5.
13 points
A piece of jewelry that regularly costs $120 is on sale for $96. What is the percent of decrease in the
price of the jewelry piece?
A 15%
B 20%
C 18%
D 30%

The statement that is true about the function is:

A function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

The minimum value of the curve = (1.9, -5.7),

The maximum value = (0, 2)

The point the function crosses the x-axis (the x-intercept) = (-0.7, 0), (0.76, 0), and (2.5, 0)

The point the function crosses the y-axis (the y-intercept) = (0, 2)

The given points can be plotted using MS Excel, from which we have:

F(x) is less than 0 over the interval from x = -∞, to x = -0.7, and the interval from x = 0.76 to x = 2.5.

Hence, the correct option is A.

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Answer:

\((4x+7)(4x-7)\)

Step by step explanation:

\(16x^2 -49\\\\=(4x)^2-7^2\\\\=(4x+7)(4x-7)~~~~~~~~~~;[a^2-b^2 =(a+b)(a-b)]\)

The probability that less than 75% of the sample students have iPhones is approximately 0.2478.

What is probability?

This is a binomial probability problem, where each student either has an iPhone or does not have an iPhone, and the probability of success (having an iPhone) is 0.789.

Let X be the number of students in the sample who have an iPhone. We want to find P(X < 0.75 * 50) = P(X < 37.5)

Using the binomial probability formula, we have:

P(X < 37.5) = Σ P(X = k), for k = 0, 1, 2, ..., 37

However, this is a tedious calculation. Instead, we can use a normal approximation to the binomial distribution, since n * p = 50 * 0.789 = 39.45 > 10 and n * (1 - p) = 50 * 0.211 = 10.55 > 10.

Using the normal approximation, we can standardize the random variable X:

Z = (X - μ) / σ

where μ = n * p = 39.45 and σ = √(n * p * (1 - p)) = √(50 * 0.789 * 0.211) = 2.88.

Then, we have:

P(X < 37.5) = P(Z < (37.5 - 39.45) / 2.88) = P(Z < -0.68)

Using a standard normal table or calculator, we find that P(Z < -0.68) is approximately 0.2478.

Therefore, the probability that less than 75% of the sample students have iPhones is approximately 0.2478.

Binomial probability is a type of probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure. It assumes that the probability of success in each trial is constant, and the trials are independent of each other. The binomial distribution is characterized by two parameters: the number of trials and the probability of success in each trial.

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Step-by-step explanation:

100% = $27.50

1% = 100%/100 = $27.50/100 = $0.275

the extra amount paid (for the tip) was

$32.45 - $27.50 = $4.95

to know how many percent that is, we need to see how often 1% fits into that amount.

so,

4.95 / 0.275 = 18

therefore the tip was 18%.

FYI - in real life the tip percentage (and corresponding amount) is calculated based on the net bill (the amount before sales tax).

Answer:

you have the highest chance of getting peanuts

The distance between the two points N(-3, -11) and P(-3, -2) is 9 units.

Given the points

N(-3,-11) and P(-3,-2)

To find the distance between two points, we can use the distance formula:

d = √((x2 - x1)²+ (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Using this formula, we can find the distance between the two points N(-3, -11) and P(-3, -2) as follows:

d = √((-2 + 11)²+ (-3 + 3)²)

This gives

d = √9²+ 0²)

So, we have

d = √81

Evaluate

d = 9

Therefore, the distance between the two points N(-3, -11) and P(-3, -2) is 9 units.

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Answer:

y + -24.8 = -13

Step-by-step explanation:

y + 6.2x(-4) = -13

y + -24.8 = -13

To determine the final answer you would need to figure out the value of Y.

Additive inverse property of real numbers was used to transition from step 3 to step 4

The property of real numbers used to transition from Step 3 to Step 4 is the additive inverse property or the property of adding the opposite. The additive inverse property states that for any real number a, there exists an additive inverse -a, such that a + (-a) = 0. In other words, adding the opposite of a number results in the sum being zero.

In Step 3 of the given expression, we have "12 + (-12) + 6x." Notice that "-12" is the opposite of "12." To simplify this expression further, we can apply the additive inverse property by combining the positive and negative numbers.

Adding 12 and its additive inverse (-12) results in 0, according to the additive inverse property. So, in Step 4, we replace "12 + (-12)" with "0." By applying the additive inverse property, the expression simplifies to "0 + 6x," which can be further simplified to just "6x."

The use of the additive inverse property is crucial in algebraic simplifications as it allows us to eliminate terms that add up to zero. This property helps streamline calculations and reduce complex expressions to simpler forms.

Overall, the transition from Step 3 to Step 4 in the given expression utilizes the additive inverse property to eliminate the sum of opposite numbers and simplify the expression to its final form, which is "6x."

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Using supplementary angle theorem

As BD bisects AC

So ∆AEC\(\cong \)∆DEC(SAS)

Also similarly

Hence it's a parallelogram

Given: BD bisects AC and ∠CBE≅∠ADE.  ABCD is a proved to be a parallelogram by proving that opposite sides are parallel to each other.

A parallelogram is a quadrilateral with opposite sides parallel.

Given in the question,

AE = EC

∠CBE = ∠ADE

result 1:

∠CBE = ∠ADE : alternate interior angles

Thus, BC is parallel to AD.

In triangles BCE and ADE,

∠CBE = ∠ADE (given)

AE = EC (given)

∠BEC = ∠DEA (opposite angles)

triangles BCE and ADE are congruent by AAS congruence.

Implying, BE = ED (cpct)

In triangles BEA and CED,

AE = EC (given)

BE = ED (cpct)

∠BEC = ∠DEA (opposite angles)

triangles BEA and CED are congruent by SAS congruence.

∠ECD = ∠EAB (cpct)

Result 2:

∠ECD = ∠EAB : alternate interior angles

Thus, BA is parallel to CD.

Since, both opposite sides of the quadrilateral are parallel, ABCD is a parallelogram.

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Statistics is referred to as a discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

This is referred to as information that has been translated into a form that is efficient for movement or processing.

Statistics involves using information that has been translated into a form that is efficient for movement or processing through different tools such as mean standard deviation etc.They help to provide more details about a set of data which makes it use very important.

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Answer:

What is a linear function? A linear function is a function whose graph is a straight line. The rate of change of a linear function is constant. The function shown in the graph below, y = x + 2, is an example of a linear function.

Graph of linear function

Graph of linear function

A linear function has a constant rate of change. The rate of change is the slope of the linear function. In the linear function shown above, the rate of change is 1. For every increase of one in the independent variable, x, there is a corresponding increase of one in the dependent variable, y. This gives a slope of 1/1 = 1.

A linear function is typically given in the form y = mx + b, where m is equal to the slope, or constant rate of change.

Examples of linear functions include:

If a person drives at a constant speed, the relationship between the time spent driving (independent variable) and the distance traveled (dependent variable) will remain constant.

Assuming no change in price, the relationship between the number of pounds of bananas a person buys (independent variable) and the total cost of the bananas (dependent variable) will remain constant.

If a person earns an hourly wage at their job, the relationship between the time spent working (independent variable) and the amount earned (dependent variable) will remain constant.

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Exponential Functions

What is an exponential function? An exponential function is a function that involves exponents and whose graph is a smooth curve. The rate of change in an exponential function is not constant. The functions shown in the graph below, y = 0.5x and y = 2x, are examples of exponential functions.

Graphs of exponential functions

Graphs of exponential functions

An exponential function does not have a constant rate of change. The rate of change in an exponential function is the value of the independent variable, x. As the value of x increases or decreases, the rate of change increases or decreases as well. Rather than a constant change, as in the linear function, there is a percent change.

An exponential function is typically given in the form y = (1 + r)x, where r represents the percent change.

Examples of exponential functions include:

Step-by-step explanation:

- Plot- Something interesting happens. After 43 nuggets, it is possible to fill any order request exactly. The number 43 is the largest number of nuggets it is not possible to make using packs of six, nine and twenty.

"Branliest will be appreciated"

The false statement from the stem-and-leaf plot is given as follows:

b. The data for Paul’s group has two modes.

The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:

4|5 = 45.

The mode of a data-set is the data-set that appears the most times in a data-set.

Hence, for Paul's group, the mode is given as follows:

44.

As it is the only observation that appears the times, hence the data has one mode, and option b gives the false statement.

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Answer:

\(\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}\)

\(x=9,\:y=13\)

the option 'd' is correct.

Step-by-step explanation:

Given the system of the equations

\(\begin{bmatrix}5x-3y=6\\ 6x-4y=2\end{bmatrix}\)

\(\mathrm{Multiply\:}5x-3y=6\mathrm{\:by\:}6\:\mathrm{:}\:\quad \:30x-18y=36\)

\(\mathrm{Multiply\:}6x-4y=2\mathrm{\:by\:}5\:\mathrm{:}\:\quad \:30x-20y=10\)

\(\begin{bmatrix}30x-18y=36\\ 30x-20y=10\end{bmatrix}\)

\(30x-20y=10\)

\(-\)

\(\underline{30x-18y=36}\)

\(-2y=-26\)

\(\begin{bmatrix}30x-18y=36\\ -2y=-26\end{bmatrix}\)

solve for y

\(-2y=-26\)

\(\mathrm{Divide\:both\:sides\:by\:}-2\)

\(\frac{-2y}{-2}=\frac{-26}{-2}\)

\(y=13\)

\(\mathrm{For\:}30x-18y=36\mathrm{\:plug\:in\:}y=13\)

\(30x-18\cdot \:13=36\)

\(30x-234=36\)

\(30x=270\)

\(\mathrm{Divide\:both\:sides\:by\:}30\)

\(\frac{30x}{30}=\frac{270}{30}\)

\(x=9\)

\(\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}\)

\(x=9,\:y=13\)

Therefore, the option 'd' is correct.

The maximum area of the rectangle is A = 9 units²

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the function for area be f ( x )

where f ( x ) = - ( x - 3 )² + 9

Let the width of the rectangle be W.

The perimeter of a rectangle is given by:

Perimeter = 2(length + width) = 12 units

12 = 2(x + width)

Simplifying this equation, we get:

6 = x + width

width = 6 - x

Now, the area of the rectangle is given by:

Area = Length x Width

Substituting the value of width in terms of x, we get:

Area = x(6 - x)

Area of rectangle A = 6x - x²

This is a quadratic function of x, which has a maximum value at the vertex of the parabola. The vertex of the parabola can be found by completing the square or by using the formula:

x = -b/(2a)

In this case, a = -1 and b = 6, so we have:

x = -6/(2(-1)) = 3

Therefore, the maximum area of the rectangle occurs when x = 3, and the value of the maximum area is:

Area of rectangle A = 3(6 - 3) = 9 square units

Hence , area of rectangle is A = 9 units²

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The graph will be piecewise. Then the graph of the function is given below.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

S(n) = 0.50n + 3.5, if 1 ≤ n ≤ 14

S(n) = 0                 , if n ≥ 15  

The graph will be piecewise. Then the graph of the function is given below.

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Answer:

Step-by-step explanation:

3x = 90 + 46 - 14

3x = 122

x=\(\frac{122}{3}\)≈40,7

Answer: 40.6 repeated

Step-by-step explanation: combine -46 and 14 which is -32. then add 32 to 90. then divide 3 on both sides. 122/3 is 40.6 repeated

Answer:

B).

Step-by-step explanation:

Add 8 to half the difference of 6 and 2 then subtract 1.

Answer:

I apologize but I haven't worked for an answer. but my mind is, what is the point of this question? everyone is familiar with the "when am I ever going to use this in life and why do I need to learn this?" but this is a whole new level of w t f.

Answer:

20% of the invited people did not attend

Step-by-step explanation:

5 out of 25 people invited didn't attend Glen's party. That means the following:

\(\frac{5}{25}\)  people didn't come which simplifies to  \(\frac{1}{5}\)

Multiply \(\frac{1}{5}\) by the giant one \(\frac{20}{20}\) so the denominator is 100 which is the denominator used to find percentages.

You end up with \(\frac{20}{100}\)

\(\frac{20}{100}\) = 20%

20% is the percentage of the people whom Glen invited did not attend the party.

To find the percentage of people who did not attend the party, we will divide the number of people who did not attend (5) by the total number of people invited (25), and then multiply by 100.

Percentage = (Number of people not attended / Total number of people invited) × 100

Percentage = (5 / 25) × 100

Percentage = 20%

So, 20% of the people whom Glen invited did not attend the party.

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Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

The solution to the given inequality is x < 10c

Inequality are expression that are not separated by an equal sign. Given the inequality expression

x/2<5c

We are to determine the value of x from the inequality as shown;

Given

X/2<5c

Multiply both sides buy 2 to have:

X/2(2)<5c(2)

x < 5(2c)
x < 10c

Hence the solution to the given inequality is x < 10c

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2k + s - 2

I don't understand the question

Answer:

2k+s-2

Step-by-step explanation:

twice means 2 and k is just a number but as a letter. plus the quantity s is just s as a number, then minus 2 is

=2k+s-2

Answer and Step-by-step explanation:

The postulate of theorem that can be used to conclude the two triangles are congruent will be the ASA congruence postulate.

ASA means Angle Side Angle, in which two Angles in a triangle are congruent, and the side in between the two angles are congruent.

So, angle TXW is congruent to angle TWR, and the side that is in between is side WX, by the reflexive property of congruence.

#teamtrees #PAW (Plant And Plant)

Answer:

14p +4q-2r

Step-by-step explanation:

Sum of (10p-r+5p+2q)

10p+5p+2q-r

15p+2q-r

Now subtract( p-2q+r) from (15p+2q-r)

(15p+2q-r) - (p-2q+r)

15p+2q-r-p+2q-r

15p-p+2q+2q-r-r

14p +4q-2r

The answer is 14p +4q-2r

Answer:

I think answer is 8.....

Answer:

6 units to the right

Step-by-step explanation:

Z(3,4) → Z'(9,4)

d = √(9-3)² + (4-4)² = √6²+0² = 6   to the right

The translation of point Z of triangle XYZ from (3, 4) to Z′(9, 4) is a move of 6 units to the right.

In Mathematics, particularly geometry, the translation of a point is the process of moving the point a specific number of units either up, down, left or right. In the case of your triangle XYZ, the original position of point Z is at (3, 4) and Z′ is positioned at (9, 4). The y-coordinate hasn't changed; it remains at 4. This tells us that the translation is not up or down. However, if we observe the x-coordinate, you’ll see that it went from 3 to 9. Changing the x-coordinate moves the point horizontally, so we know our translation is left or right. Lastly, the difference between 3 and 9 is 6. We can therefore determine that the point moved 6 units to the right.

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Volume of the cylinder is 1017.9 cubic meters.

The formula for the volume of a cylinder is given by V = πr²h, where V is the volume, r is the radius of the base, and h is the height of the cylinder. To use this formula, we need to first find the radius of the base, which is half of the diameter.

The diameter of the base is given as 12m, so the radius is 6m. The height is given as 9m. Using the formula, we can calculate the volume of the cylinder as:

V = π × 6² × 9

V = 1017.87 cubic meters (rounded to the nearest tenth)

Therefore, the volume of the cylinder is approximately 1017.9 cubic meters.

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Answer:

\(\displaystyle m = 0\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

Point (2, -3)

Point (6, -3)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Answer:

3

one

will represent

the student