There are 25 students in a class. How many ways can the teacher (randomly) pick two students for the lead roles in the class play?

Answer:

(y+17)÷18=22.5

y+17=22.5×18

y+17=405

y=405-17

y=388

By applying the definition of product between two square matrices, we find that [tex]\vec A \,\cdot \,\vec A = \left[\begin{array}{cc}1&2\\3&6\end{array}\right] \cdot \left[\begin{array}{cc}1&2\\3&6\end{array}\right][/tex] is equal to the matrix [tex]\vec A \,\cdot \,\vec A = \left[\begin{array}{cc}7&14\\21&42\end{array}\right][/tex]. (Correct choice: D)

In this question we must use the definition of product between two square matrices to determine the resulting construction:

[tex]\vec A \,\cdot \,\vec A = \left[\begin{array}{cc}1&2\\3&6\end{array}\right] \cdot \left[\begin{array}{cc}1&2\\3&6\end{array}\right][/tex]

[tex]\vec A \,\cdot \,\vec A = \left[\begin{array}{cc}7&14\\21&42\end{array}\right][/tex]

By applying the definition of product between two square matrices, we find that [tex]\vec A \,\cdot \,\vec A = \left[\begin{array}{cc}1&2\\3&6\end{array}\right] \cdot \left[\begin{array}{cc}1&2\\3&6\end{array}\right][/tex] is equal to the matrix [tex]\vec A \,\cdot \,\vec A = \left[\begin{array}{cc}7&14\\21&42\end{array}\right][/tex].

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Answer:

Yes

Step-by-step explanation: The answer is Side Angle Side (SAS)

Answer:

1/12

Step-by-step explanation:

Landing on the 5 is a 1/6 chance, landing on tails is a 1/2 chance, multiply, and you get 1/12

The exponential  equation that matches the coordinate is 3(2)^x while the linear equation is y = 6x

The standard exponential equation is expressed as y= ab^x

where

a is the base

x is the exponent

Given the coordinates (2, 12) and (4, 48)

12 = ab^2

48 = ab^4

Find the ratio

4 = b^2

b = 2

Sice ab^2 = 12

4a = 12

a = 3

The exponential  equation that matches the coordinate is 3(2)^x

For the linear equation

The standard form is y = mx + b

m is the slope = 48-12/4-2
Slope = 12/2

Slope = 6

For the y-intercept

12 = 6(2) + b

b = 0

Hence the required linear equation is. y = 6x

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The recursive definition of the geometric sequence is given as follows:

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

The recursive definition of the geometric sequence is given as follows:

For this sequence, the first term and common ratio are given as follows:

[tex]a_1 = \frac{1}{9}, q = 3[/tex].

Then the recursive definition is:

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The equation of a parabola with vertex at (-2, 2) and passes through (-3, 5) and (-1, 5) is y = 3x² + 12x + 14. The value of a in the equation is 3.

An equation is an expression that shows the relationship between two or more variables and numbers.

The graph of a quadratic equation has the shape of a parabola. The standard quadratic equation has the form:

y = ax² + bx + c

The equation of a parabola with vertex at (-2, 2) and passes through (-3, 5) and (-1, 5) is y = 3x² + 12x + 14. The value of a in the equation is 3.

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Answer:

The correct answer is A:3

Step-by-step explanation:

The statement that would most likely have a negative linear correlation coefficient is amount of money spent on baby food as a child ages

Correlation coefficient is the value that relates two variables in question. Correlation can be positive, negative or no correlation

Note that the correlation coefficients are only values from 0 and 1. The statement that would most likely have a negative linear correlation coefficient is amount of money spent on baby food as a child ages

The amount of money spent on a baby is never a function of its age. The baby will age regardless.

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Answer:

x = 42

Step-by-step explanation:

Cross multiplying is done as follows:

the denominator of the second fraction is multiplied with the numerator of the first equation and denominator of the first fraction is multiplied with the numerator of the second equation

5(3x+6) = 4(4x-3) multiply inside the parenthesis

15x + 30 = 16x - 12 transfer like terms to same side of the equation

30 + 12 = 16x - 15x

42 = x

The price of shirt is $12 and the price of tie is $2.5.

According to the statement

We have given that:

Let money spent on shirt = X and money spent on tie is Y.

So, 6X + 3Y = $79.5 and 3X + 2Y = $41 then

We have to find the the cost of each shirts.

Here we use the Elimination method.

Now,

6X + 3Y = $79.5  -(1)

3X + 2Y = $41  -(2)

By elimination method

Multiply (1) by 3 and (2) by 6 then

18X + 9Y = $238.5

18X + 12Y = $246

Then solve it and equation become

-3Y = -$7.5

Y = 2.5

It means the cost of tie is $2.5 and now the cost of shirt is

6X + 3Y = $79.5  

6X + 3(2.5) = $79.5  

6X + 7.5 = $79.5  

6X = $72

X = $12.

So, The price of shirt is $12 and the price of tie is $2.5.

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Domain refers to the term which best describes the set of all possible input values for a function and is therefore denoted as option C.

These are all the values which go into a function which is defined and is denoted as the sign below:

dom · ( f ).

They are also among the values which form the independent variables in this type of context while on the other hand, the output is referred to as the range.

These set of values are usually inputted into the function to check its acceptability and also retrieve the output gotten from the type of operation given. It is also used to identify the independent variable which are present thereby making it the most appropriate choice.

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The average force exerted on the ball during the serve is 57 N the resistive force is -1125 N.

a. Average force

Using  this formula

Force (F) = Mass ×Acceleration

Where:

Mass (m) = 57 g = 57 / 1000= 0.057 Kg

Acceleration (a) = u / t = 50 / 0.05 = 1000 m/s²

Let plug in the formula

Force (F) = 0.057 × 1000

Force (F) = 57 N

b. Resistive force

F = m(v – u) / t

Where:

Force (F) = ?

Mass (m) = 3000 Kg

Initial velocity (u) = 72 Km/h = 72 / 3.6 = 20 m/s

Final velocity (v) = 18 Km/h = 18 / 3.6 = 5 m/s

Time (t) = 40s

Let plug in the formula

Force = 3000(5 – 20) / 40

Force = 3000(-15) / 40

Force=-45,000/40

Force = -1125 N

Therefore the average force exerted on the ball during the serve is 57 N the resistive force is -1125 N.

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Answer: 3/4

Step-by-step explanation:

Parallel lines have the same slope.

Answer:

[tex]a=22, b=11\sqrt{3}[/tex]

Step-by-step explanation:

Given a 30-60-90 triangle, the shortest side is always opposite of the smallest angle, in this case 11 is opposite the 30° angle. The largest side of a 30-60-90 triangle will always be twice the smallest, giving [tex]a[/tex] a measure of [tex]22[/tex]. To get the side across the 60° angle we multiply the smallest side by the square root of 3. Meaning [tex]b=11\sqrt{3}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathsf{12:9}[/tex]

[tex]\huge\textbf{Simplifying:}[/tex]

[tex]\mathsf{12:9}[/tex]

[tex]\mathsf{= 12\div3 : 9 \div 3}[/tex]

[tex]\mathsf{= 4:3}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{4:3}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

  (c)  0.18

Step-by-step explanation:

If the x-values are exhaustive, then the p(X=x) values must total 1.00.

  0.11 +? +0.62 +0.09 = 1.00

  0.82 +? = 1.00 . . . . . . . simplify

  ? = 0.18 . . . . . . . . . subtract 0.82

P(X=3) = 0.18

Using an exponential function, it is found that the decay rate is of 6.24% a year.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

The half-life is of 10.75 years, hence A(10.75) = 0.5A(0) and this is used to find the decay rate r.

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]0.5A(0) = A(0)(1 - r)^{10.75}[/tex]

[tex](1 - r)^{10.75} = 0.5[/tex]

[tex]\sqrt[10.75]{(1 - r)^{10.75}} = \sqrt[10.75]{0.5}[/tex]

[tex]1 - r = (0.5)^{\frac{1}{10.75}}[/tex]

1 - r = 0.9376.

r = 1 - 0.9376.

r = 0.0624.

The decay rate is of 6.24% a year.

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The angle of elevation that the instruments have to record to be at the correct height is given as 79°

We have 2x + 70 = 180

We have to find the value of x

2x = 110

x = 55

y/sin x = 225/sin70

This is the use of sine rule

From here we would have

y = 225(sinx/sin70)

Remember x = 55

y =  225(sin55/sin70)

y = 196.1378

tanθ = 1000/y

tan θ = 1000/196.1378

tanθ = 5.098

θ = tan⁻¹5.098

= 78.90°

Hence the conclusion is that the angle of elevation has to be 78.9 degrees for it to be at the correct height.

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Answer:

1/3

Step-by-step explanation:

The numbers are 1, 2, 3, 4, 5, and 6.

Both 3 and 6 are multiples of 3.

So, 2/6 is the probability since there is an equal change that the arrow will land on each section.

This simplifies to 1/3.

Brainliest, please :)

Answer:

P (multiple of 3) =  [tex]\bf \frac{1}{3}[/tex]

Step-by-step explanation:

Numbers on the spinner, ξ = {1, 2, 3, 4, 5, 6}    (6 elements)

Multiples of 3 = {3, 6}   (2 elements)

P (multiple of 3) = no. of multiples of 3 / total no. of numbers on spinner

                          =  [tex]\frac{2}{6}[/tex]

                          =  [tex]\bf \frac{1}{3}[/tex]

11. m ∠ BCE = 25 °

m ∠BAD = 39°

12. n = 11. 5°

13. The quadrilaterals are rectangle and parallelogram. Option A and C

14. HK = 8cm

11. From the figure shown, we have that;

m ∠ EBC = 27°

m ∠ ADE = 52°

To find

m ∠ BCE

Note that m ∠ ADE is alternate and equal to m∠ DEC = 52 and is also on a straight line with ∠BEC

52 +  ∠BEC = 180°

∠BEC = 180 - 52° = 128°

Remember that  ∠BEC,  ∠ BCE  and ∠ EBC are angles in a triangle which sum up to 180°

128° +  ∠ BCE + 27° = 180°

∠ BCE = 180 ° - 155°

∠ BCE = 25 °

To determine m ∠BAD

65° +  76 + m ∠BAD = 180° , sum of angles in a a triangle

m ∠BAD = 180 - 141

m ∠BAD = 39°

12. Value of n is gotten by equating the two lengths

( 10n + 19) = (12n - 4)

collect like terms

10n - 12n = -4 - 19

- 2n = -23

n = -23/-2

n = 11. 5°

13. The only quadrilaterals with congruent diagonals are;

14.  To find line HK

Substract the shortest line, IJ from the longest line GL

HK = GL - IJ

HK = 15 - 7

HK = 8cm

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Answer:

x = 6

Step-by-step explanation:

y = -8

x = 8

-x = -8 = y

-x = y

now, when y is -6

-x = y = -6

-x = -6

x = 6

The value of f left parenthesis 3 right parenthesis is 45.

According to the statement

We have given that the F(x) = 5(x)^2

and we have to find the value when Sophia have a 3 right parenthesis.

So, Parenthesis are used in mathematical expressions to denote modifications to normal order of operations.

And now we have to find the value for 3 right parenthesis

And for this purpose we have to put the value X= 3 in the f(x) then

F(x) = 5(x)^2

F(3) = 5(3)^2

F(3) = 5*9

F(3) = 45.

here the value of 3 right parenthesis is 45.

So, The value of f left parenthesis 3 right parenthesis is 45.

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The parameters of the sinusoidal function graphs can be found from the coordinates of the given locations.

First graph;

a. Amplitude = 0.5

b. The period = 2•π

c. The horizontal shift = 1

d. The vertical shift = π/4

Second graph;

a. Amplitude = 2

b. The period = π

c. The horizontal shift = -π/4

d. The vertical shift = -2

First graph;

a. The amplitude is half the distance between the y-value peak point and the y-value of a throw (lowest point) on the graph.

The coordinate of a peak point in the first graph is (0, -1.5)

The coordinate of a throw point is (π/2, -2.5)

Therefore;

Amplitude = (-1.5 - (-2.5)) ÷ 2 = 0.5

b. The period is the number of cycles per second, we have;

From the graph, we have;

Therefore;

The frequency = 1/π cycle per unit length

c. The horizontal shift is the distance from the closet intersection of the midline and the rising region of the graph and the y-axis.

Therefore;

The horizontal shift = (-π/2)/2 = -π/4

d. The vertical shift is the distance from the horizontal axis to the midline of the graph.

By observation, the midline is y = -2

Therefore;

Second Graph;

For the second graph, we have;

a. Amplitude = (3 - (-1))/2 = 2

b. Frequency = 1/(2×(5•π/4 - π/4)) = 1/(2•π)

Therefore;

c. Horizontal shift = Distance between x-coordinate of the intersection of the midline and the graph and the x-coordinate of the closest peak.

Therefore;

d. Vertical shift = (3 + (-1))/2 = 1

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Answer:

90

Step-by-step explanation:

Why cant people just answer questions without guessing or answer them correctly.

Answer:

11.2 square meters

Step-by-step explanation:

This is a very simple question. Basically, it's the area of a rectangle with the area of a circle subtracted. The area of a circle is calculated with the following formula:

[tex]\pi \times r^{2} [/tex]

Where r is the radius. We know the diameter is 1m, so we can simply halve this value to find the radius of 0.5m. Substituting in this value, we find the area of the circle to be:

[tex]\pi \times {0.5}^{2} \approx0.78539816339744830961566[/tex]

Now let's calculate the area of the rectangle, which is simply 3x4=12. Subtracting our earlier value from 12, we are left with an answer of 11.2 (to 1 d.p)

The total area of the figure shown is 320 square units.

We can see that we have 4 triangular faces and one square face.

The area of a square of side length S is:

A = S²

Here we can see that the side length of the square is 10 units, then the area of the base is:

a = (10)² = 100

For a triangle of base B and height H, the area is:

[tex]A = B*H/2[/tex]

Here we can see that the base measures 10 units and the height 11 units, so the area of each triangular face is:

A' = (10)*(11)/2 = 55

Then the total area is:

area = 100 + 4*55 = 320

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Answer:

The solution is 25, 36, 49

Step-by-step explanation:

a = 1

b = 3

c = 5-3

= 2

________________________________

Un = [tex]\sf a + (n-1) \times b + \frac{(n-1)(n-2)}{2} \times c[/tex]

Un = [tex]\sf 1 + (n-1) \times 3 + \frac{(n-1)(n-2)}{2} \times 2[/tex]

Un = [tex]\sf 1 + 3n-3 + (n-1)(n-2)[/tex]

Un = [tex]\sf 1 + 3n-3 + n^{2} - 2n - n + 2[/tex]

Un = [tex]\sf n^{2} + 3n - 2n - n + 2 + 1 - 3[/tex]

Un = [tex]\sf n^{2} + 0n + 0[/tex]

Un = [tex]\sf n^2[/tex]

________________________________

Un = n²

U5 = 5²

= 25

U6 = 6²

= 36

U7 = 7²

= 49

________________________________

So, the next three members are 25, 36, 49

Two lines in a plane can intersect,overlap or be parallel.When two lines intersect they have a common point which lies on both line.This is called solution of the two simultaneous equation which when graphed represent straight lines. Adding the two equations uses  Elimination method to solve for x and y. The x and y value obtained is the common point lying on both the lines.

2x - 3y = 1

+ 2x + 3y = 2  

4x =3 Or x=3/4

Substituting x value in any of the two-equation we can find the corresponding y value .

2x-3y=1

2(3/4) - 3y =1

Solving for y

y= 1/6

The point of intersection of the two lines is ( 3/4, 1/6)

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