A class of 32 students contains 15 boys.
Twenty of the students walk to school each
day. Eight of the girls do not walk to school.
How many boys walk to school each day?

Answer:

1. x - 1

2. [tex]\sqrt{x^2-1}[/tex]

Step-by-step explanation:

[tex]f(g(x)) = \sqrt{x+1}^2 - 2\\ = x + 1 - 2\\= x - 1[/tex]

[tex]g(f(x)) =\sqrt{x^2-2+1}\\ = \sqrt{x^2-1}[/tex]

The concentration could not be 59.

The concentration of a solution is a measure of the amount of solute that has been dissolved in a given amount of solvent or solution.

Given:

solutions one of 45% concentration

other of 55% concentration.

The concentration should lie between 45 % to 55 %.

This is because it is not possible to get a mixture concentration which is lower than the lower concentrated acid or higher than the higher concentration acid.

Hence, Mixture concentration must be between 45% and 55%.

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Answer:

72ft²

Step-by-step explanation:

a square has 4 equal sides, when each one is 18ft, the total perimeter will be 18×4=72ft²

Hii!

_____________________________________________________

[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}\circ\leftharpoonup}}[/tex]

Perimeter of the rug = 72 ft

[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation}\circ\leftharpoonup}}}[/tex]

[tex]\bullet[/tex] Let's work out the perimeter

[tex]\twoheadrightarrow\sf P=4a[/tex] a=length of one side

[tex]\bullet[/tex] Stick in the values

[tex]\twoheadrightarrow\sf P=4\cdot18[/tex]

[tex]\bullet[/tex] Multiply

[tex]\twoheadrightarrow\sf P=72ft[/tex]

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Hope that this helped! Best wishes.

[tex]\stackrel\star{\textsl{Reach far. Aim high. Dream big.}}[/tex]

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Answer:

C the prove is right there on the graph

Answer:

C

Step-by-step explanation:

The graph clearly shows that all the numbers are greater than -6

The equation of the red graph is g(x)=^x+2-3.

Since the upscaling in the y-axis is not the main focus of this equation (being g(x) and not g(y)), the change is not applied to the x-axis.

The y-intercept and the slope in order to write the equation in y-intercept (y=mx+b) form. The slope is the change in y over the change in x.

Hence, we can rule out (-3)^2 and (x+3)^2 since they apply changes to the x-axis.

Finally, since this is an upscaling of the y-value on the y-axis, the answer is x^2 + 3 and not x^2 - 3.

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Answer:

10a^2b^3−8a^3b^3+12a^2b^5−8ab^4

Step-by-step explanation:

Answer:

(a).16.8 litres

(b).red-1.2 litres

white-14.3 litres

The normal distribution is also known as the Gaussian distribution. The percentage of all possible values of the variable that are less than 4 is 15.87%.

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.

A.) The percentage of all possible values of the variable that lie between 5 and 9.

P(5<X<9) = P(X<9) - P(5<X)

               = P(z<1.5) - P(-0.5<z)

               = 0.9332 - 0.3085

               = 0.6247

               = 62.47%

B.) The percentage of all possible values of the variable that exceed 1.

P(X>1) = 1 - P(X<-2.5)

          = 1-0.0062

          = 0.9938

          = 99.38%

C.) The percentage of all possible values of the variable that are less than 4.

P(X<4) = P(X <4)

           = P(z<-1)
           = 0.1587

           = 15.87%

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Answer:

460

Step-by-step explanation:

4 tens is equivalent to 40, so 500-40 is = to 460.

Hope this helps! :D

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[tex]\large \bold {ANSWER}[/tex]

[tex]\large \bold {SOLUTION}[/tex]

5 hundreds is 5 multiplied by 100, so it equals 500. 4 tens is 4 times 10, so 40.

So 5 hundreds minus 4 tens is 460.

Answer:

-8

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

-8/5=(6-(-2))/(x-(-3))

-8/5=(6+2)/(x+3)

-8/5=8/(x+3)

5=-(x+3)

5=-x-3

-x=5+3

-x=8

x=-8

Answer:

40

Step-by-step explanation:

Answer:

y = 3

Step-by-step explanation:

2x + 3y = 9

-2x + 2y = 6

We have to add these two equations which gives us 5y = 15. Now, if you divide by 5 on both sides you get y = 3.

Answer:

(4, -3)

Step-by-step explanation:

A vertex is just a point where 2 lines going in different directions meet. so the answer is (4, -3)

Answer:

A.

Step-by-step explanation:

Hello, this is what we call matrix. multiplication matrix to be precised.

so it is;

5×2=10

5×3=15

5×4=20

5×9=45

5×-1= -5.

5×-7= -35

5×11=55

5×5=25

5×-3= -15.

i hope you understand. That is matrix for you but it has different categories

Answer:

x=15.1

Step-by-step explanation:

In a right triangle, the side across from the right angle is always the hypotenuse.

The other two sides are termed "legs".

Once one of the other two angles is chosen as the angle to work from, then the two legs can be defined as the "opposite" and the "adjacent"

The leg touching the angle is the "adjacent" leg (or adjacent side), and the leg across from the angle is the "opposite" leg (or opposite side).

[tex]\sin(\theta)=\dfrac{\text{opposite side}}{\text{hypotenuse}}[/tex]

[tex]\cos(\theta)=\dfrac{\text{adjacent side}}{\text{hypotenuse}}[/tex]

[tex]\tan(\theta)=\dfrac{\text{opposite side}}{\text{adjacent side}}[/tex]

In this situation, the given angle is in the bottom right.  A value is given for the side opposite the given angle, and the requested value is on the hypotenuse.

So, the two sides of interest are the "opposite" and the "hypotenuse".  The trigonometric function that relates these two sides is the sine function.

[tex]\sin(\theta)=\dfrac{\text{opposite side}}{\text{hypotenuse}}[/tex]

[tex]\sin(68^o)=\dfrac{(14)}{(x)}[/tex]

Evaluating the sine function in a calculator (in degree mode):

[tex]0.9271838546...=\dfrac{14}{x}[/tex]

Multiply both sides by x:

[tex](0.9271838546...)x=\left (\dfrac{14}{x} \right)x[/tex]

[tex](0.9271838546...)x=14[/tex]

Divide both sides by the decimal number:

[tex]\left (\dfrac{(0.9271838546...)x}{0.9271838546...} \right)=\dfrac{14}{0.9271838546...}[/tex]

[tex]x=15.0994864...[/tex]

Rounded to the nearest tenth, x=15.1

Answer:

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

To calculate f(2), just replace x in the equation of f(x) with 2:

[tex]f(x) = 5(x + 2)\\\\f(2) = 5(2+2)\\\\f(2) = 5(4)\\\\f(2) = 20[/tex]

Answer:

y = -5x

Step-by-step explanation:

gradient = delta y / delta x

gradient = -10 / 2

gradient = -5

y = mx + b

5 = -5(-1) + b

5 = 5 + b

b = 0

y = -5x

Answer:

x>-60

Step-by-step explanation:

Combine multiplied terms into a single fraction

2/5x - 9 < 3/5x + 3

2x/5 - 9 < 3/5x + 3

Find common denominator

2x/5 - 9 < 3/5x + 3

2x/5 + 5(-9)/5 < 3/5x + 3

Combine fractions with the common denominator

2x + 5(-9)/5 < 3/5 + 3

I HOPE YOU GOT THE ANSWER JUST SIMPLIFY IT (2x + 5(-9)/5 < 3/5 + 3) AND YOU WILL GET THE ANSWER YOURSELF AS I HAVE GIVEN ABOVE PLS MARK ME AS THE BRAINLILEST IF YOU LIKE TO AND MY ANSWER HELPED YOU:)

Answer:

[tex]\boxed {x > -60}[/tex]

Step-by-step explanation:

2/5x - 9 < 3/5x + 3

-1/5x < 12

x > -12 x 5

x > -60

Answer:

.0032 .032 .32 3299

Step-by-step explanation:

0.32% =.0032

3.2% = .032

.32

3299

Answer: 10 inches

Step-by-step explanation:

Diagonals of a parallelogram bisect each other, so the top of the jack is 5(2)=10 inches off the ground.

The proportion can be used to find the distance on the map (x) that represents 50 miles will be x/50 = 5 / 200. Then the correct option is A.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

The scale on a map shows that 200 miles is represented by 5 inches on a map.

Then the proportion can be used to find the distance on the map (x) that represents 50 miles will be

x/50 = 5 / 200

Then  the correct option is A.

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Answer:

a=9

b=9

c=18

Step-by-step explanation:

c(a+b)+a+b=36

2a+2b=36

a+b=18

c=18

The dimensions of each pen that will maximize the total enclosed area would be as; Length 81 feet; Width 81 feet.

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.

Let the Dimension of each pen

Length = x

Width = y

Area = xy

Perimeter equation

2(x + y) = 324

 x + y = 162

Substituting the perimeter equation

Area = x(162 - x)

Area = -x^2 + 162x

If the zeros of the quadratic are 0 and 162, then the median will be at where the maximum area occurs.

162/ 2

= 81

Hence, The dimensions of each pen that will maximize the total enclosed area would be as; Length 81 feet; Width 81 feet.

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Answer: For this real-valued function;

[tex]fog = 2\sqrt{x-1} + 1\\ Domain = [1, )[/tex]

Step-by-step explanation:

If f and g are functions, then the composite function or composition, of g and f is defined by

[tex]( f o g ) (x) = f(g(x))[/tex]

Given the functions [tex]f(x)=2x+1[/tex] , [tex]g(x)=\sqrt{x-1}[/tex],

Now composition for this;

[tex]fog = f(g(x))f(g(x)) = f(\sqrt{x-1} )[/tex]

[tex]f(\sqrt{x-1})[/tex]means we are to interchange variable x in [tex]f(x)[/tex] with the function [tex]\sqrt{x-1}[/tex]

[tex]f(\sqrt{x-1}) = 2(\sqrt{x-1})+1f(\sqrt{x+1}) = 2(\sqrt{x-1})+1fog = 2(\sqrt{x-1})+1[/tex]

The function inside the square root, x-1, must be more significant than or equal to zero (x-10), for the function to exist on any real-valued function.

[tex]if, x-1 \geq 0\\x\geq 0+1\\x \geq 1[/tex]

As a result, the range of the variable x must only include values that are larger than or equal to 1.

Hence, Domain = [1, )

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An expression is defined as a set of numbers, variables, and mathematical operations. The value of (16/81)^(1/2) is 4/9.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The value of the given expression (16/81)^(1/2) can be calculated as shown below,

[tex](\dfrac{16}{81})^{\frac12}\\\\=\sqrt{\dfrac{16}{81}}\\\\= \dfrac49[/tex]

Hence, the value of (16/81)^(1/2) is 4/9.

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Answer:

★The square root of 16/81 = 4/9.

Answers:

2% bond: $11000

4% bond: $13000

========================================================

Explanation:

x = amount invested in the 4% bond

y = amount invested in the 2% bond

Amounts are in dollars

The two amounts add to $24,000 so

x+y = 24000

y = -x+24000 is one equation to set up

0.04x = interest earned from the 4% bond

0.02y = interest earned from the 2% bond

0.04x+0.02y = total interest earned = $700

0.04x+0.02y = 700 is another equation to set up

------------

The system of equations is

[tex]\begin{cases}y = -x+24000\\0.04x+0.02y = 700\end{cases}[/tex]

Apply substitution. Solve for x.

0.04x+0.02y = 700

0.04x+0.02(-x+24000) = 700

0.04x-0.02x+480 = 700

0.02x= 700-480

0.02x= 220

x= 220/(0.02)

x = 11000

Use this to find y

y = -x+24000

y = -11000+24000

y = 13000

Russell has to sell 270 cable packages to make the total pay of both the companies as same.

Suppose that Russell sells x cable packages such that the total pay of both the companies is the same.

Then the revenue Russell would make at the first company is $17000+20x

And, the revenue Russell would make at the second company is

$14300+30x

Since, the above two values are equal

so, 17000+20x=14300+30x

⇒17000-14300=30x-20x

⇒10x=2700

⇒x=270

The above problems are called mathematical modelling.

Mathematical modelling is the process of locating such equations to explain actual occurrences.

These formulae are referred to as mathematical models together with the definitions given to the variables.

Therefore, Russell has to sell 270 cable packages to make the total pay of both the companies as same.

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