Scientists are sending a rover to the moon. Their plan is to study a rectangular area of the moon by placing a grid over the map as shown. On the grid, 1 unit represents 1 kilometer (km).

the Rover will land at (3.5,1) , explore up to (3.5,4), and then over (2,4).

PART A. what are the coordinates of the fourth vertex of the rectangle that the scientist plan to explore ?

PART B.
what is a horizontal length of the rectangle? what is the vertical length of the rectangle

PART C. find the area of the Moon exploration area in square kilometers. Show your work. ​

Determinants are defined only for square matrices, so I assume you are given the 3×3 matrix

[tex]A = \begin{bmatrix}-2 & -4 & -3 \\ -1 & -9 & -8 \\ -15 & -5 & 6 \end{bmatrix}[/tex]

Let's compute the determinant by taking the cofactor expansion along the first column:

[tex]\det A = -2 \det\begin{bmatrix}-9 & -8 \\ -5 & 6\end{bmatrix} + \det\begin{bmatrix}-4 & -3 \\ -5 & 6\end{bmatrix} - 15 \det \begin{bmatrix}-4 & -3 \\ -9 & -8\end{bmatrix}[/tex]

[tex]\det A = -2 ((-9)\times6-(-8)\times(-5)) + ((-4)\times6 - (-3)\times(-5)) \\ ~~~~~~~~~~~~~~~- 15 ((-4)\times(-8)-(-3)\times(-9))[/tex]

[tex]\det A = -2(-54-40) + (-24 - 15) - 15 (32 - 27)[/tex]

[tex]\det A = \boxed{74}[/tex]

Answer:The answer is 8 sides

Step-by-step explanation:

Using the normal distribution, considering it's symmetry, it is found that the value of C is of 2.19.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The standard normal distribution has mean and standard deviation given, respectively, by:

[tex]\mu = 0, \sigma = 1[/tex].

Hence, considering the symmetry of the normal distribution, the value of c is Z with a p-value of (1 + 0.9715)/2 = 0.98575, hence c = Z = 2.19.

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Answer:

$473

Step-by-step explanation:

We divide 5676 by 12 and we get 473

$473 they lose each month (?)

Step-by-step explanation:

calculator

Answer:

[tex] { - 7y}^{2} + 20y + 32[/tex]

Step-by-step explanation:

1.) -7y times y = -7y(squared)

2.) -7y times -4 = 28y

3.) -8 times y = -8y

4.) -8 times -4 = 32

5.) Combine like terms

[tex] { - 7y}^{2} + 28y - 8y + 32 = { - 7y}^{2} + 20y + 32[/tex]

Answer:

Depending on the unit your answer needs to be in, it would be 88 cubic feet or 3.25926 cubic yards

If your question asks you to round to the nearest hundredth it would be 3.26 cubic yards.

Step-by-step explanation:

To find the volume of soil:

Volume= Length x Width x Depth/Height

Volume= 44ft x 2ft x 1ft

Volume= 88 cubic feet or 3.25926  (there are 27 cubic feet in a cubic yard, 88/27=3.25926)

hope this helps! :)

Answer:

A,D,F

Step-by-step explanation: Because it not a fraction or decimal in it its an whole number

Answer:

a) There is a 59.87% probability that none of the LED light bulbs are defective.

b) There is a 31.51% probability that exactly one of the light bulbs is defective.

c) There is a 98.84% probability that two or fewer of the LED light bulbs are defective.

d) There is a 100% probability that three or more of the LED light bulbs are not defective.Step-by-step

explanation:

For each light bulb, there are only two possible outcomes. Either it fails, or it does not. This means that we use the binomial probability distribution to solve this problem.

Answer:

I think maybe u=6.71 but I'm not sure. wait for another answer

Answer:

A

Step-by-step explanation:

the domain is the definition of the valid x (input) values.

the range is the definition of the valid y (result) values.

as the function is defined by listing the specific points, the function only consists of individual points and not of connecting lines.

therefore the domain and range cannot be continuous intervals (otherwise the function would suddenly also include points not in the original list).

so, B and D are wrong.

and A is right, because the domain contains the x values, and the range the y values.

Answer:

0.341

Step-by-step explanation:

Multiply the probabilities: 0.55 * 0.62 = 0.341

Step-by-step explanation:

Scale factor red to blue meaning 42 to 7

42÷7=6

Scale factor is 6

Perimeter of the blue quadrilateral = ?

If perimeter of red = 204

Then we use this following proportion

[tex]204 \div 42 = x \div 7[/tex]

[tex] \frac{204}{42} = \frac{x}{7} [/tex]

Then we cross multiply

42x=7×204

42x=1428

x=34

Area of the blue quadrilateral = ?

If area of the red quadrilateral = 2880

Then we use the following proportion

[tex]2880 \div 42 = x \div 7[/tex]

[tex] \frac{2880}{42} = \frac{x}{7} [/tex]

Then we cross multiply

42x=2880×7

42x=20160

x=480

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

to get the slope of any straight line, we simply need two points off of it, so let's use the ones provided in that

[tex]\begin{array}{|cc|ll} \cline{1-2} \stackrel{years}{x}&\stackrel{population}{y}\\ \cline{1-2} 1990&1027974\\ 2013&688701\\ \cline{1-2} \end{array}\hspace{5em} (\stackrel{x_1}{1990}~,~\stackrel{y_1}{1027974})\qquad (\stackrel{x_2}{2013}~,~\stackrel{y_2}{688701}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{688701}-\stackrel{y1}{1027974}}}{\underset{run} {\underset{x_2}{2013}-\underset{x_1}{1990}}} \implies \cfrac{-339273}{23}\implies -14751\qquad \stackrel{rate~of}{change}[/tex]

let's notice, is negative since the population decreased.

The volume of the larger cylinder will be 36π cm³. Then the correct option is A.

The complete question is attached below.

A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.

The ratio of the volume to surface area will be

V / SA = πr²h / 2πrh

Then we have

Two similar cylinders have surface areas of 24 cm² and 54 cm².

The volume of the smaller cylinder is 16π cm³.

Then the volume of the larger cylinder will be

Let x be the volume of the larger cylinder.

Then we have

x / 54 = 16π / 24

      x = 36π cm³

Then the correct option is A.

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Answer: (6,3)

Step-by-step explanation:

Since C is 2 units from the line of reflection, and it lies on the left of the line of reflection, C' will lie 2 units to the right of the line of reflection.

Therefore, C'=(6,3).

The graph that represents function h is the graph in; Option C

The parent function is; f(x) = tan (x)

The transformed function is; h(x) = -tan(¹/₂x)

Now, from general tangent function we know that; y = tan(Bx)

Thus, period = π/(¹/₂)

From the given transformation that produced the h(x) function and when we look at the given graphs, the one that represents the function h is Option C.

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Answer:

[tex]p = 3\\\\q= 1[/tex]

Step-by-step explanation:

[tex]x^2 -6x +10\\\\=x^2 -2 \cdot 3x +3^2 -3^2 +10\\\\=(x-3)^2 -9+10\\\\=(x-3)^2 +1\\\\\text{By comparing with}~ (x-p)^2 +q, \\\\p = 3\\\\q = 1[/tex]

Answer:

to find for one divide 9 dollars 60 pounds by 3 to get the coast of one candy

The possible base and height of a second triangle are 12 and 7, respectively

An inverse variation is represented as:

Base * Height = k

Where k is the constant of variation.

In this case, k is the area

So, we have:

Base * Height  = Area

For the first triangle, we have:

14 * 6 = Area

Evaluate

Area = 84

Substitute Area = 84 in Base * Height  = Area

Base * Height  = 84

Express 84 as the product of two numbers

Base * Height  = 12 * 7

By comparison;

Base =12 and Height = 7

Hence, the possible base and height of a second triangle are 12 and 7, respectively

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The region that contains the most dispersed data is between the upper quartile and the median.

A box plot is used to study the distribution and level of a set of scores. The box plot consists of whiskers which measure the minimum and maximum numbers.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.  

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The equation of the line that is perpendicular to the line and passes through the point (15,-5) is y = -x + 10

The complete question is

What is the y-intercept of the equation of the line that is perpendicular to the line y = x + 10 and passes through the point (15, –5)?

A perpendicular means a line which intersects the other line at 90 degree.

Line given y = x+10

slope = 1

Slope of the line perpendicular to the above line = -1

and it passes through the point  (15, –5)

The equation will become

y = mx +c

-5 = -1 * 15 + c

15-5 = c

c = 10

Therefore the equation is y = -x +10

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Answer: d

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

Answer:

7x-4 = -28

4y+8 = 4(y + 2)

Step-by-step explanation:

Answer:

x ≤ 0

Step-by-step explanation:

The number line's direction is left, any number that is left on a number line behind zero has a less value. Greater than or equal!

[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=5.9 \end{cases}\implies V=\cfrac{4\pi (5.9)^3}{3}\implies V\approx 860.3~in^3[/tex]

Answer:

a = -3

b = 9

c = -3

Step-by-step explanation:

[tex]a. (2^{5} )(2)^{-8} =2^{a} \\2^{(5-8)} =2^{a} \\2^{-3}=2^{a}[/tex]

[tex]a=-3[/tex]

[tex]b.\frac{4^{7} }{4^{-2} } =4^{b} \\4^{(7-(-2))} } =4^{b} \\4^{(7+2)} =4^{b}[/tex]

[tex]4^{9} =4^{b}[/tex]

[tex]b=9[/tex]

[tex]c. \frac{7^{9} }{7^{c} } =7^{12}[/tex]

[tex]7^{9-c} =7^{12}[/tex]

[tex]9-c=12[/tex]

[tex]c=9-12[/tex]

[tex]c=-3[/tex]

Hope this helps

Step-by-step explanation:

similar shapes means that they have the same angles, and there is one scale factor that applies to all sides and other lines in the shapes (like heights).

therefore the ratios between 2 correlated lines are all the same.

so,

2/7 = 5/height

2×height / 7 = 5

2×height = 7×5 = 35

height = 35/2 = 17.5 in