)\) separately:

\(\(\frac{\partial f}{\partial x} = 7e^x \sin y\)\)

\(\(\frac{\partial f}{\partial y} = 7e^x \cos y\)\)

Substituting the values \(\((0, \frac{\pi}{3})\)\) into the partial derivatives:

\(\(\frac{\partial f}{\partial x} (0, \frac{\pi}{3}) = 7e^0 \sin \frac{\pi}{3} = \frac{7\sqrt{3}}{2}\)\)

\(\(\frac{\partial f}{\partial y} (0, \frac{\pi}{3}) = 7e^0 \cos \frac{\pi}{3} = \frac{7}{2}\)\)

Now, calculating the dot product between the gradient and the vector \(\(\mathbf{v}\)):

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \begin{bmatrix} \frac{7\sqrt{3}}{2} \\ \frac{7}{2} \end{bmatrix} \cdot \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Using the dot product formula:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \left(\frac{7\sqrt{3}}{2} \cdot -5\right) + \left(\frac{7}{2} \cdot 12\right)\)\)

Simplifying:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = -\frac{35\sqrt{3}}{2} + \frac{84}{2} = -\frac{35\sqrt{3}}{2} + 42\)\)

So, the directional derivative \(\(D_{\mathbf{u}} f(0 \frac{\pi}{3})\) in the direction of the vector \(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\) is \(-\frac{35\sqrt{3}}{2} + 42\).\)

To know more about derivative visit-

brainly.com/question/31422048

#SPJ11

Answer: -33/5

Step-by-step explanation:

The volume is measured at the bottom of the meniscus when the liquid level is between the two etched marks on the pipet.

1. Place the graduated pipet on a flat surface and make sure it is level

2. Draw the liquid up until the meniscus is level with the etched line that corresponds to the desired volume

3. Make sure the liquid is not touching the etched line above it

4. Observe the bottom of the meniscus and take the reading at the point where the liquid level is between the two etched lines

The volume is measured at the bottom of the meniscus when the liquid level is between the two etched marks on the pipet.

Learn more about volume here

https://brainly.com/question/16134180

#SPJ4

Answer:

answer is a

Step-by-step explanation:

Describe the end behavior of the given function.

$(-) = 0) – 2

O A. As x decreases, (x) approaches 2.

OB.

As x decreases, Ax) approaches negative infinity.

OC. As xincreases, fx) approaches infinity.

OD. As x increases, Ax) approaches -2

Answer:

C.

Step-by-step explanation:

(Use desmos graphing calculator to graph it...)

The value of x is 28 millimeters in the composite figure of two right-angled triangles lying next to each other

A composite figure is a figure that is produced from the combination of two geometric shapes together.

The diagrammatic expression of a composite figure consists of two right-angled triangles lying next to each other can be seen in the image attached below.

For the left-side right-angled triangle, we have:

13² = h² + 5²

h² = 13² - 5²

h = √(169-25)

h = 12

Recall from the diagram that:

h² = pq

∴

12² = 5x

x = 144/5

x ≅ 28 millimeters

Learn more about composite figures here:

https://brainly.com/question/15981553

#SPJ1

The ladder will reach up to a height of approximately 27.39 feet (rounded to two decimal places).

We can use the Pythagorean theorem to solve this problem. Let's call the distance from the base of the ladder to the house "x". Then, according to the Pythagorean theorem:

\(x^2 + 48^2 = 50^2\)

Simplifying this equation, we get:

\(x^2 + 2304 = 2500\)

Subtracting 2304 from both sides, we get:

\(x^2 = 196\)

Taking the square root of both sides, we get:

x = 14

So the ladder is currently 14 feet away from the house. If Mila pulls the ladder 6 feet farther away from the house, it will be 20 feet away from the house. We can use the same equation to find out how high up the ladder will reach:

\(x^2 + y^2 = 50^2\)

Substituting x = 20 and simplifying, we get:

\(y^2 = 1500\)

Taking the square root of both sides, we get:

y = 5√30

for such more question on  height

https://brainly.com/question/27987869

#SPJ11

The value of x in the quadratic equation using quadratic formula to the nearest hundredths place is x = 1.29 and x = 2.71.

The correct answer choice is option B.

2x² - 8x + 7 = 0

\(x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }\)

\(x = \frac{ -(-8) \pm \sqrt{(-8)^2 - 4(2)(7)}}{ 2(2) }\)

\(x = \frac{ 8 \pm \sqrt{64 - 56}}{ 4 }\)

\(x = \frac{ 8 \pm \sqrt{8}}{ 4 }\)

\(x = \frac{ 8 \pm 2\sqrt{2}\, }{ 4 }\)

\(x = \frac{ 8 }{ 4 } \pm \frac{2\sqrt{2}\, }{ 4 }\)

\(x = 2 \pm \frac{ \sqrt{2}\, }{ 2 }\)

\(x = 2.70711\)

or

\(x = 1.29289\)

Hence,

Approximately, x = 1.29 or x = 2.71

Read more on quadratic formula:

https://brainly.com/question/1214333

#SPJ1

Answer:

l = 40 m

Step-by-step explanation:

The formula for area of a rectangle is

A = lw, where

Step 1:  Since we're given the area and width, we plug in these two values for A and w and to solve for l (length):

360 = 9l

Step 2:  Divide both sides by 9 to solve for l

(360 = 9l) / 9

40 m = l

Optional Step 3:  We can check our answers by checking that the product of 40 and 9 is 360

40 * 9 = 360

360 = 360

The BN structure model with more than 10 nodes can be established. The structure refers to the way the variables are related.

A Bayesian Network (BN) is a probabilistic graphical model that illustrates a set of variables and their probabilistic dependencies. A BN structure is made up of nodes and edges. Nodes represent variables, and edges represent the connections between the variables. The BN structure model can be established by using various algorithms, including structure learning and parameter learning.The BN structure with more than 10 nodes is a complex model with numerous variables and their dependencies. The structure's meaning is how the variables are interrelated, allowing us to estimate the probabilities of certain events or scenarios. The nodes in the structure represent various factors that affect the outcome of an event, and the edges between them demonstrate how these factors are related.The BN structure model is used in many fields, including medical diagnosis, fault diagnosis, and decision making.

The Bayesian Network structure model with more than 10 nodes is a powerful tool for analyzing complex systems. It helps to understand the interrelationships between variables and estimate the probabilities of different events or scenarios. This model is useful in various fields and provides insights into many complex phenomena.

To know more about Nodes visit:

brainly.com/question/32227668

#SPJ11

Step-by-step explanation:

Slope is equal to the change in y over the change in x, or rise over run.

\(m = \frac{change \: in \: y}{change in \: x\: } \)

The change in x is equal to the difference in x-coordinates (also called run), and the change in y is equal to the difference in y-coordinates (also called rise).

\(m = \frac{y2 - y1}{x2 - x1} \)

Substitute in the values of x and y into the equation to find the slope.

\(m = \frac{ - 4 - ( - 4)}{9 - (4)} \)

Simplify.

\(m = 0\)

Therefor, The slope is 0.

Answer:

Slope: 0

Step-by-step explanation:

The formula to finding slope is \(\frac{y1-y2}{x1-x2}\)

We have the points (4,-4) and (9,-4)

So plug in:

\(\frac{-4-(-4)}{4-9}\)

Simplify:

\(\frac{0}{-5}\)

Slope: 0

Answer:

the first one

Step-by-step explanation:

It passes the vertical line test

Answer: The first one.

Step-by-step explanation:

Area of △CMB ≈ 23.33 in² ,Area of △AMC ≈ 52.50 in²,Area of △ABC ≈ 75.83 in².

The problem step by step.

Given that AM:MB = 3:2, we can express the areas of triangles △CMB, △AMC, and △ABC in terms of their corresponding sides.

1. Area of △CNB = 35 in²

Since N is the midpoint of CM, we know that the ratio of the areas of △CNB and △CMB is the same as the ratio of their corresponding bases. Therefore, the area of △CMB can be determined as follows:

Area of △CMB = (2/3) * Area of △CNB = (2/3) * 35 = 70/3 in² ≈ 23.33 in²

2. Area of △AMC

Since AM:MB = 3:2, we can consider the area ratio as the square of the side ratio. Therefore, the area of △AMC can be determined as follows:

Area of △AMC = (3/2)² * Area of △CMB = (9/4) * (70/3) = 630/12 in² ≈ 52.50 in²

3. Area of △ABC

The area of △ABC can be obtained by summing the areas of △CMB and △AMC:

Area of △ABC = Area of △CMB + Area of △AMC = 70/3 + 630/12 = 280/12 + 630/12 = 910/12 in² ≈ 75.83 in²

To summarize:

Area of △CMB ≈ 23.33 in²

Area of △AMC ≈ 52.50 in²

Area of △ABC ≈ 75.83 in²

For more questions  on Area .

https://brainly.com/question/2607596

#SPJ8

Step-by-step explanation:

Convert kilogram into gram first.

\(1 kg = 1000g\)

\(2kg = 1000 \times 2 \\ = 2000\)

a:b = a/b

125:2000= 125/2000

If u divide u get

1/16

a:b = a/b

1/16= 1:16

Ratio is now found.

Answer:

2 kg = 2000 gms

So, ratio of 2kg to 250 gms is 2000/250 = 8:1 or we can write

2kg:250::8:1

In words, we say 2 kg or 2000 gms to 250 gms ratio is as 8 is to 1

Step-by-step explanation:

was it helpful

The midpoint has coordinates (19,19) as per the midpoint formula.

The statement is false.

The statement is false. The midpoint of the segment joining two points is determined by taking the average of their x-coordinates and the average of their y-coordinates. In this case, the two given points are (0,0) and (38,38).

To find the x-coordinate of the midpoint, we take the average of the x-coordinates of the two points:

(x1 + x2) / 2

= (0 + 38) / 2

= 38 / 2

= 19

Therefore, the x-coordinate of the midpoint is 19, which matches the statement. However, to determine if the statement is true or false, we also need to check the y-coordinate.

To find the y-coordinate of the midpoint, we take the average of the y-coordinates of the two points:

(y1 + y2) / 2

= (0 + 38) / 2

= 38 / 2

= 19

The y-coordinate of the midpoint is also 19. Therefore, the coordinates of the midpoint are (19,19), not 19 as stated in the statement. Since the midpoint has coordinates (19,19), the statement is false.

To learn more about the midpoint;

https://brainly.com/question/28224145

#SPJ4

The given expression is

The first option is correct.

The fourth option is correct.

Adding 8 and 15, we get

The second option is correct.

The segment lengths for this triangle are given as follows:

Similar triangles are triangles that share these two features given as follows:

There are three triangles in this problem, all of which are similar.

The length of segment PX can be obtained with triangles PQR and PXY, as follows:

PX/30 = 10/40

PX/30 = 1/4

4PX = 30

PX = 7.5.

The length of segment XQ is found applying the segment addition postulate, as follows:

PQ + XQ = 30

7.5 + XQ = 30

XQ = 22.5.

The length of segment XY can also be obtained with the similarity of triangles PXY and PQR, as follows:

XY/36 = 10/40

XY/36 = 1/4

4XY = 36

XY = 9.

The length of segment ZW is obtained with the similarity of triangles PZW and PQR, as follows:

ZW/36 = 24/40

ZW/36 = 0.6.

ZW = 36 x 0.6

ZW = 21.6.

More can be learned about similar triangles at brainly.com/question/14285697

#SPJ1

well, let's move like the crab, backwards, let's start with b), then we'll do a)

b)

\({\Large \begin{array}{llll} y=ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=2\\ y=75 \end{cases}\implies 75=ab^2 \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=5\\ y=9375 \end{cases}\implies 9375=ab^5\implies 9375=ab^{2+3}\implies 9375=ab^2 b^3\)

\(\stackrel{\textit{substituting from the 1st equation}}{9375=\underset{ab^2}{(75)} b^3}\implies \cfrac{9375}{75}=b^3\implies 125=b^3 \\\\\\ \sqrt[3]{125}=b\implies \boxed{5=b}\hspace{5em}\stackrel{\textit{we know that}}{75=ab^2}\implies 75=a5^2\implies 75=25a \\\\\\ \cfrac{75}{25}=a\implies \boxed{3=a}\hspace{5em} {\Large \begin{array}{llll} y = 3(5^x) \end{array}}\)

a)

\(\begin{cases} x=0\\ y=j \end{cases}\implies j=3(5^0)\implies j=3(1)\implies j=3 \\\\\\ \begin{cases} x=4\\ y=k \end{cases}\implies k=3(5^4)\implies k=3(625)\implies k=1875\)