What ratios and rates? how can you use ratios and rates to describe quantities and solve problems?

Answer:  Choice B

Explanation: The phrase "cash on hand" means the amount of money the company has. It could be literal cash as the phrase directly implies. Or it could be near equivalents to cash. A near equivalent is something you can convert to cash fairly easily, meaning a bank would readily accept it. The only drawback is that it's not actual cash so its not as liquid as cash itself. Also, you would need to take into account the delay time between deposit and when the bank balance is updated.

The required value of the given expression which satisfy it is b = 3/5.

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

We have,

3 - 2(b - 2) = 2 - 7b

= 3 - 2b - 4 = 2 - 7b

= 5b = 3

= b = 3/5

Thus, required value of the b for the given function is b = 3/5.

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Step-by-step explanation:

please review the attachment. That's the answer.

Answer:

B

Step-by-step explanation:

the zeros are the values of x on the x- axis where the graph crosses

the graph crosses the x- axis at 1 and 3

then the zeros are x = 1 , x = 3

The probability that there are fewer than 2 tornadoes in a 22-year period is, 0.214

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

Since the probability of a tornado in any given year is 0.08,

the probability of no tornado in any given year is;:

=  1 - 0.08

= 0.92.

Let X be the number of tornadoes in a 22-year period.

X follows a binomial distribution with n = 22 and p = 0.08.

We want to calculate the probability that there are fewer than 2 tornadoes in a 22-year period.

This can be written as:

P(X < 2) = P(X = 0) + P(X = 1)

Using the binomial probability formula, we can calculate:

P(X = 0) = (22 choose 0) x (0.08)⁰ x (0.92)²² ≈ 0.038

P(X = 1) = (22 choose 1) x (0.08)¹ x (0.92)²¹ ≈ 0.176

Therefore,

P(X < 2) = P(X = 0) + P(X = 1) ≈ 0.214

So the probability that there are fewer than 2 tornadoes in a 22-year period is approximately 0.214 or 21.4%.

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Answer:

he had to go to china for the milk and while he was there he got kidnapped so it might be a while

sorry bro

Step-by-step explanation:

Answer:

Step-by-step:

he is just trying to find the best milk he can don't even worry about it just  become rich he's sure to come back then-

The function operation (f/g)(x) in the functions f(x) = √( x² - 1 ) and g(x) = √( x - 1 ) is √( x + 1).

A function is simply a relationship that maps one input to one output.

Given the functions in the question;

To evaluate (f/g), replace the function designators in f/g with the actual functions.

(f/g)(x) = f(x) / g(x)

(f/g)(x) = ( √( x² - 1 ) ) / ( √( x - 1 ) )

Now, rewrite 1 as 1²

(f/g)(x) = ( √( x² - 1² ) ) / ( √( x - 1 ) )

Factor using difference of square

(f/g)(x) = ( √( (x - 1)(x + 1 ) ) / ( √( x - 1 ) )

Combine into a single radical

(f/g)(x) = √( ( (x - 1)(x + 1) ) / ( x - 1 ) )

Now, cancel out the common factors (x-1)

(f/g)(x) = √(  (x + 1) / 1 )

(f/g)(x) = √( x + 1)

Therefore, the function operation (f/g)(x) is √( x + 1).

Option A) √( x + 1) is the correct answer.

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Answer:

For the nearest 10th of a centimeter, the value of h is 460 cm

Step-by-step explanation:

To find length of h we can use Law of Sines  . The Law states that for a triangle with sides a, b, and c and angles A, B, and C opposite to those sides, the following equation holds:

a/sin A = b/sin B = c/sin C

In ΔGHI, let h be the length of the side opposite angle H, and let i be the length of the side opposite angle I.

Now:

h/sin 122° = i/sin 26°

We can find h by cross multiplying:

h = i * sin 122° / sin 26°

  =459.9

Here,

h = 459.9 cm

By taking approximation we get 460 cm

Answer:

This answer is actually 1280.3

Step-by-step explanation:

The number of pounds in  [tex]1\frac{1}{2}[/tex] pounds and and 8 ounces is 2 pounds.

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

We know that 1 pound = 16 ounces.

As there are [tex]1\frac{1}{2}[/tex] pounds=1.5×16= 24 ounces.

The total number of ounces in   [tex]1\frac{1}{2}[/tex] pounds and 8 ounces is

24+8

32 ounces.

Now let us convert Ounces to pounds.

we divide the number of ounces by 16.

Therefore, 32 ounces is equal to 32/16 = 2 pounds.

Hence, 2 pounds will be there in  [tex]1\frac{1}{2}[/tex]  pounds and 8 ounces

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The statement regarding the census in this problem is classified as a True statement.

Population: Collection or set of individuals or objects or events whose properties will be studied.

Sample: The sample is a subset of the population, and a well chosen sample, that is, a representative sample will contain most of the information about the population parameter. A representative sample means that all groups of the population are inserted into the sample.

A Census is when a group of the population is chosen, that is, a sample is chosen, hence the statement for this problem is true.

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Answer: no

Step-by-step explanation:

The values for the length AC and the angles of the right-angled triangle ABC are AC = 12.37, α = 75.96 , and θ = 14.04 using the trigonometric ratios of tangent.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths. The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the right-angled triangle ABC, we shall calculate for the angle B and side lengths a and b as follows:

AC² = 3² + 12² {Pythagoras rule}

AC = √(9 +144)

AC = √153

AC = 12.3693

tanα = 12/3 {opposite/adjacent}

α = tan⁻¹(4) {cross multiplication}

α = 75.9638

tanθ = 3/12 {opposite/adjacent}

θ = tan⁻¹(1/4){cross multiplication}

θ = 75.9638

Therefore, the values for the length AC and the angles of the right-angled triangle ABC are AC = 12.37, α = 75.96 , and θ = 14.04 using the trigonometric ratios of tangent.

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Vertex A will be located at (-1, 0) after a rotation of -90°

Vertex B will be located at (-5, 3) after a rotation of 90°

Vertex C will be located at (6, -7) after a -180° rotation

Vertex D will be located at (1, -4) after a 270° rotation

The transformation rule for rotation of -90°

(x, y) → (y, -x)

A (0, -1) → (-1, 0)

The transformation rule for rotation of 90°

(x, y) → (-y, x)

B (3, 5) → (-5, 3)

The transformation rule for rotation for -180°

(x, y) → (-x,-y)

C (-6, 7) → (6, -7)

The transformation rule for rotation for 270° rotation

(x, y) → (-y, x)

D (-4, -1) → (1, -4)

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The measure of angle ∠ACB is 45 degrees

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

A (-3, 2), B (0, 0), C (2, 3)

The graph is attached

The lines AB and BC are perpendicular lines

This means that

∠B = 90 degrees

Calculate the length AB and BC using

distance = √[(x2 - x1)² + (y2 - y1)²]

So, we have

AB = √[(-3 - 0)² + (2 - 0)²] = √13

BC = √[(0 - 2)² + (0 - 3)²] = √13

The angle C is then calculated as

tan(C) = AB/BC

tan(C) = √13/√13

tan(C) = 1

Take the arctan of both sides

C = 45

Hence, the measure of ∠ACB is 45 degrees

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The value of the equation is y = 4c + 18 , where c is the cost of each teacup and c = $ 6

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.

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 data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The total cost Rebecca spend on teacups = $ 42

The cost of the large teapot = $ 18

The cost of small teacups be = c

The number of small teacups = 4

So , the equation will be

Total cost Rebecca spend on teacups = cost of the large teapot + ( number of small teacups x cost of small teacups )

Substituting the values in the equation , we get

42 = 18 + 4c

y = 4c + 18   be equation (1) , where y is the total cost

On simplifying the equation , we get

Subtracting 18 on both sides of the equation , we get

4c = 24

Divide by 4 on both sides of the equation , we get

c = $ 6

Therefore , the cost of each teacup is $ 6

Hence , the equation is y = 4c + 18

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The solution is the union of the solutions from both inequalities. That is, x is either greater than 3.2 or less than -0.75. So, the final solution is: -0.75 < x < 3.2.

What is  inequalities?

An inequality is a mathematical statement that represents a comparison between two values, and indicates the relationship of one value being greater than, less than, or equal to the other. It is usually represented using symbols such as ">" (greater than), "<" (less than), ">=" (greater than or equal to), "<=" (less than or equal to), and "≠" (not equal to). For example, the inequality "2x + 3 > 7" expresses that the value of the expression "2x + 3" is greater than 7 for some values of x.

Inequalities are used to describe a range of values that satisfy a certain condition. The solution to an inequality is a set of values that make the inequality true.

To solve the inequality "5x - 4 > 12 or 12x + 5 < -4", we can start by solving each inequality separately and then combining the solutions to find the final solution.

Adding 4 to both sides, we get 5x > 16

Dividing both sides by 5, we get x > 3.2

So, the solution to this inequality is x > 3.2

Subtracting 5 from both sides, we get 12x < -9

Dividing both sides by 12, we get x < -0.75

So, the solution to this inequality is x < -0.75

Final solution: Combining the solutions from both inequalities:

Since "or" is used in the inequality, the solution is the union of the solutions from both inequalities. That is, x is either greater than 3.2 or less than -0.75. So, the final solution is: -0.75 < x < 3.2.

So the solution to the inequality "5x - 4 > 12 or 12x + 5 < -4" is -0.75 < x < 3.2.

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For the function f(x) = log4(x - 2) + 2, the domain is (2,∞) and range is (-∞,∞).

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The logarithmic function f(x) = log4(x - 2) + 2 is defined only for x-2 > 0, or equivalently, x > 2.

So, the domain of the function is all real numbers greater than 2, or -

Domain: x > 2

Now let's consider the range of the function.

The logarithmic function takes positive values for positive inputs, and it approaches negative infinity as x approaches zero from the right.

Since f(x) = log4(x-2) + 2, the function takes values greater than 2 when x is greater than 4, and it approaches 2 as x approaches 2 from the right.

So, the range of the function is -

Range: -∞ > f(x) > ∞

Therefore, the function has range and domain as (-∞,∞) and (2,∞) respectively.

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find the length of the x

a^2 + b^2 = c^2

12x^2 + b^2 = 13^2

144 + b^2 = 169

b^2 = 25

b = 25; x = 5

use the formula

a = (1/2)(24)(5)

a = (1/2)(120)

area = 60

Work Shown:

4.5% of 125 = 0.045*125 = 5.625

That rounds to 5.63

Answer:

5.625

Step-by-step explanation:

This equation has infinitely many solutions.

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Here, we have

Given: 3x+4y = -10...(1),

y = -3/4x - 5/2....(2)

We solve this linear equation and we get

We multiply equation (2) by 4 and we get

4y + 3x = -5(2)

4y + 3x = -10

Hence, this equation has infinitely many solutions.

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The solution to the system of equations is x = -1 and y = 1.

A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."

The system of equation is given as:

2x - 3y = -5 .........(1)

3x + y = -2 ........(2)

Equation 2 can be written as:

y = -2 - 3x

Substituting the value of y in equation 1 we have:

2x - 3(-2 - 3x) = -5

2x + 6 + 9x = -5

11x + 6 = -5

11x = -5 -6

11x = -11

x = -1

Substituting the value of x in equation 2 we have:

3x + y = -2

3(-1) + y = -2

-3 + y = -2

y = -2 + 3

y = 1

Hence, the solution to the system of equations is x = -1 and y = 1.

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Answer:

2

Step-by-step explanation:

1 plus 1 due to the characterisation of the number 1 increasing by 1 gives you 2

Using commutative and associative properties of addition, the solution for given expression is -5.

What is commutative and associative property?

The associative and commutative characteristics are universal principles that apply to addition and multiplication. The associative property states that rearranging the numbers will get the same result, while the commutative property states that rearranging the numbers will yield the same result.

These properties tell that one can add in any order, the result will always be the same.

We are given an expression as 8+(-8-5).

So, in this instead of adding from left to right, we can see that the 8 + (-8) will be zero and only -5 will be left as an answer.

Hence, the solution for given expression is -5.

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Answer:

Step-by-step explanation:

Here's a step by step solution with more details:

Let's call the length of the two equal sides of the triangle as x.

The third side, which is 1 1/3 cm longer, will have a length of x + 1 1/3 cm.

The perimeter of the triangle is 5 2/5 cm, so we can write an equation using the lengths of the sides:

x + x + (x + 1 1/3) = 5 2/5

Simplifying the equation:

2x + 1 1/3 = 5 2/5

Subtracting 1 1/3 from both sides:

2x = 4 1/5

Dividing both sides by 2:

x = 2 2/5

So the two equal sides of the triangle are 2 2/5 cm and the third side is 2 2/5 + 1 1/3 = 3 7/15 cm.

Answer:

One equal side = [tex]1\frac{16}{45}[/tex]cm and third side is [tex]2\frac{31}{45}[/tex]cm

Step-by-step explanation:

This is describing an isosceles triangle

1[tex]\frac{1}{3}[/tex] = [tex]\frac{4}{3}[/tex]

5[tex]\frac{2}{5}[/tex] = [tex]\frac{27}{5}[/tex]

Let

x = one of the two equal sides of the triangle

∴ Third side of triangle = [tex]\frac{4}{3} + x[/tex]

Perimeter of a triangle = Sum of all three sides:

[tex]\frac{27}{5}[/tex] [tex]= x + x + (\frac{4}{3} + x)[/tex]

Expand the parenthesis using the Distributive Law and bring all the like terms together:

[tex]=\frac{27}{5} = 2x + \frac{4}{3} + x[/tex]

[tex]= \frac{27}{5} = 3x + \frac{4}{3}[/tex]

[tex]= \frac{27}{5} -\frac{4}{3} = 3x[/tex]

The two denominators of the two fractions have to be manipulated to be made the same:

[tex]= (\frac{3}{3})(\frac{27}{5}) - (\frac{5}{5})(\frac{4}{3}) = 3x[/tex]

[tex]= \frac{81}{15} - \frac{20}{15} = 3x[/tex]

[tex]= \frac{81 - 20}{15} = 3x[/tex]

[tex]= \frac{61}{15} = 3x[/tex]

Cross-multiplication is added:

[tex]= (61)(1) = (15)(3x)[/tex]

[tex]= 61 = 45x[/tex]

Isolate x and make it the subject of the formula:

x = [tex]\frac{61}{45}[/tex]

x = One of the two equal sides = [tex]1\frac{16}{45}[/tex]cm

∴Third side:

= [tex]\frac{61}{45} + \frac{4}{3}[/tex]

= [tex]\frac{61}{45} + (\frac{15}{15})(\frac{4}{3})[/tex]

= [tex]\frac{61}{45} + \frac{60}{45}[/tex]

= [tex]\frac{61 + 60}{45}[/tex]

= [tex]\frac{121}{45}[/tex]

= [tex]2\frac{31}{45}[/tex]cm

This is a word problem and the value of the unknown number is equal to 25

Word problems are mathematical problems which involves the use of ordinary words, instead of mathematical symbols.

Let us represent the unknown number with the letter x so that we derive the equation;

1 + 6x = 151

we subtract 1 from both sides of the equation

1 - 1 + 6x = 151 - 1

6x = 150

divide through by the coefficient of x which is 6

6x/6 = 150/6

x = 25

Therefore, the value of the unknown number for the word problem is equal to 25

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Answer:

Flase, no real numbers (2+-8)

Step-by-step explanation:

First, you conjoined the equations (-6x+2=-6x-8).  Then you conjoined the variables first, (-6x+6x=0). Now you have 2=-8, which is not true.