\(2\sqrt{x} +\sqrt{x} 21\\\)

Answer:

26 children

Step-by-step explanation:

Step 1 Create a system of equations

Firstly, we know that it cost $1.50 for children and $4 for adults and we know that 505$ is the total amount collected

So if x = number of children and y = number of adults

Then 1.50x + 4x = 505

We also know that 220 total people entered which consists of adults and children.
Again, if x = number of children and y = number of adults

Then we can say that x + y = 220

So we now have the two equations

1.50x + 4y = 505 and x + y = 220

Step 2 Solve the equation

There are many methods you can use to solve this equation however I'd recommend the substitution method as we can easily solve for x or y in the equation x + y = 220 and isolate one of the variables, we can then easily substitute that into the other equation.

Isolating y

x + y = 220

==> subtract x from both sides

y = 220 - x

We now substitute y into the other equation and solve for x(# of children)

1.5x + 4y = 505

==> plug in y = 220 - x

1.5x + 4(220 - x) = 505

==> distribute 4

1.5x + 440 - 4x = 505

==> combine like terms

-2.5x  + 440 = 505

==> subtract 440 from both sides

-2.5x = -65

==> divide both sides by -2.5

x = 26

So 26 children attended the fair that day.

Answer:

Decimal: 0.275           Percentage: 27.5

Step-by-step explanation:

False. very few tools are available to assist system analysts and end users in analyzing data.

There are many tools available to assist system analysts and end users in analyzing data. Some commonly used tools include spreadsheets (such as Microsoft Excel), data visualization software (such as Tableau or Power BI), statistical analysis software (such as R or SPSS), and business intelligence software (such as SAP or Oracle).

These tools allow analysts and end users to process, manipulate, and visualize large volumes of data, as well as to perform complex statistical analyses and modeling. Additionally, with the advent of big data technologies, such as Hadoop and Spark, analysts and end users can now analyze vast amounts of data in real-time, using distributed computing systems.

In summary, there are many tools available to assist system analysts and end users in analyzing data, and these tools continue to evolve and improve over time.

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Answer:

6/8

Step-by-step explanation:

the answer is:

3/4

hope this helps :)

Answer:

The number of chairs

Step-by-step explanation:

The equation is 2z + 3

2 ( = multiply by)

z ( # of chairs)

+3 ( the 3 extra chairs in the back)

Answer:

The number of tables

Step-by-step explanation:

Sens there is twice as many chairs as tables, the number 2 represents the chairs. The 3 represents the 3 extra chairs in the back. so the only logical object to represent z is the number of tables.

Answer:

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The correct inequality that represents the given situation is: A.) n - 87 < 320.

The situation states that Samuel played a video game and gained some points. Let's represent the points he gained as 'n'.

Next, it is mentioned that he lost 87 points. To represent this in the inequality, we subtract 87 from the initial points gained, which gives us 'n - 87'.

Finally, the situation specifies that Samuel finished with less than 320 points. This means that the final score, represented by 'n - 87', is less than 320.

This inequality represents that the initial points gained by Samuel (n) minus 87 points is less than 320 points, indicating that his final score is less than 320 points after losing 87 points.

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The values of the first six terms of the sequence are

1) a₀ = -1

2) a₁ = 2

3) a₂ = -4

4) a₃ = 8

5) a₄ = -16

6) a₅ = 32

The given sequence is defined recursively as follows

aₙ = -2aₙ-1

where a₀ = -1.

This means that each term in the sequence is equal to twice the negative of the previous term. To find the first few terms of the sequence, we can start with the given value of a0 and apply the recursive formula repeatedly to generate the next terms.

Using this approach, we get

a₁ = -2a₀ = -2(-1) = 2

a₂ = -2a₁ = -2(2) = -4

a₃ = -2a₂ = -2(-4) = 8

a₄ = -2a₃ = -2(8) = -16

a₅ = -2a₄ = -2(-16) = 32

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The Vertex is  (1/2, -3/4), Axis of symmetry is x = 1/2, Maximum value is -3/4 and Range is (-∞, -3/4]

To identify the vertex, axis of symmetry, maximum or minimum value, and the range of the parabola y = -x^2 - x, we can use the standard form of a quadratic equation: y = ax^2 + bx + c.

Comparing the given equation to the standard form, we have a = -1, b = -1, and c = 0.

1. Vertex:
The x-coordinate of the vertex is given by the formula x = -b / (2a). Plugging in the values, we get:
x = -(-1) / (2 * (-1)) = 1/2

To find the y-coordinate of the vertex, we substitute the x-coordinate back into the original equation:
y = -(1/2)^2 - (1/2) = -1/4 - 1/2 = -3/4

So, the vertex is (1/2, -3/4).

2. Axis of symmetry:
The axis of symmetry is the vertical line passing through the vertex. In this case, it is x = 1/2.

3. Maximum or minimum value:
Since the coefficient of x^2 is negative (-1), the parabola opens downwards and the vertex represents the maximum value. Therefore, the maximum value is y = -3/4.

4. Range:
The range of the parabola is the set of all possible y-values. Since the parabola opens downwards and has a maximum value of -3/4, the range is (-∞, -3/4].

In summary:
- Vertex: (1/2, -3/4)
- Axis of symmetry: x = 1/2
- Maximum value: -3/4
- Range: (-∞, -3/4]

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Answer:

60T = 12x - 1

Step-by-step explanation:

In speed distance and time, time(t) is given by

time = distance(d)/speed(s)

total distance ran = x miles

case 1

d = 1 mile

speed = 4 miles per hour

as time = distance(d)/speed(s)

t = 1/4

____________________________

case 2

speed = 5 miles per hour

it is given that out of x miles for first mile and last mile her speed was 5 miles per hour

thus distance for this speed can be calculated by

subtracting first and last mile from x miles

therefore

distance = x-2 miles\

t = (x-2)/5

_____________________________________

case 3

distance = 1 mile

speed = 6 miles per hour

t = 1/6

______________________________

Total time T as required  will be sum of time for the 3 case calculated above

T = 1/4 + (x-2)/5 + 1/6

T = 1/4 + (x - 2)/5 + 1/6   (taking LCM of 6,5,4 as 60 and solving)

T = (15 + 12x - 24 + 10)/60

T = (12x - 1)/60

60T = 12x - 1

Thus, equation 60T = 12x - 1 represents her time T

Answer:

Step-by-step explanation:

please

a. In the event that Jada uses 15 cups of apple juice, 10 cups of sparkling water will she require.

b. If Jada uses 6 glasses of sparkling water, 9 cups of apple juice will she need.

c. The equation that shows s and j are s=2/3 j

Given that,

Using 2 cups of sparkling water for every 3 cups of apple juice, Jada creates sparkling juice.

We have to find

a. In the event that Jada uses 15 cups of apple juice, how much sparkling water will she require is

It need 2 cups of sparking water for every 3 cups of apple juice.

So, for 15 = 5×3 cups of apple juice, Jade needs 5×2 = 10 cups of sparking water.

b. If Jada uses 6 glasses of sparkling water, how much apple juice will she need is

We need 3×2 cups of sparking water

So, she needs 3×3 =9 cups of apple juice.

c. Assume that s stands for the volume of sparkling water and j for the volume of apple juice. Describe the relationship between s and j are using an equation.

We know that

s=kj

Where

k = 2/3

So,

s=2/3 j

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The farmer wants a rectangular area enclosed and only needs a fence on three sides then the dimensions for the maximum area, the length will be 150 meters and the width will be 75 meters.

Given,

In the question:

A farmer wants to build an enclosure to keep her sheep safe. The fencing comes in 1-meter segments. She has 300 segments available.

To find the dimensions that maximize the area of her enclosure

Now, According to the question:

Let the width of the rectangle is x.

For both sides, it will be 2x.

So, the length will be,

(300 - 2x)

For maximum area,

A(x) = 300x - 2x²

A'(x) = 300 - 4x

Critical point A'(x) = 0

300 - 4x = 0

4x = 300

x = 75

So, the width of the rectangle is 75 meters and,

length  = (300 - 2x)

length = 300 -150

length = 150 meters.

Hence, The farmer wants a rectangular area enclosed and only needs a fence on three sides then the dimensions for the maximum area, the length will be 150 meters and the width will be 75 meters.

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The correct expression that represents the distance between the friends is 4 steps.

To calculate this

Joy walked 12 steps forward and Shaunte walked 8 steps backward. To find the distance between the two friends, we can add the number of steps they each took, so the expression would be:

12 + (-8) = 12 - 8 = 4

So the correct expression that represents the distance between the friends is 4 steps.

Note that the negative sign in front of Shaunte's steps indicates that she walked backward, and the positive sign in front of Joy's steps indicates that she walked forwards.

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Using Algebraic expression solution ,

The cost of three hats is $18 .

We have given that,

A hat company charge for design fee $4 per hat .

i.e design fee of one hat = $4

total cost of 5 hats = $30

let the cost of one hat without design fee be $x and total cost of one hat is $(x+4) .

using the above statement, we get an algebraic expression,

5( x+ 4)= 30

we solve the above algebra expression,

=> 5x + 20 = 30

=> 5x = 10

=> x = 2

so, cost of a hat without design fee is $2

and total cost of one hat is $6.

we have to calculate cost of 3 hats .

cost of one hat in hat company= $ 6

cost of three hats in hat company= $(6×3)

= $18

Hence, the total cost of 3 hats is $18.

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By using the equation for the line of best fit, the salary for an employee who has seven (7) years of experience is: D. $55,573.

A line of best fit is a statistical tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association between a data.

In this scenario, the employee's salary would be plotted on the y-axis of the scatter plot while the years of experience would be plotted on the x-axis of the scatter plot.

By critically observing the scatter plot (see attachment) which models the data in the given table, an equation for the line of best fit is given by:

y = 2233.3x + 39940

Next, we would use the above equation for the line of best fit to predict the salary for an employee with 7 years of experience:

y = 2233.3(7) + 39940

y = 15,633.1 + 39940

y = 55,573.1 ≈ $55,573.

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Answer:  125 miles

if you do the math you will get the same answer.

Answer:

800 miles

Step-by-step explanation:

It is called the y-coordinate

The point itself is called a coordinate, vertically, the vertical component of the coordinate is called the y-coordinate, while horizontally, the horizontal component of the coordinate is called the x-coordinate.

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Answer:

The answer to ((-5) - 9+ (7+(-6)))*(-4) is 52

\(\sf Answer: \)

\(52\)

\(\sf Step-By-Step~ Explanation: \)

\(Equation\)

\(((-5) - 9 + (7+(-6))) \times (-4)\)

\(Subtract~~9~~and~~-5 = -14.\)

\((-14 + 7 - 6)~(-4)\)

\(Add~~-14~~and~~7 = -7\)

\((-7-6)~(-4)\)

\(Subtract~~6~~and~~-7 = -13\)

\(-13~(-4)\)

\(Lastly,~~multiply~~-13~~and~~-4 = 52\)

\(52\)

\(\huge\boxed{\sf Answer \ 52}\)

4.5% annually

Simple interest is the amount of interest added to a singular sum of money at a fixed rate.

Formula

The formula for simple interest is A = P(1+rt). In this formula, A is the total amount of money in the account, P is the original amount deposited, r is the rate of interest as a decimal, and t is the time in years.

Calculations

To find the rate, plug the information we know into the formula above

Divide both sides by 100

Subtract 1 from both sides

Divide both sides by 5

This gives us the rate as a decimal. So, to find the rate as a percent. Do this by moving the decimal 2 places to the right (or just multiply by 100, they do the same thing). This means that the rate of simple interest is 4.5%.

Answer:

5 ounces if you meant 2/5 of a serving is 2 ounces of pasta

Step-by-step explanation:

Answer:

2divided by 2/5 equals 1/5

Step-by-step explanation:

I'm not 100% positive 91%

Using the equation of the proportional relationship, the number of miles she would drive on 50 gallons is: 1,660 miles.

A direct proportional relationship can be defined by the equation, y = kx, where the constant of proportionality between the variables is given as the value of k.

First, we need to write an equation that defines the table of values given. To do this, find the constant of proportionality by using any pair of values from the table, say (6, 199.2):

Number of gallons used = x

Number of miles driven = y

Constant of proportionality, k = y/x = 199.2/2

k = 33.2

To write the equation for the proportional relationship, substitute k = 33.2 into y = kx:

y = 33.2x

To find the how many miles she would drive on 50 gallons, substitute x = 50 into y = 33.2x:

y = 33.2(50)

y = 1,660 miles.

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The series on the right-hand side is a convergent p-series with p = 2. Therefore, by the comparison test, the original series converges as well.

To prove that if lim an/bn = 0 and bn is convergent, then an is also convergent, we can use the limit comparison test. Since bn is convergent, we know that its terms approach 0. Therefore, we can choose a positive number ε such that 0 < ε < bn for all n. Then, we have:

lim (an/bn) = 0
=> for any ε > 0, there exists N such that for all n > N, |an/bn| < ε
=> for all n > N, an < εbn

Since ε is a positive constant and bn is convergent, we know that εbn is also convergent. Therefore, by the comparison test, an is convergent as well.

To show that the series ∑(ln n)/(n^3 ln n^1/2 e^n) converges, we can use the comparison test again. Note that:

ln n^1/2 = (1/2)ln n
ln n^3 = 3ln n

Therefore, we can rewrite the series as:

∑[(1/2)/(n^2 e^(ln n))] = (1/2)∑(1/(n^2 n^ln(e)))

Since n^ln(e) > 1 for all n, we have:

(1/2)∑(1/(n^2 n^ln(e))) < (1/2)∑(1/n^2)

The series on the right-hand side is a convergent p-series with p = 2. Therefore, by the comparison test, the original series converges as well.

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Answer:

8times -12

Step-by-step explanation:

hope that helps

Expression 4(2x - 3) will have an analogous expression of 12x - 12.

The link between numbers, variables, and functions using mathematical signs like addition, subtraction, multiplication, and division is referred to as expression in mathematics.

Mathematical expression is defined as the relationship between numerical variables and mathematical operations such addition, subtraction, multiplication, and division.

Given expression is 4(2x - 3 ). The equivalent expression will be solved as below,

E = 4(2x - 3 )

E = 8x - 12

Hence, 8x – 12 will be the equivalent expression.

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Answer:

yes

Step-by-step explanation:

Answer:

If there is an odd number of numbers, this middle number is the median. If there is an even number of numbers add the two middles and divide by 2. The result will be the median.

Step-by-step explanation:

Step-by-step explanation:

p=1500

R=10%

t=20yrs

SI=PTR/100

=1500*10*20/100

=3000

amount(A)=P+I

=1500+3000

=4500

Answer:

If only one vertical line intersects the graph at exactly one point, the graph represents a function.

Answer:

see explanation

Step-by-step explanation:

substitute x = 0 and x = 1 into the polynomial and evaluate

0³ + 6(0) - 5 = 0 + 0 - 5 = - 5

1³ + 6(1) - 5 = 1 + 6 - 5 = 2

since polynomial < 0 at x = 0 and > 0 at x = 1

Then the graph crosses the x- axis between 0 and 1

This indicates the solution lies between x = 0 and x = 1

Answer:

(4;-1)

Step-by-step explanation:

Answer: 138

Step-by-step explanation: all the numbers are written in 3 significant figures so, your answer must be in 3 significant figures; 67.4 + 43.2 + 27.3 = 137.9 so, now write this in 3 significant figures which is 138 (round off the 7).