Read the following prompt and type your response in the space provided.
Sarah has a $30 music gift card. Each day she uses it to buy a $1.99 song download. For how many days will the gift card have still have a balance of more than $18?

Write an inequality to solve the problem and then solve showing your work. Explain what the solution to the inequality means.

.

The equation of the parabola with focus (2, -1) and vertex (2, 5) is

[tex](x-2)^2[/tex]= -24(y - 5).

An equation of a parabola with focus ( 0, p ) and directrix y = − p is

[tex]x^2[/tex] = 4py, p < 0

Here, we have the focus = (2, -1) and vertex = (2, 5)

substituting the values in the above equation we get,

p = -1 - 5 = -6

hence, p = -6

now let us find the equation of the parabola as follows-

[tex](x-2)^2[/tex]= 4p(y - 5)

[tex](x-2)^2[/tex]= 4 (-6) (y - 5)

[tex](x-2)^2[/tex]= -24(y - 5)

Hence, the equation of the parabola with focus (2, -1) and vertex (2, 5) is

[tex](x-2)^2[/tex]= -24(y - 5).

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The percentage of all customers who prefer soft drinks and coffee if 45% of customers preferred sports drinks over soft drinks, is 58%, so option D is correct.

A set is a clearly defined group of things in mathematics. Set names and symbols begin with a capital letter.

Given:

45% of customers preferred sports drinks over soft drinks, n(S) = 45%,

58% also preferred coffee to tea, n(C) = 58 %

46% of those who enjoy soft drinks preferred tea to coffee, n(C∩S) = 46%

Calculate the percentage of all customers who prefer soft drinks and coffee as shown below,

n(C∪S) =  n(S) + n(C) -  n(C∩S)

n(C∪S) = 45 + 58  - 46

n(C∪S) = 58%

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Answer:

30%.

Step-by-step explanation:

In simple terms, you have to divide 100/55, and 100/54, and multiply the two answers, which leaves you with 0.297. rounding to 0.3, which is 30%

Based on the highest wavelength in the cosmic microwave background spectrum, rank these eras from left to right, from shortest to longest, 500,000 years after the Big Bang.

Peak Wavelength - The maximum wavelength at which a light source's radiometric emission spectrum is observed is referred to as the peak wavelength. Simply put, it represents photo-detectors rather than the human eye's perception of any emission from the light source.

The temperature can be calculated using the Wien displacement law and the peak wavelength. On a chromaticity diagram, the variation in apparent hue of stars at various temperatures can be traced.

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Based on the information given in the question the  (0, 2kπ) maybe the spiral point or center point of the nonlinear system. The stability of (0, 2kπ) is indeterminate.

An equation comprising one or more functions and their derivatives is known as a differential equation in mathematics. A function's derivative expresses the rate of change of the function at a specific moment. It is mostly employed in the sciences of physics, engineering, and biology.

F = (1 + x) sin y = 0

G = 1 − x − cos y = 0

we know that all the critical points are (0, 2kπ), (2,(2k + 1)π). Since the F, G are

continuous differentiable, the system is almost linear near the critical points.

µ

Fx Fy Gx Gy=µsin y (1 + x) cos y−1 sin y

The linear system near critical point (2,(2k + 1)π) is

du/dt = −3v, dv/dt = −u

where u = 2 + x, v = (2k + 1)π + y. The eigenvalues of the linear system are −√3,√3,hence the critical point (2,(2k + 1)π) is saddle point and unstable. The linear system

near critical point (0, 2kπ) is

du/dt = v

dv/dt = −u, where u = x, v = 2kπ + y. The eigenvalues of the linear system are −i, i, hence the

critical point (0, 2kπ) is center point and stable of the corresponding linear system. Then (0, 2kπ) maybe the spiral point or center point of the nonlinear system. The stability of (0, 2kπ) is indeterminate.

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To find the rate in still water, we need to find the average speed of the boat. The total distance traveled by the boat is 192 + 360 = 552 kilometers. The total time taken is 3 + 4 = 7 hours.

So, the average speed of the boat is 552/7 = 78.857 km/hr.

To find the rate of the current, we need to find the difference in speed between the upstream and downstream journeys. The difference in speed is 360/4 - 192/3 = 90 - 64 = 26 km/hr.

So, the rate of the current is 26 km/hr.

Therefore, the rate in still water is 78.857 km/hr and the rate of the current is 26 km/hr.

the most conservative sample size for the estimation of the population proportion is 4471, rounded up to the nearest whole number.

Using the formula n = (Zα/2)^2(p*(1-p))/E^2, where:

n = sample size

Zα/2 = z-score for 0.025 (α/2) = 1.96

p = 0.5 (assumed to be the estimated proportion of the population)

E = 0.029 (specified absolute tolerance)

n = (1.96^2)*(0.5(1-0.5))/0.029^2 = 4471

Therefore, the most conservative sample size for the estimation of the population proportion is 4471, rounded up to the nearest whole number.

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The value of the vehicle after 12 years of purchase will be $13,500.

Here, we are given that a vehicle purchased for $25,000 depreciates at a constant rate of 5%.

Therefore, the value of the vehicle after 1 year will reduce by-

25,000 × 5/100

= 250 × 5

= 1250

Thus, the value after 1 year will become = 25,000 - 1250 = 23750

In the same manner, the value will keep on reducing every year. Thus, the value after 12 years will become-

25,000 [tex](1- 5/100)^{12}[/tex]

= 25,000 [tex](1 - 0.05)^{12}[/tex]

= 25,000 [tex](0.95)^{12}[/tex]

= 25,000 × 0.54

= 250 × 54

= 13,500

Thus, the value of the vehicle after 12 years of purchase will be $13,500.

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The Pythagorean for the triangle with a length of two legs x and y and the hypotenuse length as z is z²=x²+y².

The perpendicular, base (adjacent), and hypotenuse (opposite) are the names of the triangle's three sides. Perpendicular forms a right angle with the triangle base. The hypotenuse is the greatest side opposing the right angle (90 degrees) of a triangle. According to the Pythagorean Theorem, the square of the length of the hypotenuse will always result from adding the squares of the lengths of two legs of a right-angle triangle.

Given the length of one leg is x and the length of another leg is y. The length of the hypotenuse is z. Then, by the Pythagorean Theorem, z²=x²+y².

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The intersection of the two medians results in a 1:2 division. Consequently, the KP value is 15.5.

Given,

Triangle ABC is shown;

Triangle;-

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

Here,

If AK = 31 and we are aware that the two medians coincide, then the division is 1:2.

Then,

KP/AK = 1/2

KP = AK / 2

KP = 31/2

KP = 15.5

Therefore,

The value of KP is 15.5 units.

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The numeric value of the expression [(3 ⇑ 1) ⇑ 2] − [3 ⇑ (1 ⇑ 2)] is given as follows:

70.

The operator for this problem is given as follows:

a ⇑ b = a² + b².

Then the operations are made following the precedence of operations, due to the parenthesis, as follows:

Then the expression can be written as follows:

[(3 ⇑ 1) ⇑ 2] − [3 ⇑ (1 ⇑ 2)] = [10 ⇑ 2] − [3 ⇑ 5].

Then the operators are calculated as follows:

Finally, the subtraction is applied between these two results to obtain the numeric value of the expression, as follows:

104 - 34 = 70.

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Answer:

Step-by-step explanation:

Rick desposits 3$ into his account:

b=Rick's bank balance

b+3

The following week, he deposits 3 times that amount:

3*3=9

2nd week= b+9

Each ewek after that, he deposits 3 times the amount he did the previous week:

3rd week = b+9x3

3rd week = b+27

How much does it deposit in all during the first 3 weeks?

1st week = $3

2nd week = $9

3rd week = $27

3+9+27=39

Rick deposits $39 in the first 3 weeks

Answer for second question:

d=dollars

w=weeks

d=[tex]d=3^2[/tex]

"One who performs his duty without attachment, surrendering the results unto the Supreme Lord, is unaffected by sinful action, as the lotus leaf is untouched by water." - Krishna, Bhagavad Gita 5.10

Thanks, I hope I could help

Miraculous21

Answer:

Point A does not lie on the curve y = x²

Step-by-step explanation:

Given points:

 [tex]\sf A: \left(\dfrac{3}{2}, \dfrac{9}{2}\right)[/tex]

 [tex]\sf B: \left(-1,1 \right)[/tex]

 [tex]\sf C: \left(4,16 \right)[/tex]

 [tex]\sf D: \left(\dfrac{1}{2}, \dfrac{1}{4}\right)[/tex]

To determine if the given points lie on the curve y = x², simply substitute the x-value of each point into the equation and compare y-values.

Point A

[tex]\boxed{\begin{aligned}x=\dfrac{3}{2} \implies y&=\left(\dfrac{3}{2} \right)^2\\\\y&=\dfrac{3^2}{2^2}\\\\y&=\dfrac{9}{4}\end{aligned}}[/tex]

As 9/4 ≠ 9/2, point A does not lie on the curve.

Point B

[tex]\boxed{\begin{aligned}x= -1\implies y&=\left(-1 \right)^2\\y&=1\end{aligned}}[/tex]

As 1 = 1, point B does lie on the curve.

Point C

[tex]\boxed{\begin{aligned}x=4 \implies y&=\left( 4\right)^2\\y&=16\end{aligned}}[/tex]

As 16 = 16, point C does lie on the curve.

Point D

[tex]\boxed{\begin{aligned}x=\dfrac{1}{2} \implies y&=\left(\dfrac{1}{2} \right)^2\\\\y&=\dfrac{1^2}{2^2}\\\\y&=\dfrac{1}{4}\end{aligned}}[/tex]

As 1/4 = 1/4, point D does lie on the curve.

As per the statement in the question, the expression will be x + 52.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per given information in the question,

Let the unknown number is x.

The statement says that the number is more than 52.

Then, the expression according to the statement will be,

= x + 52

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Answer:

Step-by-step explanation:

The slope of the graph of y = -3x is -3. The slope of a line is the amount that the line rises or falls for every unit it moves horizontally. In this case, the line rises by -3 units for every 1 unit it moves horizontally. This means that the slope of the line is -3.

Answer:

[tex]\$856.03[/tex]

Step-by-step explanation:

The Continuous Compound Interest Formula is derived from the Compound Interest Formula: [tex]A = P(1 + \frac{r}{n})^{nt}[/tex], as the number of times interest is applied, goes to infinity. Through some simple algebraic manipulation, we get the formula: [tex]A = Pe^{rt}[/tex] (e is known as Euler's Number and is notation for a constant value like [tex]\pi[/tex])

Since Valeria invested 770 in an account with an interest of 53% paying monthly, we want to find how much time it takes to triple her money, and then plug that into Zoey's equation.

So let's generally solve for time in the equation:

[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

First divide by P

[tex]\frac{A}{P} = (1 + \frac{r}{n})^{nt}[/tex]

From here, it helps to take the base 10 log of both sides, so we can apply logarithmic properties, in this case we want to bring the exponent down.

[tex]log(\frac{A}{P}) = nt * log(1 + \frac{r}{n})[/tex]

Now from here' lets divide both sides by the log (the one on the right side) and "n" to give us:

[tex]\frac{log(\frac{A}{P})}{n * log(1 + \frac{r}{n})} = t[/tex]

Now whenever we need to calculate time, we simply need to plug in these values. We're given the following information from the problem:

[tex]P = 770\\r = 0.53\\n = 12\text{ compound monthly means 12 per year}\\A= 2,310 \text{ this is just 770 * 3, since we're looking for when Valeria's money triples}[/tex]

Plugging in the values we get:

[tex]\frac{log(\frac{2310}{770})}{12*log(1+\frac{0.53}{12}}=t[/tex]

Plugging this into a calculator, gives an approximate value of:

[tex]2.1183\approx t[/tex]

From here we simply need to plug values into the continuous compound interest formula: [tex]A=Pe^{rt}[/tex]

We're given the following information:

[tex]A = 770\\r= 0.03\\[/tex]

and we know that:

[tex]t\approx 2.1183[/tex]

since we solved for that.

So now let's just plug values into the equation!

[tex]A\approx 770 * e^{0.05 * 2.1183}\\A \approx 856.03[/tex]

So now we have our solution!

Answer:

  x = 3

Step-by-step explanation:

You want the equation of vertical line BD that includes point B(3, 2).

The equation of a vertical line is ...

  x = c . . . . . . for some constant c

Since we want the line to go through a point B(3, 2) with x-coordinate 3, that is the value the constant must have.

  x = 3 . . . . . the equation of line BD

__

Additional comment

Ordinarily, this rectangle would be named ABDC, with the vertices named in order around the figure.

Answer: D

Step-by-step explanation: It is D because the: "'m" in: "i'm" means: I am. The: 'I'm" is referring to you.

in C, the: "i'll" means: I will. After the: "tell", it doesn't make sense because it's not referring to someone. In between the: "tell" and "I", you should include: you. Overall, it should've sounded like: I'll tell you when I hear from him.

In B, the: "i'll" means I will. If you say in starting at this POS, It would sound: I will buy this car if I will like it. this does not make sense because instead of: i'll, you should replace it with: I.

In A, the: "don't" doesn't make sense because saying starting at a POS: I don't go to work tomorrow unless I feel better. You should replace the: "don't" with: won't.

Overall, D is the most acceptable answer.

The number of students who participate in competition for each grade are 223 and 208 and their sum is 431.

A fraction is a number written in the form a / b, where a and b are integers and b ≠ 0.

The number a is called as the numerator and b is the denominator.

(a) The total number of students are 595.

Then, the number of students in seventh grade is 3/5 × 595 = 357

Now, the number of students participated in competition is given as,

5/8 × 357

⇒ 223.125

Since, the number of students cannot be a decimal, it is taken as 223.

(b) The number of students in eighth grade is 2/5 × 595 = 238

Now, the number of students participated in competition is given as,

7/8 × 238

⇒ 208.25

Since, the number of students cannot be a decimal, it is taken as 208.

(c) The total number of students participating in competition is given as,

⇒ 223 + 208 = 431

Hence, the required number of students for 7th and 8th grade and their sum are given as 223, 208 and 431 respectively.

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No, the lines are not perpendicular because Line m has a slope of 2/3 and line p has a slope of  -5/3.

Its slope would be:

[tex]m = \dfrac{y-q}{x-p}[/tex]

Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.

For two lines to be perpendicular then the slopes are reciprocal of each other.

Line m: (-3,2)  (3,6)

line m: 2/3

Line p: (3,-4)  (-3,6)

x₁=3   x₂=-3   y₁=-4   y₂=6

p = -5/3

Therefore,

m ⊥ p is False.

The slopes are not negative reciprocal of each other. therefore the lines are not perpendicular.

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There is 0.17% of the time is Judy idle.

It will take 25 minutes on average, does a student spend waiting in line.

The waiting line on average is 4.1 customers.

The probability that an arriving student will find at least one other student waiting in line is 0.68.

Given students arrive at the Administrative Services Office at an average of one every 6 minutes, and their requests take on average 5 minutes to be processed.

The service counter is staffed by only one clerk, Judy gumshoes, who works eight hours per day.

Assume Poisson arrivals and exponential service times.

It was said in the question Students arrive at the Administrative Services Office at an average of one every 15 minutes which means that:

λ = 60/6 = 10customers/hr

μ = average of 5 minutes = 60/5 = 12customers/hr

1) What percentage of time is Judy idle?

The percentage when Judy was idle = 1- λ/μ = 1- 0.83= 0.17

%Service time = 0.83

%idle time = 0.17

There is 0.17% of time is Judy idle.

2) How much time, on average, does a student spend waiting in line?

A student spends waiting in line then we make use of the formula below:

λ /μ(λ-μ )

= 0.41 × 60

= 25 minutes

It will take 25 minutes on average, does a student spend waiting in line.

3) How long is the waiting line on average?

To calculate How long the waiting line is on average;

average waiting time x arrival rate = 0.41hrs x 10 customers/hr =  4.1 customers

The waiting line on average is 4.1 customers.

What is the probability that an arriving student will find at least one other student waiting in line?

P1( Probability of having a customer to attend to) = 0.17 x 0.83 = 0.141

P2( Probability of having 2 customer to attend to) = 0.17 x 0.83 x 0.83 = 0.117

The probability of finding at least one customer = 1 -[ po + p1]

= 1 - 0.17 - 0.141 = 0.68

The probability that an arriving student will find at least one other student waiting in line is 0.68.

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Answer:

O No, because 3²+9² <17²

Step-by-step explanation:

O No, because 3²+9² <17²

Step-by-step explanation:

If €2 of grapes cost $6

$1 =2/6

=€0.3

The expression for the interest earned on each account and the balance after 3 years are;

1) Interest = P(1 + 0.039t)

Balance = $485.90

2) Interest = P(1.039)^(t)

Balance = $487.91

3) Interest = P(1.039)^(t)

Balance = $487.91

4) Interest = 435e^(0.039t)

Balance = $488.99

We are given different formulas for interest and we are told to find the balance of each option after 3 years. Thus, we have;

1) P(1 + rt)

Where;

P is principal = $435

r is rate = 0.039

t is time = 3 years

We have;

Balance = 435(1 + (0.039 * 3))

Balance = $485.90

2) P(1 + (r/n))^(nt)

Where;

P is principal = $435

r is rate = 0.039

t is time = 3 years

n is number of times interest is compounded per year  = 1 (because it is yearly)

Thus;

A = 435(1 + (0.039/1))^(3 * 1)

A = $487.91

3) Same as 2 above

4) P₀e^(rt)

where;

P₀ is principal = $435

r is rate = 0.039

t is time = 3 years

Thus;

A = 435(e^(0.039 * 3)

A = $488.99

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The maximum number of pages the report can have in scientific notation is equal to 2.0×10⁶ pages.

Scientific Notation is the expression in which numbers are written in the powers of 10 so that their expression can be used in calculation and also it makes calculation easy. To find the maximum number of pages the report can have, we need to divide the size of the USB drive, which is 4×10⁶ KB, by the size of each page, which is 2 KB/page. Doing this gives us:

4×10⁶ KB / 2 KB/page = 2×10⁶ pages

Rounding to one decimal place gives us: 2,000,000.0 pages

So, the maximum number of pages the report can have is 2,000,000.0 pages. In scientific notation, this is: 2.0×10⁶ pages.

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Answer:

Suma= 80 + (4 × 40) + (4 × 20) + (4 × 10) + (4 × 5)

Suma= 80 + 160 + 80 + 40 + 20

Suma= 400

Step-by-step explanation:

The sum of the first five terms of the geometric progression is 1705.

To calculate the sum of the first five terms of a geometric progression, we need to determine the first term and the common ratio. Given that the third term is 80 and the ratio is 4, we can find these values.

In a geometric progression, each term is obtained by multiplying the previous term by the common ratio. Let's denote the first term as "a" and the common ratio as "r."

Given that the third term is 80, we can write the equation:

a * r² = 80

We are also given that the ratio is 4, so we have:

r = 4

Substituting this value of r into the equation, we get:

a * (4)² = 80

a * 16 = 80

16a = 80

a = 5

Now that we have determined the first term (a = 5) and the common ratio (r = 4), we can calculate the sum of the first five terms using the formula for the sum of a geometric series:

Sum = a * (1 - rⁿ) / (1 - r)

Plugging in the values, we have:

Sum = 5 * (1 - 4⁵) / (1 - 4)

Simplifying the calculation:

Sum = 5 * (-1023) / (-3)

Sum = 1705

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The logistic model of the projected magazine sales is P = e¹⁰⁰⁰/1+e¹⁰⁰⁰

What is meant by logistic model?

In math, logistic model refers a statistical analysis method to predict a binary outcome, such as yes or no, based on prior observations of a data set.

Here we have given that our new magazine initially sells 400 copies per month. research indicates that a vigorous advertising campaign could increase sales by 30% each month if our market were unlimited. but research also indicates that magazine sales in our area are unlikely to exceed 2000 per month.

Here we need to make a logistic model of projected magazine sales.

As per the formula of logistic model, while we looking into the given question, we identified the values,

a = 400

x = 30% => 0.3

b = 2000

Then the logistic model of the given situation is written as,

=> P = e⁴⁰⁰⁺⁰°³ˣ²⁰⁰⁰/ 1 +  e⁴⁰⁰⁺⁰°³ˣ²⁰⁰⁰

=> P = e¹⁰⁰⁰/1+e¹⁰⁰⁰

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Answer: Thermal energy

Step-by-step explanation:

Thermal energy is the sum of the kinetic and potential energy of all the particles in an object.

Answer:   The correct answer is therefore A) $74.40.

Step-by-step explanation: To calculate Social Security tax for Betsy at $1,200, we need to find the amount of tax that is due on that amount of income. According to the schedule, Social Security tax is applied at a rate of 6.2% on income up to $128,400. Therefore, the amount of tax due on $1,200 of income would be $1,200 x 6.2% = $<<12006.2.01=74.4>>74.4.

The two figures would be similar if the value of x is 31 mm. Thus option D.

On comparison of two or more shapes, they will only be similar if they all have a set of common corresponding properties. These properties may be due to their corresponding length of sides, or measure of internal or external angles.

To determine the value of x that would make the shapes to be similar, compare the corresponding sides of the shapes.

So that we have;

[tex]\frac{14.5}{29}[/tex] = [tex]\frac{15.5}{x}[/tex]

make x the subject of the formula

x = [tex]\frac{29*15.5}{14.5}[/tex]

  = 31

x = 31 mm

The value of x that would make the two figures similar is 31 mm.

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One of the four fundamental mathematical operations is addition. The length of the missing side is 6 yd.

What exactly is addition?

Addition is one of the four basic mathematical operations, along with subtraction, multiplication, and division. The total quantity or sum of two whole numbers is obtained by adding them together.

According to the question,

All the line intersecting at right angles . So,

The lines AB, CD, and EF are parallel in the diagram, we can write the length of AB as,

AB length = EF length - CD length

= 14yd - 8yd

= 6yd

As a result, the missing side length is 6yd

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