Christian recorded the grade-level and instrument of everyone in the middle school School of Rock below.
Seventh Grade Students
Instrument # of Students
Guitar 6
Bass 4
Drums 7
Keyboard 2
Eighth Grade Students
Instrument # of Students
Guitar 4
Bass 15
Drums 13
Keyboard 6

Based on these results, express the probability that a student chosen at random will play the bass as a fraction in simplest form.

The square root of 625 is 25 and the square root of 25 is 5. Therefore, option A and F are the correct answers.

The square root of a number is the inverse operation of squaring a number. The square of a number is the value that is obtained when we multiply the number by itself, while the square root of a number is obtained by finding a number that when squared gives the original number.

A) [tex]625^{\frac{1}{2}[/tex]

= [tex](25^2)^{\frac{1}{2}[/tex]

= 25

F) 25

= 5

Therefore, option A and F are the correct answers.

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Answer:

605

Step-by-step explanation:

11x55=605

Answer:

Step-by-step explanation:

To solve this equation, we can start by using the identity cos(A-B) = cosAcosB + sinAsinB. Substituting A=sin x and B=1, we have:

2cos(sin x - 1) = cos(sin x)cos(1) + sin(sin x)sin(1)

We can then substitute this expression on the left-hand side of the original equation and simplify:

4sinxcosx^2 - 1 = cos(sin x)cos(1) + sin(sin x)sin(1)

Rearranging terms, we have:

4sinxcosx^2 - cos(sin x)cos(1) - sin(sin x)sin(1) = 1

We can now use the identity sin^2x+cos^2x=1 to simplify the left-hand side further:

4sinxcosx^2 - (sin^2x + cos^2x)cos(1) = 1

Simplifying further:

4sinxcosx^2 - (cosx)cos(1) = 1

Now we can divide both sides by cos(1):

4sinxcosx^2/cos(1) - cosx = 1/cos(1)

Rearranging terms:

cosx(4sinxcosx^2/cos(1) - 1) = 1/cos(1)

Finally, we can use the identity cos2x = 2cos^2x - 1 to simplify the left-hand side further:

(2cos^2x - 1)(4sinxcosx^2/cos(1) - 1) = 1/cos(1)

We can then divide both sides by (4sinxcosx^2/cos(1) - 1):

2cos^2x - 1 = 1/cos(1) (4sinxcosx^2/cos(1) - 1)

And finally, we can solve for cosx:

cosx =  1/2 + 1/2cos(1) (4sinxcosx^2/cos(1) - 1)

This is the solution to the equation.

Answer:

The cost of the water is $5.70.

Step-by-step explanation:

7.05-1.35=5.70 You just have to - 7.05 by 1.35

Answer:

1, 2, 3, 4, 6, 9, 12, 18, and 36.

Step-by-step explanation:

All of these are factors of 36.

They can all be divisors with no remainder

The slope of the line is C) [tex]\frac{6}{5}[/tex].

What is slope?

Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined. The difference between the line's y and x coordinate changes is known as the slope of the line. Any two distinct places along the line can be used to determine the slope of any line.

Here the given point is [tex](x_1,y_1)=(-5,-1)[/tex] and [tex](x_2,y_2)=(5,11)[/tex]

Now using slope formula then,

=> Slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> Slope m = [tex]\frac{11-(-1)}{5-(-5)}[/tex]

=> slope m = [tex]\frac{11+1}{5+5}[/tex]

=> slope m = [tex]\frac{12}{10}[/tex]

=> slope m = [tex]\frac{6}{5}[/tex]

Hence the slope of the line is C) [tex]\frac{6}{5}[/tex].

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The domain of the function is  (-∞, 1), (1, ∞).

the correct option is (C)

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

Given:

As, we know the domain are the input values in the function.

So, From the graph the domain starts from -∞ to reach 1 then there is change in slope.

Next the domain starts from  to ∞.

Now, range is the output value as (-4, 1).

Hence, the domain is (-∞, 1), (1, ∞).

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The list of all sets which are subsets of the given set; {Lennon, McCartney} as required is; { }, {Lennon}, {McCartney}, {Lennon, McCartney}.

It follows from the task content that the list of all subsets of the given set is to be determined.

It is noteworthy to know that the empty set, {} is a subset of all sets.

Also, if all the elements of a set A are present in another set B; it can be inferred that the set A is a subset of set B.

On this note, the list of all sets which are subsets of the given set; {Lennon, McCartney} is; { }, { Lennon }, { McCartney }, { Lennon, McCartney }.

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The scientific notation of the given number is 6.11×10⁻⁴. Therefore, option E is the correct answer.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.

The given decimal number is 0.000611.

0.000611 in scientific notation, we get

6.11×10⁻⁴

Therefore, option E is the correct answer.

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The latera surface area of the triangular prism is  425 inches².

The isosceles triangular prism is unfolded into the net shown below. Therefore, the lateral surface area of the triangular prism can be found as follows:

The lateral surface area of the triangular prism is the product of the perimeter of the triangle and the height of the prism.

Hence,

lateral surface area of the triangular prism = ph

where,

Therefore,

lateral surface area of the triangular prism = (9 + 9 + 7)17

lateral surface area of the triangular prism = 25 × 17

lateral surface area of the triangular prism = 425 inches²

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Answer: 3

Hope this helps :)

Step-by-step explanation:

1+2+3+4+5=15

15/5=3

Answer:

The inverse of a function, denoted as f^-1 (x), is a new function that "undoes" the original function. To find the inverse of a function, you need to switch the x and y variables and then solve for y. To find the inverse of f(x) = 1/3 x - 5, you need to switch the x and y variables and then solve for y:

Step-by-step explanation:

To solve for y, you need to get x alone on one side of the equation:

x + 5 = 1/3 y

3x + 15 = y

The inverse of f(x) = 1/3 x - 5 is f^-1 (x) = 3x + 15

It is important to note that not all functions have an inverse, only functions that are one-to-one or "injective" functions have inverses.

Answer: 3x + 15 = the inverse function of f(x)

Explanation:

First of all, arrange the equation and leave the "x" alone.

x/3 - 5 = y (Multiply both sides by 3)

x - 15 = 3y (Then, leave "x" alone)

x = 3y + 15 (As the final step, change x and y variables.)

y = 3x + 15 (This is the inverse function of f(x).)

Answer: Let's call the present age of the son x and the present age of the father y.

We know that y = 3x and that six years ago, the sum of their ages was 45.

So, we can write the equation:

x + (y-6) = 45

x + (3x-6) = 45

4x = 51

x = 12.75

The present age of the son is 12.75 years.

Step-by-step explanation:

Step-by-step explanation:

different between each value is 4

Answer:

39000meter

hope it will help you

Answer:

The correct answer is: parallel

The two equations are in the form of y = mx + b and y = mx + b, which are the standard forms of linear equations.

and the slope of the two equations are different, so they are not coincident and not intersecting. They are parallel lines that never meet, so the system of equations is parallel.

Answer:

Step-by-step explanation:

To graph 10x-3y=15, start by rearranging the equation to the slope-intercept form of y = mx + b, where m = the slope and b = the y-intercept. 10x-3y=15 becomes 3y = 10x - 15. Solve for y by dividing both sides by 3 to get y = (10/3)x - 5.

Now that the equation is in the slope-intercept form, draw a graph on a coordinate plane. Start by plotting the y-intercept at (0, -5). Next, use the slope of 10/3 to determine the rise and run of the line. The rise is +10 and the run is +3. Starting at the y-intercept, draw a line that moves up 10 and to the right 3, and continue doing this until you reach the end of the graph. This line is the graph of 10x-3y=15.

Answer:

y=10/3x+5

(0,5), (3,15)

Step-by-step explanation:

First, put the graph in slope-intercept form. We can do this by subtracting 10x from both sides.

-3y=-10x-15

Next, we divide by -3.

y=10/3x+5

If you don't know how to graph an equation with slope-intercept form,

it is in the format of y=mx+b, where m is the slope (in this case, 10/3) and b is the y-intercept (in this case 5, or (0,5)). First graph the y-intercept.

(0,5).

Then implement the slope. Here we would go up by 10 and then go right by 3. This makes our second point (3,15).

Now that we have two points (0,5) and (3,15), just construct your line.

1.) The 50% of R100 = R50

2.) The 0.5 of R100 = R50

3.) The ½ of R100 = R50.

Percentage is defined as the part of a whole which is represented per 100 and the symbol which is used is %.

Therefore, is can be concluded since the same value was gotten that 50% = 0.5 = ½.

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Answer: (15 + 72) + 19

Explanation: "Associative Law = (a + b) + c = a + (b + c)"

The term that represents the cost of the shoes after the discount is (1 - 0. 025)s. Option D

Algebraic expressions are described as mathematical expressions that consist of factors, constants, variables, terms and coefficients.

They are also made up of arithmetic operations, which includes;

From the information given, we have that there was a 25% discount on all the shoes Declan bought

Given the expression;

c + ( 1 - 0.25)s + 0. 08[c + (1 -0.25)s ]

expand the bracket

c + s - 0. 25s + 0. 08( c - s - 0. 25s)

expand the parentheses

c + s - 0. 25s + 0. 08c - 0. 08s - 0.02

But for the cost of the shoes after the 25% discount, we have;

(1 - 0. 025)s

Hence, the expression is (1 - 0. 025)s

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Answer:

a) n(A)7

b) 140

Step-by-step explanation:

a) numbers in the set

b)since n(A)=7

20A=20×7

=140

Answer: The area of the floor of the store room is 1080 m^2

Step-by-step explanation:

We can begin by using the information provided about the ratios of the dimensions of the store room to set up a system of equations.

Let's call the height of the store room h, the length l, and the breadth b.

From the first ratio given, we know that:

h/l = 5/4

From the second ratio given, we know that:

h/b = 2/3

We can also use the information about the total area of the four walls to set up another equation.

The total area of the four walls is the sum of the area of the top and bottom walls (length x height) and the area of the two side walls (breadth x height).

So we have:

2lh + 2bh = 2760

We can now use the first two equations to solve for one of the variables in terms of the other two.

We can cross-multiply and simplify the first equation:

l = (4/5)h

We can cross-multiply and simplify the second equation:

b = (3/2)h

We can now substitute these expressions for l and b into the equation for the total area of the four walls:

2(4/5)h^2 + 2(3/2)h^2 = 2760

Solving for h, we get:

h = 30

Now that we know the value of h, we can use the equations l = (4/5)h and b = (3/2)h to find the values of l and b.

l = (4/5)h = (4/5)(30) = 24

b = (3/2)h = (3/2)(30) = 45

Now we have all the information we need to find the area of the floor, which is the product of the length and breadth of the store room

Area of floor = lb = 2445 = 1080 m^2

Explanation: By using the information about the ratios of the dimensions of the store room and the total area of the four walls, we set up a system of equations and used algebra to solve for the height, length and breadth of the store room. With this information, we were able to find the area of the floor of the store room.

A graph of the absolute function y = |x + 2| - 4 with five points that fit on the axes is shown in the image attached below.

In Mathematics, an absolute value function is a type of function that is composed of an algebraic expression, which is placed within absolute value symbols and it typically measures the distance of a point on the x-axis to the x-origin (0) of a cartesian coordinate (graph).

Next, we would use an online graphing calculator to plot the given absolute value function y = |x + 2| - 4 as shown in the graph attached below.

By observing critically the graph (see attachment), the five ordered pairs (points) that fit on its axes include the following:

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Answer:

1. Nevoia de a te certa sau de a-i critica pe cei din familie prin limbaj cu conotatii negative sau prin tonul vocii.

2. Nerespectarea deciziilor familiei sau nerespectarea responsabilitatilor asumate.

3. Abuzul verbal sau emotional, inclusiv insultele sau minciunile.

4. Negarea dreptului la intimitate sau la spatiu personal.

5. Ignorarea afectiunii si a momentelor importante din familie.

If In ΔEFG, e = 690 inches, ∠F=94° and ∠G=46° then the length of g is 800 inches.

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

The sum of interior angles of a triangle are 180 degrees.

In ΔEFG, e = 690 inches, ∠F=94° and ∠G=46

We need to find the ∠E then the length of g.

∠E+∠F+∠G=180

∠E+94+46=180

∠E+140=180

∠E=40 degrees

By using sinE rule we have to find the length of g.

SinE/E=sinG/G

sin40/690=sin46/x

0.642/690=0.72/x

0.00093=0.72/x

x=0.72/0.0009

x=800 inches

Hence, the length of g is 800 inches.

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The interest paid at the term end will be $5400.

What is interest and its types(Simple and compound interest)?

Interest is the cost of borrowing money, where the borrower pays a fee to the lender for the loan. The interest, typically expressed as a percentage, can be either simple or compounded. Simple interest is based on the principal amount of a loan or deposit. In contrast, compound interest is based on the principal amount and the interest that accumulates on it in every period. Simple interest is calculated only on the principal amount of a loan or deposit, so it is easier to determine than compound interest.

​The formula for these are

Simple Interest= P×r×n

where:

P=Principal amount

r=Annual interest rate

n=Term of loan, in years

Compound Interest=P×(1+r)^t−P

where:

P=Principal amount

r=Annual interest rate

t=Number of years interest is applied

Here,

Interest rate will be risk percentage + LIBOR

i.e.4.8%

Hence,  the interest can be found by using formula for simple interest

Therefore,

SI=P*r*t

=$450000*0.048*0.25               (Time is 3 month or  0.25 years.)

SI (Interest paid)=$5400

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The total interest paid for the period of three months will be $5225 on the loan amount of $450000.

What is interest?

The interest is the charges levied on the amount which we borrow from any bank for a particular period of time.

Here in the question given data is

P= $450000

R=2.2%+2.8%=5%

T=1/4 years or three months

So from the simple interest formula

SI= PNR/100

SI=15000×5×1/`100×4

SI=$5625

Hence the total interest paid for the period of three months will be $5225 on the loan amount of $450000.

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Answer:

Step-by-step explanation:

The solutions to this equation are x = 1.273 and x = -0.273.

When x = 1.273, 3 cos (x) + 4 = 5.

When x = -0.273, 3 cos (x) + 4 = 5.

Rounding to 3 decimal places, the solutions to the equation on the indicated interval are x = 1.273 and x = -0.273.

On solving the provided question, we can say that the value of the quadratic equation would be x = 0.18

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

The roots of a quadratic equation ax^2 + bx + c = 0 can be found using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

The given equation is 2x² + 5x - 1 = 0

Hence, the larger root of the given quadratic equation would be x = 0.18.

[tex]x = \frac{-5 + \sqrt{5^2 - 4(2)(-1)} }{2(2)} \\x = 0.18\\or \\x = -2.68\\[/tex]

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The fractions that have the same value as 16 ÷ (–3), include:

The quotient of the problem given is - 4.

To find the equivalent fractions to ,16 ÷ (–3), first solve for the quotient:

= 16 ÷ (–3)

= - 5. 33

Then, solve the fractions in the options to see if they give the same result as when you solved 16 ÷ (–3).

Fraction : 16 over negative 3

= 16 / -3

= - 5.333

This has the same value

Fraction : negative 16 over negative 3

= -16 / -3

= 5. 333

This does not have the same value

Fraction : negative 16 over 3

= - 16 / 3

= - 5. 333

This has the same value

Fraction : 16 over 3

= 16 / 3

= 5. 333

This is not the same value

Fraction: Negative (StartFraction 16 over 3 EndFraction)

= - ( 16 / 3 )

= - 5. 33

This is the same

The quotient of - 20 / 5 :

= - 20 / 5

= - 4

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