a satellite is composed of 30 modular units, each of which is equipped with a set of sensors, some of which have been upgraded. each unit contains the same number of non-upgraded sensors. if the number of non-upgraded sensors on one unit is 15 the total number of upgraded sensors on the entire satellite, what fraction of the sensors on the satellite have been upgraded?

Answer: y= (x+2)^2 + 7

Step-by-step explanation:

y= (x+2)^2 + 7

y = (x+2) (x+2) +7

y= x^2 + 2x + 2x + 4 +7

y= x^2 + 4x + 11

The probability of choosing a fruit snack replaced and then choosing a granola bar is 5/36.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Given, Mellisa has options to choose from 3 different snacks,

N(GB) = 4, N(C) = 3, and N(FS) = 5.

So, The sample space N(S) = N(GB) + N(C) + N(FS).

N(S) = 12.

The probability of choosing a fruit snack is,

P(FS)

= N(FS)/N(S).

= 5/12.

Given, She puts it back so replaced and hence the events are independent.

So, The probability of choosing a granola P(GB) = N(GB)/N(S).

= 4/12.

= 1/3.

Therefore The combined probability is (5/12)×(1/3).

= 5/36.

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Answer:

x = 5.4

Step-by-step explanation:

[tex]\frac{7.2}{4}[/tex] = [tex]\frac{x}{3}[/tex]  Cross multiple and solve for x

4x = (7.2 x3)

4x = 21.6  Divide both sides by 4

x = 5.4

Answer:

x = 5.4

Step-by-step explanation:

[tex]\frac{x}{7.2} =\frac{3}{4}[/tex]

[tex]x=\frac{(7.2)(3)}{4} =\frac{21.6}{4} =5.4[/tex]

Hope this helps

The system is consistent and independent.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

We have the system of equations:

y = 4x - 4

y = -4x + 4.

Let's take the quotient between both the equations as;

(y/y) = (4x - 4)/(-4x + 4)

1 = (4x - 4)/(-4x + 4)

Solve for x;

1*(-4x + 4) = 4x - 4

-4*x + 4 = 4x - 4

-4x - 4x = -4 - 4

-8*x = -8

x = -8/-8 = 1.

To find the value of y, we can input this value of x in one of the equations:

y = 4 x1 - 4 = 0.

Then we have only one solution, (1, 0).

Therefore, the system is consistent and independent.

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Using linear pairs, [tex]y=102[/tex].

Using the angle sum in [tex]\triangle TRS[/tex], [tex]x=70[/tex].

Answer:

47.46

Step-by-step explanation:

Answer: The answer is A. 47.46°.

Step-by-step explanation: Hope this helps.

The complex number (25 + 22i)² in simplest form a + ib is 141 + 1100i

A complex number is a number in the form z = x + iy where

To find the complex number (25 + 22i)² in the form a + ib, we proceed as follws.

(25 + 22i)² = (25 + 22i)((25 + 22i)

Expanding the brackets, we have that

(25 + 22i)² = (25 + 22i)((25 + 22i)

(25 + 22i)² = [25 × 25 + 25 × 22i + 25 × 21 + (22i)²]

(25 + 22i)² = [625 + 550i + 550i + 484i²]

(25 + 22i)² = [625 + 550i + 550i + 484 × (-1)] Since i² = -1

(25 + 22i)² = [625 + 550i + 550i - 484]

Collecting like terms, we have that

(25 + 22i)² = [625 - 484 + 550i + 550i]

(25 + 22i)² = 141 + 1100i

So, (25 + 22i)² = 141 + 1100i

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Ordered pair (3, 1) and (3, 2) causes the relation to not be a function; The same x-value has different y-values.

How do you find out if a set of ordered pairs is a function or not?

For a set of ordered pairs to be a function, there must not be any two points that have the same first elements. This means that, the

x-coordinates must not repeat for any two given points.

According to the given question:

Given ordered pairs of a relation are

(0, 0.5), (0.5, 1), (3, 1), (1, 6), (3, 2)

Domain set of the relation= {0, 0.5, 1, 3}

Co-Domain set of the relation = {0.5, 1, 2, 6}

Clearly the image of the x-coordinate 3 is not unique.

Hence, (3, 1) and (3, 2); The same x-value has different y-values.

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f(x) +g(x)= (3x-2)+(5x+2)

=3x-2+5x+2 (-2or +2 become cancelled )

=3x+5x

8x

x = 18

The Distance from point A to point B is: 3.4 ft when θ = 28° and The value of θ is: 54.8°

Given,

A spring is attached at one end to support B and at the other end to collar A.

Part A:  Reference angle (θ) = 28°

We have to find out the distance of point A to point B.

Adjacent = 3 ft (given)

Apply the trigonometry function to find AB

cos θ = adj / hypotenuse

Substituting all the values ,

cos 28°= 3/AB

AB = 3/cos 28°

 AB = 3.4 ft (nearest tenth of a foot)

Part B:

It is given that Distance  from point A to point B is 5.2 feet

We have to calculate the Value of θ

adjacent = 3 ft

hypotenuse = AB = 5.3 ft

To find θ , We will again apply the trigonometry function

cos θ = adjacent/hypotenuse

Substituting all the given values

cos θ = 3/5.3

θ = cos⁻¹ ( 3 / 5.3)

θ = 54.8°

That is,

The length of point A to point B is 3.4 feet

The value of θ is 54.8°

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Answer:

124

Step-by-step explanation:

1,240/10 is 124. You divide by 10.

The number of packages of 10 for the 1240 pot holders is 124.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of pot holders = 1240

Number of pot holders in one pack = 10

The number of packages.

= 1240 ÷ 10

= 1240/10

= 124

Thus,

The number of packages of 10 is 124.

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range(2,11,2) because range is a tool for defining a range between two numbers and adding a step value.

Range is the difference between the highest and lowest values ​​in a range of numbers. To calculate the range, subtract the smallest number from the largest number in the set.

The number in a list or set between the lowest and maximum is referred to as a range. Line up all the numbers before locating the region. After that, take away (get rid of) the lowest number from the greatest number. The solution provides the list's range.

range(2,11,2) because range is used to create a range between number and add step value

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A table of values that represents a proportional relationship must have a constant rate and must pass through the origin

From the question, we have the following parameters that can be used in our computation:

A table that is has proportional relation

A table of values can be represented as

x    y

a    b

c   d

......

.....

For the table of values to be proportional, the following must be true

x    y

0    0

a    b

c   d

......

.....

Also, it must have a constant ratio

i.e. b/a = d/c

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The inverse of y = √x - 10 + 4 is y = x^2 + 26 + 8x

What in mathematics is inverse?

A function that "undoes" another function is known as an inverse in mathematics. To put it another way, if f(x) produces y, then y will produce x when y is fed into f's inverse function. Invertible refers to a function that has an inverse, which is represented by the symbol f1.

Given that:

J(x) = √x - 10 + 4

y = √x - 10 + 4

now replace x with y

x = √y - 10 + 4

now solve for y , x = √y - 10 + 4

x + 4= √y - 10

Squaring both the side

x^2 + 16 + 8x = y - 10

y = x^2 + 26 + 8x

Hence the inverse of y = √x - 10 + 4 is y = x^2 + 26 + 8x

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The height of the tail post is 13.74 m.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given that, after travelling 11.45 metres from her school, she lays a flat mirror on the ground in the center, with an x drawn on it. When she can clearly see the top of the goalpost depicted in the x.

She moves 1.25 metres to the other side of the mirror. Her spouse calculates that there are 1.15 metres between her eyes and the earth.

Suppose the height of the tail post is x,

The geometric relation is,

1.5/1.25 = x/11.45

Apply cross multiplication

1.5×11.45=1.25x

17.175=1.25x

Divide both sides by 1.25

x=13.74

Hence,  if she moves 1.25 metres to the other side of the mirror. Her spouse calculates that there are 1.25 metres between her eyes and the earth. The height of the tail post is 13.74 m.

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The inequality for the given situation is 25,000x-20,000,000≤5,000,000 and the solution for the obtained inequality is x≤1000.

Given that, it costs chevy $20,000,000 to develop and market a new model of cars.

The profit or gain is equal to the selling price minus the cost price. Loss is equal to the cost price minus the selling price.

Let the number of cars sold be x.

So, selling price of cars is $25,000x

Profit =Selling price-Cost price

⇒ 25,000x-20,000,000≤5,000,000

Solve the inequality

Add 20,000,000 on both the sides of an inequality, we get

25,000x≤25,000,000

⇒ x≤25,000,000/25,000

⇒ x≤1000

Therefore, the inequality for the given situation is 25,000x-20,000,000≤5,000,000 and the solution for the obtained inequality is x≤1000.

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Answer: I mean- can you found it out yourself by studying. There's your answer.

Step-by-step explanation:

just study not cheat.

Answer:

8 and 4

Step-by-step explanation:

Answer: 8 and 4

Step-by-step explanation:

Total ways of required selection is 686, obtained from the sum of the cases of 3, 4 and 5 women in the committee.

Combinations are mathematical operations that count the variety of configurations that can be made from a set of objects, where the order of the selection is irrelevant. You can choose any combination of the things in combinations.

Given that 5 persons are to be selected with a condition of minimum 3 women. Therefore the different possibilities are:

1) 3 women and 2 men

2) 4 women and 1 man

3) 5 women

Final answer will be the sum of the above results.

Total ways to select 3 women from 6 women and 2 men from 8 men,

Total ways =  ⁶C₃ * ⁸C₂

Similarly total ways for 4 women and 1 man =  ⁶C₄ * ⁸C₁

Total ways for 5 women = ⁶C₅ * ⁸C₀

Add the three results to get the final answer,

Total number of ways = (⁶C₃ * ⁸C₂) + (⁶C₄ * ⁸C₁ ) + (⁶C₅ * ⁸C₀)

Total number of ways = 560 + 120 + 6 = 686

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Answer:

  4619 inches

Step-by-step explanation:

You want the length of side g in ∆GHI where G=102°, H=10°, and h=820 inches.

The law of sines tells us ...

  g/sin(G) = h/sin(H)

  g = h·sin(G)/sin(H) = (820 in)sin(102°)/sin(10°)

  g ≈ 4619 in

The length of side g is 4619 inches.

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Answer: x = 7

Step-by-step explanation:

Sum of the interior angles of a triangle must equal 180.

41 + (7x) + 90 = 180

7x = 180 - 90 - 41

7x = 49

x = 49/7 = 7

After solving the equation we know ABCD is a parallelogram.

What is parallelogram?

A parallelogram is a two-dimensional shape with four straight sides. All of the sides are equal in length and the opposite sides are parallel. Additionally, opposite angles are also equal. The shape is called a parallelogram because parallel lines are present on either side. Parallelograms can come in many different forms, such as rectangles and rhombuses. The properties of a parallelogram include the fact that the diagonal line that divides the parallelogram into two halves bisects the angles. Additionally, the cross product of the two diagonals is equal to the area of the parallelogram. Parallelograms are used in a variety of areas, including architecture, engineering, and mathematics. Depending on the application, parallelograms can be used to construct a variety of shapes, such as circles and ellipses.

Given: A (2,5), B (7,6), C (6,2), D (1,1)

AB ⇒ A (2,5), B (7,6) = [tex]\sqrt{(x_{2}-x_{1} ) ^{2} +(y_{2}-y_{1} )^{2} }[/tex]

⇒ [tex]\sqrt{(-5+1)^{2}+(-6-2)^{2} }[/tex]

⇒ [tex]\sqrt{(-4)^2+(-8)^{2} }[/tex]

⇒ [tex]\sqrt{16+64} =\sqrt{80}[/tex]

CD ⇒ C (6,2), D (1,1) = [tex]\sqrt{(x_{2}-x_{1} ) ^{2} +(y_{2}-y_{1} )^{2} }[/tex]

⇒ [tex]\sqrt{(7-3)^{2}+(6+2)^{2} }[/tex]

⇒ [tex]\sqrt{(4)^2+(8)^{2} }[/tex]

⇒ [tex]\sqrt{16+64} =\sqrt{80}[/tex]

BC = B (7,6), C (6,2) ⇒ [tex]\sqrt{(x_{2}-x_{1} ) ^{2} +(y_{2}-y_{1} )^{2} }[/tex]

⇒ [tex]\sqrt{(3+5)^{2}+(-2+6)^{2} }[/tex]

⇒ [tex]\sqrt{(8)^{2} +(4)^{2} }[/tex]

⇒ [tex]\sqrt{16+64} =\sqrt{80}[/tex]

AD ⇒ A (2,5), D (1,1) = [tex]\sqrt{(x_{2}-x_{1} ) ^{2} +(y_{2}-y_{1} )^{2} }[/tex]

⇒ [tex]\sqrt{(7+1)^{2}+(6-2)^{2} }[/tex]

⇒ [tex]\sqrt{(8)^{2} +(4)^{2} }[/tex]

⇒ [tex]\sqrt{16+64} =\sqrt{80}[/tex]

As, AB = CD = BC = AD all sides are equal.

Hence proved, ABCD is a parallelogram.

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The equation of the parabola that has a force at (3, 9) and directrix at y = -5 will be x² - 6x + 65 = 28y.

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

Let (x, y) be the locus point. Then the equation is given as,

(x - 3)² + (y - 9)² = (y - 5)²

Simplify the equation, then we have

(x - 3)² + (y - 9)² = (y - 5)²

x² - 6x + 9 + y² - 18y + 81 = y² + 10y + 25

x² - 6x + 65 = 28y

The equation of the parabola will be x² - 6x + 65 = 28y.

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The product of matrices A and B is matrix C

a)  [tex]C = (3 )[/tex]

b)  [tex]C = \begin{pmatrix}-30\end{pmatrix}[/tex]

c)  [tex]C = \begin{pmatrix}14&20\end{pmatrix}[/tex]

d)  [tex]C =\begin{pmatrix}20&5\end{pmatrix}[/tex]

What is multiplication of matrices?

The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. The first matrix must have the same number of columns as the second matrix has rows. The number of rows of the resulting matrix equals the number of rows of the first matrix, and the number of columns of the resulting matrix equals the number of columns of the second matrix

Given data ,

a)

Let the 2 matrices be A and B

The value of matrix A is

[tex]A = \begin{pmatrix}4&5\end{pmatrix}[/tex]

The value of matrix B is

[tex]B = \begin{pmatrix}2\\ \:-1\end{pmatrix}[/tex]

The product of matrix A and B is C

The value of matrix C is

[tex]C = \begin{pmatrix}4&5\end{pmatrix}\begin{pmatrix}2\\ -1\end{pmatrix}[/tex]

On simplifying the matrix C , we get

[tex]C = \begin{pmatrix}4\cdot \:2+5\left(-1\right)\end{pmatrix}[/tex]

[tex]C = (3 )[/tex]

Therefore , the value of matrix C is [tex]C = (3 )[/tex]

b)

Let the 2 matrices be A and B

The value of matrix A is

[tex]A = \begin{pmatrix}2&6\end{pmatrix}[/tex]

The value of matrix B is

[tex]B = \begin{pmatrix}-3\\ \:-4\end{pmatrix}[/tex]

The product of matrix A and B is C

The value of matrix C is

[tex]C = \begin{pmatrix}2&6\end{pmatrix}\begin{pmatrix}-3\\ -4\end{pmatrix}[/tex]

On simplifying the matrix C , we get

[tex]C = \begin{pmatrix}2\left(-3\right)+6\left(-4\right)\end{pmatrix}[/tex]

[tex]C = \begin{pmatrix}-30\end{pmatrix}[/tex]

Therefore , the value of matrix C is  [tex]C = \begin{pmatrix}-30\end{pmatrix}[/tex]

c)

Let the 2 matrices be A and B

The value of matrix A is

[tex]A = \begin{pmatrix}1&2\end{pmatrix}[/tex]

The value of matrix B is

[tex]B = \begin{pmatrix}4&6\\ 5&7\end{pmatrix}[/tex]

The product of matrix A and B is C

The value of matrix C is

[tex]C =\begin{pmatrix}1&2\end{pmatrix}\begin{pmatrix}4&6\\ 5&7\end{pmatrix}[/tex]

On simplifying the matrix C , we get

[tex]C = \begin{pmatrix}1\cdot \:4+2\cdot \:5&1\cdot \:6+2\cdot \:7\end{pmatrix}[/tex]

[tex]C = \begin{pmatrix}14&20\end{pmatrix}[/tex]

Therefore , the value of matrix C is  [tex]C = \begin{pmatrix}14&20\end{pmatrix}[/tex]

d)

Let the 2 matrices be A and B

The value of matrix A is

[tex]A = \begin{pmatrix}0&5\end{pmatrix}[/tex]

The value of matrix B is

[tex]B = \begin{pmatrix}3&6\\ 4&1\end{pmatrix}[/tex]

The product of matrix A and B is C

The value of matrix C is

[tex]C =\begin{pmatrix}0&5\end{pmatrix}\begin{pmatrix}3&6\\ 4&1\end{pmatrix}[/tex]

On simplifying the matrix C , we get

[tex]C = \begin{pmatrix}0\cdot \:3+5\cdot \:4&0\cdot \:6+5\cdot \:1\end{pmatrix}[/tex]

[tex]C =\begin{pmatrix}20&5\end{pmatrix}[/tex]

Therefore , the value of matrix C is  [tex]C =\begin{pmatrix}20&5\end{pmatrix}[/tex]

Hence ,

The product of matrices A and B is matrix C

a)  [tex]C = (3 )[/tex]

b)  [tex]C = \begin{pmatrix}-30\end{pmatrix}[/tex]

c)  [tex]C = \begin{pmatrix}14&20\end{pmatrix}[/tex]

d)  [tex]C =\begin{pmatrix}20&5\end{pmatrix}[/tex]

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An inequality that combines two simple inequalities is known as a compound inequality.

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The subject formula is v= 2s/t- u.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

s = 1/2(u+v)t

Now, we have to work for variable 'v'

2s = ( u+ v)t

2s/ t = u+ v

v= 2s/t- u

Hence, the subject formula is v= 2s/t- u.

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Answer:

Length = 50 ft

Width = 15 ft

Area = 750 ft²

Step-by-step explanation:

Define the variables:

Create two equations with the given information.

Given:

⇒ 3L = 10W

Given:

⇒ 2W + 2L = 130

Rearrange the second equation to make W the subject:

⇒ 2(W + L) = 130

⇒ W + L = 65

⇒ W = 65 - L

Substitute this into the first equation and solve for L:

⇒ 3L = 10(65 - L)

⇒ 3L = 650 - 10L

⇒ 13L = 650

⇒ L = 50

Substitute the found value of L into the second equation and solve for W:

⇒ 2W + 2(50) = 130

⇒ 2W + 100 = 130

⇒ 2W = 30

⇒ W = 15

Therefore:

Substitute the found values of W and L into the formula for area of a rectangle to find the area of the pool:

⇒ Area = W × L

⇒ Area = 15 × 50

⇒ Area = 750 ft²