You and your friends decide to take a road trip to Florida for Winter Break. It will cost you $60 per day to visit Orlando and $100 per day to visit Tampa. You have $760 to spend on this trip and will stay for 10 days. What two equations could help you determine how many days you can afford to stay in each city?

We create a number line with a range from 0 to 1.0 and divide it into 5 equal segments to demonstrate the equality between 0.200 and 1/5.

The visual representation of numbers on a straight line, either horizontally or vertically, is known as a number line. When numbers are written down on a number line, it is straightforward for humans to compare them and perform basic arithmetic operations on them. One might assume that a number line starts at zero (0). There are only negative numbers to the left of zero and only positive numbers to the right of zero. In other words, as we move to the right on a number line, the value of the numbers increases. This shows that the numbers on the right are more numerous than those on the left.

To know more about the number line, visit:

https://brainly.com/question/13189025

#SPJ9

Answer:

Step-by-step explanation:

\(4\sqrt{3-\frac{1}{x} } -\sqrt{\frac{x}{3x-1} } =3\\4\sqrt{\frac{3x-1}{x} } -\sqrt{\frac{x}{3x-1} } =3\\\\put ~\sqrt{\frac{3x-1}{x}} =a\\4a-\frac{1}{a} =3\\4a^2-1-3a=0\\4a^2-4a+1a-1=0\\4a(a-1)+1(a-1)=0\\(a-1)(4a+1)=0\\a=1,-\frac{1}{4}\\\)

\(\sqrt{\frac{3x-1}{x} } =1\\3x-1=x\\3x-x=1\\2x=1\\x=\frac{1}{2}\)

when a=-1/4

\(\sqrt{\frac{3x-1}{x} } =-\frac{1}{4} \\\)

\(\frac{3x-1}{x} =\frac{1}{16} \\48x-16=x\\47x=16\\x=\frac{16}{47}\)

\(\frac{(1-2x)^2 \times (x^2-9)}{-x^2-x+6} \geq 0,\\both ~numerator ~and~denominator ~are~of~same~sign.\\\frac{(1-2x)^2(x^2-9)}{-x^2-3x+2x+6} \geq 0\\\frac{(1-2x)^2(x+3)(x-3)}{-x(x+3)+2(x+3)} \geq 0\\\frac{(1-2x)^2(x+3)(x-3)}{(x+3)(-x+2)} \geq 0\\(1-2x)^2\geq 0~(always)\\x\neq -3\\case.~1.\\both~numerator~and~denominator >0\\\frac{x-3}{-x+2} \geq 0\\x-3\geq 0\\x\geq 3\\-x+2> 0\\-x>-2\\x<2\\so~ solution~ is~ (-\infty,-3)U(-3,2)U[3,\infty)\)

case 2.

both numerator and denominator are negative.

\(x-3\leq 0\\x\leq 3\\-x+2\leq 0\\-x\leq -2\\x\geq 2\\solution~is~(-\infty,-3)U(-3,3]U[2,\infty)\)

Answer:

you would need to find the price before tax of the game. (B)

Answer:

V= video game $

.50V=.75

Now divide,

.75 divided by .05=15= V

So the video game wquals $15.

Now Check your answer

15 times (x) .05= .75

There you go :)

Step-by-step explanation:

Answer:

6 days

Step-by-step explanation:

Answer:

he had the tux for 6 days because he paid the cleaning fee

Step-by-step explanation:

The height  of the box that has the smallest possible surface area is  20m .

In the question ,

it is given that ,

the box has a square base ,

let the side of the box = "x" m

and let the height of the box = "y" m

volume of the box is given as 32000 m³,

So , x²y = 32000

y = 32000/x²

let the surface area of the box be "S" , that means

surface area(S) = area of base + total area of the 4 sides

= x²y + 4xy

Substituting the value of y = 32000/x² , we get

= x² + 4x(32000 / x²)

= x² + 128,000 / x,       x > 0

to minimize the area we differentiate it with respect to x,

we get ,

= 2x - 128,000 / x²

= (2x³ - 128,000) / x²

Substituting S' = 0 ,  we get , 2x³ = 128,000

x³ = 64,000

x = 40

and y = 32000/(40)² = 20 m .

Therefore , The height  of the box that has the smallest possible surface area is  20m .

The given question is incomplete , the complete question is

A box with a square base and open top must have a volume of 32,000 m³ . Find the height of the box that has the smallest possible surface area ?

Learn more about Surface Area here

https://brainly.com/question/28348566

#SPJ4

The statement "If a set of vectors {v₁, v₂, ...., vp} in Rⁿ is linearly dependent, then p>n" is False.

Let {v₁, v₂, ...., vp} be a set of p vectors in Rⁿ, then the following are equivalent statements:

1. The set of vectors is linearly dependent.

2. There exist constants c₁, c₂, ... cp, not all of them zero, such that:

c₁v₁+c₂v₂+...+cpvp = 0 (zero vector)

For the above to be possible, the following must hold true: p≥n

Because in Rⁿ, each vector has n components.

So, the total number of unknowns is p, while the total number of equations that we have is n.

Hence p≥n for the system of linear equations above to have a non-zero solution.

Hence, the statement "If a set of vectors {v₁, v₂, ...., vp} in Rⁿ is linearly dependent, then p>n" is False.

To learn more about set of vectors from the given link.

https://brainly.com/question/15519257

#SPJ11

Answer:

5 units

Step-by-step explanation:

Even if there is a transformation, it is asking for the length.

Therefore the length of WZ is 5 units

The rule for h(f(x)) is obtained by taking the function f(x) and putting it into the function h(x) in place of x. The correct answer is h(f(x)) = 2x - 11.

The composition of functions h(f(x)) means that we first apply the function f(x) and then apply the function h(x) to the output of f(x). So, to find the rule for h(f(x)), we need to substitute the function f(x) into the function h(x) wherever we see x.

Starting with f(x) = x - 7, we substitute (x - 7) for x in h(x) = 2x + 3:

h(f(x)) = h(x - 7) = 2(x - 7) + 3

Simplifying this expression, we get:

h(f(x)) = 2x - 11

Therefore, the rule for h(f(x)) is h(f(x)) = 2x - 11.

Learn more about Composition of Functions at

brainly.com/question/30660139

#SPJ1

The solution of the algebraic equation is (2, 1)

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

x + y = 3

x - 2y = 0

In the above equations we can see that

Both equations have different slopes and they are linear equations

This means that they would intersect at a point

From the graph, we have the intersectoon point to be (2, 1)

Hence, the solution is (2, 1)

Read more about equation here:

brainly.com/question/13048424

#SPJ1

The geometric series is convergent and the sum of the series is given by the term as \(S_n=\frac{a}{1-r} = \frac{8}{\pi -1}\).

Measures of central tendencies can be used in mathematics and statistics to quickly convey the summary of values for the entire data collection. The mean, median, mode, and range are the most crucial measurements of central trends.

The data set's mean will provide you a general notion of the data among these. The average of numbers is determined by the mean. Arithmetic Mean (AM), Geometric Mean (GM), and Harmonic Mean are the many forms of means (HM).

The geometric series is,

\(\sum_{n=1} \frac{8}{\pi ^n}\) = \(\frac{8}{\pi} +\frac{8}{\pi ^2} +\frac{8}{\pi ^3} +...\)

Here a = 8/π

Common ratio r = \(\frac{1}{\pi}\) which is numerically less than 1.

By geometric series test the given series is convergent,

Now, \(S_n=\frac{a}{1-r} = \frac{8}{\pi -1}\).

Learn more about Geometric series:

https://brainly.com/question/24643676

#SPJ4

Complete question:

Determine whether the geometric series is convergent or divergent. sigma_n = 1^infinity 8/pi^n convergent divergent If it is convergent, find its sum. (If the quantity diverges, enter DIVERGES.)

Answer: a) -8/9

b) The series is convergent

c) 1/17

Step-by-step explanation:

The series a+ar+ar²+ar³⋯ =∑ar^(n−1) is called a geometric series, and r is called the common ratio.

If −1<r<1, the geometric series is convergent and its sum is expressed as ∑ar^(n−1) = a/1-r

a is the first tern of the series.

a) Rewriting the series ∑(-8)^(n−1)/9^n given in the form ∑ar^(n−1) we have;

∑(-8)^(n−1)/9^n

= ∑(-8)^(n−1)/9•(9)^n-1

= ∑1/9 • (-8/9)^(n−1)

From the series gotten, it can be seen in comparison that a = 1/9 and r = -8/9

The common ratio r = -8/9

b) Remember that for the series to be convergent, -1<r<1 i.e. r must be less than 1 and since our common ratio of -8/9 is less than 1, the series is convergent.

c) Since the sun of the series tends to infinity, we will use the formula for finding the sum to infinity of a geometric series.

S∞ = a/1-r

Given a = 1/9 and r = -8/9

S∞ = (1/9)/1-(-8/9)

S∞ = (1/9)/1+8/9

S∞ = (1/9)/17/9

S∞ = 1/9×9/17

S∞ = 1/17

The sum of the geometric series is 1/17.

Answer:

a.12.6   b.8.0

Step-by-step explanation:

So, XZ= 7x+1 and PZ= 4x-1. To figure out XP we have to subtract those two.

(7x+1)-(4x-1)

3x-2

3(8)-2

24-2

22

XP=22

Answer:

ANSWER

A: 11

Step-by-step explanation:

hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh just trust me it won't let me post without and explanation

Answer:

Domain

Step-by-step explanation:

Answer:

  2.36 liters

Step-by-step explanation:

The volume Janet wants is 1/3 of 1/2 of the volume of a sphere with radius 15 cm. The formula for the volume of a sphere is given.

The water volume is ...

  V = (1/3)(1/2)(4/3π)(15 cm)³ = 750π cm³ ≈ 2356 cm³

There are 1000 cm³ in 1 liter, so Janet needs about ...

  2356 cm³/(1000 cm³/L) = 2.356 L

Janet should put about 2.36 liters of water in the fish tank.

Answer:

it is all I could.

Hope it helps

To justify the statement ln(17) = 2.833 mathematically, we can use the definition of the natural logarithm function.

The natural logarithm of a number x, denoted as ln(x), is defined as the exponent to which the base e (approximately 2.71828) must be raised to obtain the number x.

In this case, we have ln(17) = 2.833. To justify this statement mathematically, we can rewrite it using the definition of the natural logarithm:

e^(2.833) = 17

Here, e represents the base of the natural logarithm function, which is approximately 2.71828. By raising e to the power of 2.833, we should obtain the value of 17.

So, the mathematical equation to justify the statement ln(17) = 2.833 is e^(2.833) = 17.

To know more about Logarithm, visit:

brainly.com/question/30226560
#SPJ11

Answer:

16

Step-by-step explanation:

64 divided by 4 is equal to 16.

Answer:

a

Step-by-step explanation:

The measure of center that would best summarize the plot is given as follows: Median of 11.

The measure of variability is given as follows: IQR of 1.5.

A box and whisker plots shows these five features from a data-set, listed as follows:

From the plot, these features are given as follows:

The median is the best measure of center of the data-set.

There is an outlier at 16, hence the best measure of variability is the IQR, given by the difference between the Q3 and the Q1, hence:

IQR = 11.5 - 10

IQR = 1.5.

More can be learned about box plots at https://brainly.com/question/12343132

#SPJ1

Answer:

A

Step-by-step explanation:

correct me if I'm wrong

The inequality expression (2/3)y - 4 ≥ 2 when evaluated is y ≥ 3

Inequality expressions are those statements in mathematics that use symbols like <, >, ≤, or ≥ to compare two values.

From the question, we have the following inequality expression given as

(2/3)y - 4 ≥ 2

Add 4 to both sides of the inequality

So, we have the following representation

2/3y ≥ 2

Multiply both sides of the inequality expression by 3/2

y ≥ 3

Hence, the solution to the given inequality expression is y ≥ 3

Read more about inequality at

https://brainly.com/question/25275758

#SPJ1

The standard form of the equation of the ellipse with the given characteristics is (x+5)^2/49 + (y-2)^2/40 = 1.

To find the standard form of the equation of an ellipse, we need to know the coordinates of the foci and the endpoints of the major axis.

In this case, the foci are given as (-5,-1). The foci of an ellipse are points inside the ellipse that help define its shape. The distance between each focus and any point on the ellipse is constant.

The endpoints of the major axis are given as (-5,-5) and (-5,9). The major axis is the longest diameter of the ellipse and passes through the center of the ellipse.

The center of the ellipse can be found by taking the average of the x-coordinates and the y-coordinates of the endpoints of the major axis. In this case, the x-coordinate is -5 for both endpoints, and the average of the y-coordinates is (-5 + 9) / 2 = 2. Therefore, the center of the ellipse is (-5, 2).

The distance between the center and each focus is a constant value called "c". To find "c", we can use the distance formula between the center and one of the foci:

c = sqrt((-5 - (-5))^2 + (-1 - 2)^2) = sqrt(0 + 9) = 3.

The distance between the center and each endpoint of the major axis is another constant value called "a". In this case, a = 9 - 2 = 7.

Now we have all the necessary information to write the standard form of the equation of the ellipse:

where (h, k) is the center of the ellipse and a and b are the lengths of the semi-major and semi-minor axes, respectively.

Plugging in the values, we have:

(x + 5)^2 / 49 + (y - 2)^2 / 40 = 1.

Therefore, the standard form of the equation of the ellipse is (x + 5)^2 / 49 + (y - 2)^2 / 40 = 1.

To learn more about ellipse, click here: brainly.com/question/30995361

#SPJ11

After approximately 113 minutes, there will be only 40 bacteria remaining.

Half-life is defined as the time it will took a substance to reduce to half of its initial amount. The half-life of a substance is determined with respect to the rate of the reaction. It can be calculated using the formula below.

N(t) = N₀(1/2)^(t/T)

where N(t) = amount of substance remaining after time t

N₀ = initial amount of substance

t = time

T = half-life

If the sample begins with 500 bacteria, and after 16 minutes there are 350 bacteria, then

N₀ = 500, and N(t) = 350 when t = 16 minutes

Substitute the given values and solve for the half-life.

N(t) = N₀(1/2)^(t/T)

350 = 500(1/2)^(16/T)

T = 31.09 minutes

Using the formula, solve for t when n(t) = 40.

N(t) = N₀(1/2)^(t/T)

40 = 500(1/2)^(t/31.09)

t = 113.30 minutes

t ≅ 113 minutes

Learn more about half-life here: brainly.com/question/3788119

#SPJ4

Answer:

6 cream puff and 4 ice creams

Step-by-step explanation:

i = ice cream

p = cream puff

p+i= 10

1.50p + 1.20 i = 13.80

Multiply the first equation by -1.2

-1.20p -1.20 i = -12.00

Add this to the second equation

1.50p + 1.20 i = 13.80

-1.20p -1.20 i = -12.00

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

.3p = 1.80

Divide each side by .3

p =6

Now find i

p+i = 10

6+i= 10

i= 10-6 =4

Answer:

d is the answer ✌sin ०=3000/3050

Answer: 10 hours

Step-by-step explanation:

happy to help

Based on the equation in the question , the R2 would be 0.934.

To compute R2, we need to use the formula:

R2 = SSR / SST

Given that SSR = 14,141.7 and

SST = 15,128.4,

We can substitute these values into the formula:

R2 = 14,141.7 / 15,128.4

R2 ≈ 0.934

b. To compute Ra2, we need to subtract R2 from 1:

Ra2 = 1 - R2

Substituting the value of R2 we calculated in part a:

Ra2 ≈ 1 - 0.934

Ra2 ≈ 0.066

c. A large R2 value indicates that the estimated regression equation explains a large amount of the variability in the data.

In this case, R2 is approximately 0.934, which means that the estimated regression equation explains about 93.4% of the variability in the data.

So, the answer is "Yes".

To know more on Regression visit:

https://brainly.com/question/32505018

#SPJ11

Answer:

48

Step-by-step explanation:

72/6 =12

12(4)=48

The equivalent expression of 5\(x^{3/2}\) is  5√(x³). The correct option is last one.

Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Given:

An expression,

5\(x^{3/2}\)

To find the equivalent expression:

We have to simplify the expression,

5\(x^{3.1/2}\)

= 5(x³)\(){1/2}\)

= 5√(x³)

The above expression is an equivalent expression.

Therefore, 5√(x³) is an equivalent expression.

To learn more about the equivalent expression;

https://brainly.com/question/28170201

#SPJ1