Jessica bought CDs that were each the same price. Including sales tax, she paid a total of . Of that total, was tax. What was the price of each CD before tax?

Answer:

The rational number 1 is the multiplicative identity for rational numbers.

Step-by-step explanation:

I hope this will help you buddy

Answer:

d) 1/12

Step-by-step explanation:

Answer:

b. x + 4

Solution:

Student's age = x

Teacher's age = 6 + 2x

Principal's age = 10 + 3x

Difference in the age of the teacher and principal

(10 + 3x) - (6 + 2x)

= 10 + 3x - 6 - 2x

= (10 - 6) + (3x - 2x)

= 4 + x

The solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

Given the inequality,

    f(x²-2) < f(7x-8) over D₁ = (-∞, 2)

We need to find the values of x that satisfy this inequality.

Since we know that f is increasing over its domain, we can compare the values inside the function to determine the values of x that satisfy the inequality.

First, we can find the values of x that make the expressions inside the function equal:

x² - 2 = 7x - 8

Simplifying, we get:

x² - 7x + 6 = 0

Factoring, we get:

(x - 6)(x - 1) = 0

So the values of x that make the expressions inside the function equal are x = 6 and x = 1.

We can use these values to divide the domain (-∞, 2) into three intervals:

-∞ < x < 1, 1 < x < 6, and 6 < x < 2.

We can choose a test point in each interval and evaluate

f(x² - 2) and f(7x - 8) at that point. If f(x² - 2) < f(7x - 8) for that test point, then the inequality holds for that interval. Otherwise, it does not.

Let's choose -1, 3, and 7 as our test points.

When x = -1, we have:

f((-1)² - 2) = f(-1) < f(7(-1) - 8) = f(-15)

Since f is increasing, we know that f(-1) < f(-15), so the inequality holds for -∞ < x < 1.

When x = 3, we have:

f((3)² - 2) = f(7) < f(7(3) - 8) = f(13)

Since f is increasing, we know that f(7) < f(13), so the inequality holds for 1 < x < 6.

When x = 7, we have:

f((7)² - 2) = f(47) < f(7(7) - 8) = f(41)

Since f is increasing, we know that f(47) < f(41), so the inequality holds for 6 < x < 2.

Therefore, the solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

Learn more about inequality here:

https://brainly.com/question/25944814

#SPJ1

5 apples divide by 5

Then result is 5/5= 1 apple

Answer:

f(7)= -48

Step-by-step explanation:

Evaluate f(x)= -3(9+x) for x=7.

Substitute 7 for x in f(x)=-3(9+x), obtaining f(7)= -48

Answer: 0.9554

Step-by-step explanation:

Let \(\overline{X}\) be the sample mean.

Given: Mean weight\((\mu)\) of an adult is 65 kilograms with a standard deviation\((\sigma)\) of 13 kilograms.

Sample space = 92

The probability that the sample mean would be greater than 62.7 kilograms:

\(P(\overline{X}>62.7)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{62.7-65}{\dfrac{13}{\sqrt{92}}})\\\\=P(Z>-1.70)\\\\=P(Z<1.70)\ \ \ \[P(Z>-z)=P(Z<z)]\\\\=0.9554\)[ By p-value table]

Hence, the required probability= 0.9554

Answer:

x = 16

Step-by-step explanation:

Opposite sides are equal in a parallelogram

AD = BC

5x - 12 = 3x + 20

5x - 3x = 20 + 12

2x = 32

x = 32/2

x = 16

If the random variable x is normally distributed with a mean equal to 0.45 and a standard deviation equal to 0.40, then P(x ≥ .75) is 0.9227.

A z-score describes the position of a raw score in terms of its distance from the mean when measured in standard deviation units. The z-score is positive if the value lies above the mean and negative if it lies below the mean.

Given the problem above, we need to find what the z-score is when P(x ≥ .75).

The formula for calculating a z-score is given by:

\(Z=\dfrac{\text{x}-\mu}{\sigma}\)

Where:

Now,

\(Z=\dfrac{\text{x}-\mu}{\sigma}\)

\(Z=P(\text{x} \geq 0.75) = \huge \text(\dfrac{P(Z \geq (0.75 - 0.45)}{0.40}\huge \text)\)

\(Z= P\huge \text (\dfrac{Z \geq0.30}{0.40}\huge \text)\)

\(Z=P(Z \geq 0.75) = 1 - P(Z < 0.75)\)

\(Z=1 - 0.077337\)

\(Z\thickapprox 0.9227\)

Therefore, the z-score of P(x ≥ .75) is 0.9227.

Learn more about the z-score at:

https://brainly.com/question/31871890

The length of one side of the cube is 2 feet.

The surface area of a cube is given by the formula:

SA = 6s²

s is the length of one side of the cube.

The surface area of the cube is 24 ft².

Substituting this value into the formula we get:

24 = 6s²

Dividing both sides by 6 we get:

4 = s²

Taking the square root of both sides we get:

s = 2

a cube's surface area:

The cube's side length is given by SA = 6s²

The cube has a surface area of 24 feet2.

When we enter this value into the formula we obtain:

24 = 6s²

If we multiply both sides by 6 we get:

4 = s²

We obtain s = 2 by taking the square root of both sides.

For similar questions on cube

https://brainly.com/question/1972490

#SPJ11

Step-by-step explanation:

First convert the amount of dough into an improper fraction:

\(3\frac{3}{4}\:\text{lbs} = \dfrac{15}{4}\:\text{lbs}\)

Each roll is 1/8 lb so divide the amount of dough by this amount:

\(\dfrac{\left(\dfrac{15}{4}\:\text{lbs}\right)}{\left(\frac{1}{8}\:\text{lb/roll}\right)} = \left(\dfrac{15}{4}\:\text{lbs}\right)\cdot \left(8\:\dfrac{\text{roll}}{\text{lb}}\right) = 30\:\text{rolls}\)

Answer:

A is the correct answer

check the picture below.

now, we know the directrix is at y = 1, and the focus point is at 1,3, well, notice the picture, the distance between those fellows is just 2 units.

the vertex is half-way between those fellows, therefore, the vertex will be at 1,2.

the distance "p", from the vertex to either the directrix or focus, is really just 1 unit.  Since the focus point is above the directrix, is a vertical parabola, and it opens upwards, like in the picture, and since it opens up, the "p" value is positive, or +1.

The area of the triangle with angle B = 128°, side a = 86, and side c = 37 is approximately 2302.7 square units.

To find the area of a triangle when one angle and two sides are given, we can use the formula for the area of a triangle:

Area = (1/2) * a * b * sin(C),

where a and b are the lengths of the two sides adjacent to the given angle C.

In this case, we have angle B = 128°, side a = 86, and side c = 37. To find side b, we can use the law of cosines:

c² = a² + b² - 2ab * cos(C),

where C is the angle opposite side c. Rearranging the formula, we have:

b² = a² + c² - 2ac * cos(C),

b² = 86² + 37² - 2 * 86 * 37 * cos(128°).

By substituting the given values and calculating, we find b ≈ 63.8.

Now, we can calculate the area using the formula:

Area = (1/2) * a * b * sin(C),

Area = (1/2) * 86 * 63.8 * sin(128°).

By substituting the values and calculating, we find the area of the triangle to be approximately 2302.7 square units.

For more question on area  visit:

https://brainly.com/question/2607596

#SPJ8

An expression that equals 24 + 3B in standard form is: 36 + 9m

What is standard form ?

To find an expression that equals 24 + 3B in standard form, we first need to find the value of B and then substitute it into the expression.

Given that B = 3m + 4, we can substitute it into 24 + 3B to get:

24 + 3B = 24 + 3(3m + 4)

Simplifying the expression inside the parentheses, we get:

24 + 9m + 12

Combining like terms, we get:

36 + 9m

Therefore, an expression that equals 24 + 3B in standard form is:

36 + 9m

What is an expression?

In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, ×, ÷, etc.) that represents a value or a relationship between values. Expressions can be simple, such as a single number or variable, or complex, such as a combination of several terms with different operators.

For example, 2x + 3y - 5 is an expression that consists of three terms (2x, 3y, and -5) with two operators (+ and -). This expression can be evaluated for different values of x and y to obtain different numerical results.

Expressions can be used to represent mathematical formulas, describe geometric shapes and patterns, and solve real-world problems in a wide range of fields, including science, engineering, finance, and statistics.

To know more about  standard form, visit:

https://brainly.com/question/551289

#SPJ1

Complete question is: An expression that equals 24 + 3B in standard form is: 36 + 9m,

Answer:

a)2

B)2

Step-by-step explanation:

Answer: f < 9

Step-by-step explanation:

first, cross multiply 2 and 2:

f - 5 < 4

f < 9

Answer:

f < 9

Step-by-step explanation:

=> (f-5)/2 < 2

multiplying both sides by 2

=> 2(f-5)/2 < 2×2

=> f-5 < 4

adding 5 to both sides

=> f-5+5 < 4+5

=> f < 9

Answer:

the population in 2015 is 8201.0695

Step-by-step explanation:

Given that

There is a population of the 50 timber wolves

And, the exponential function given is

p(t) = 50 × e^(0.85 × t)

Here t denotes the time period i.e.

= 2015 - 2009

= 6

So,

= 50 × e^(0.85 × 6)

= 8201.095

Hence, the population in 2015 is 8201.0695

Answer:

x=-24/a

Step-by-step explanation:

18-ax=42 isolate x by subtracting 18 from both sides to get -ax=24 then divide by a negative 1 to get ax=-24 then divide by a to isolate x to get x=-24/a

Answer:

41.93 degrees

Step-by-step explanation:

475

1) If 5 out of 10 patients receive medication, then we have this ratio:

2) If 950 patients go to the hospital for the same reason, we can write out the following ratios to get to know what we expect:

Note that we could cross multiply those ratios.

3) Hence, we can expect that 475 people receive a prescription for medication.

Answer:  \(y^9\)

This is the same as saying y^9

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

Explanation:

When we apply the square root to the expression \(a^{2b}\), we end up with \(a^b\)

\(\sqrt{a^{2b}} = a^b\)

The exponent 2b divides in half to get b

Based on that rule, we can then say:

\(\sqrt{y^{18}} = y^{18/2} = y^9\)

Answer:

1/8

Step-by-step explanation:

Answer:

Ummmm 2 I think

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

The 3.5 million initial population of the country in the year 2000 and 6.5 million in 2015 indicates that the values of the exponential growth formula that models the population, f(x) = P₀·a⁽ˣ ⁻ ²⁰⁰⁰⁾, are

(a) P₀ = 3.5 million

a ≈ 1.02507

(b) In the year 2010, the population of the country is about 4.48 million

(c) The year during which the country's population might reach 11 million is the year 2046

An exponential function is one in which the input variable is an exponent of the growth or decay factor.

The population of the country A in the year 2000 = 3.5 million

The projected population of the country in 2025 = 6.5 million

(a) The specified formula that could be used to model the population of country A is; \(f(x) = P_0\cdot a^{x - 2000}\)

The value of P₀, can be obtained from the information that the population of the country in x = 2000 is f(2000) = 3.5 million as follows;

\(f(2000) =P_0\cdot a^{2000 - 2000} = P_0 \times a^0 = P_0\times 1 = P_0\)

\(f(2000) = 3.5\ million\)

Therefore

P₀ = 3.5 million (substitution property of equality between the values)

In the year 2025, x = 2025, and f(2025) = 6.5 million, therefore;

\(f(2025) =P_0\cdot a^{2025 - 2000} = 6.5\ million\)

P₀ = 3.5 million, therefore;

\(f(2025) =3.5\ million \times a^{2025 - 2000} =3.5\ million \times a^{25} = 6.5\ million\)

a²⁵ = 6.5 ÷ 3.5 = 13/7

\(a =\left(\dfrac{13}{7} \right)^{\frac{1}{25} } = \left(\dfrac{13}{7} \right)^{0.04}\approx 1.02507\)

(b) The country's population in the year 2010 can be obtained by plugging in x = 2010 in the formula for finding the population of the country as follows;

\(f(2010) =3.5 \ million \times \left(1.02507\right)^{2010 - 2000} \approx 4.48\ million\)

The population of the country in 2010 is about 4.48 million

(c) The year during which the country's population might reach 11 million can be found using the function, f as follows;

\(f(x) =11\ million = 3.5 \ million\times \left(1.02507 \right)^{x - 2000}\)

\((x-2000) \times ln\left(1.02507\right) =ln\left(\dfrac{11}{3.5} \right)\)

\((x-2000)= \dfrac{ ln\left(\dfrac{11}{3.5} \right)}{ln\left(1.02507\right) } \approx 46.25\)

The year in which the population of the country will be 11 million, is therefore;

x ≈ 2000 + 46.25 ≈ 2046

The population of the country will be 11 million in the year 2046

Learn more about exponential functions here:

https://brainly.com/question/11464095

#SPJ1

Answer:

i totally get you, math is hard

Step-by-step explanation:

Answer:

understandable

Step-by-step explanation:

but whats the question

When writing a proof, you should construct the first statement by copying the “prove” statement(s) from the original problem. The Option B is correct.

When constructing the first statement in a proof, it is important to begin with copying the “prove” statement(s) from the original problem. This involves writing the next statement based on the given or previously proven statements.

It is not helpful to write a justification for the first statement in the right column without considering its logical connection to the problem. By beginning with a logically connected statement, the proof can proceed in a clear and organized manner which leads to a valid conclusion.

Read more about proof

brainly.com/question/29969150

#SPJ1

The area of the triangle with the given vertices is 11.5 square units.

The area of a triangle can be calculated using the coordinates of its vertices using the following formula.

To find the area of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃), we can use the following formula:

A = (x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂))/2

Using this formula with the given vertices (0, 6), (2, −3), and (3, 4), we get:

A = (0(-3 − 4) + 2(4 − 6) + 3(6 − (-3)))/2

A = (0 - 4 + 27)/2

A = 23/2

A = 11.5

Therefore, the area of the triangle with the given vertices is 11.5 square units.

To know more about vertices, visit:
https://brainly.com/question/24877689
#SPJ1