this one is easy
Evaluating expressions
make six expressions and show how you got the answer

In the land area of Statesville, NC there would be 133.54 persons per square foot.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, One mile is 5280 feet so a square mile is

(5280 × 5280) = 27878400 square feet.

Therefore, The number of persons in each square foot should be,

= 322900000/27878400  persons per square foot.

= 3229000/278784 persons per square foot.

= 133.54 persons per square foot.

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The value of 6 1/2 divided by 1 2/3 is 3 9/10

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

6 1/2 divided by 1 2/3

When represented as an expression, we have

6 1/2 / 1 2/3

Convert to improper fractions

13/2 / 5/3

Express as products

13/2 * 3/5

So, we have

39/10

Express as mixed number

3 9/10

Hence, the solution is 3 9/10

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On the coordinate plane, the segment from D(-6, 3) to E(2, 3) forms one side of ADEF. The possible point F are (5,-4), (1, 10), (7,4), (-6, 10).

Since we are aware that the triangle's area is 28 square units and that the base is the segment DE, which has a length of 8 units, we can construct the equation:

Area equals (1/2) × base × height =  (1/2) × 8 × height=28

We can calculate the height and discover that it is 7 units.

Point F must be situated 7 units above or below the line DE since the triangle's height is perpendicular to the base DE. Therefore, any position that is 7 units above or below the line DE, which is determined by the equation y = 3, is considered to be at point F.

So the possible point F are (5,-4), (1, 10), (7,4), (-6, 10)

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Complete question -

On the coordinate plane, the segment from D(-6, 3) to E(2, 3) forms one side of ADEF. The

triangle has an area of 28 square units. Select all of the points where F could be. (5,-4), (1, 10), (7,4),(-6, 10)

Yes b can be written as linear combination of 3 vectors

A linear combination of vectors is a sum of scaled vectors, where the scaling factors are scalars. In other words, it's a linear combination of the form a_1v_1 + a_2v_2 + ... + a_n*v_n, where v_1, v_2, ..., v_n are vectors and a_1, a_2, ..., a_n are scalars. This is a fundamental concept in linear algebra and vector spaces and is used in many areas of mathematics and physics.

if b is linear combination of [tex]a_1,a_2,a_3[/tex]

then [tex]xa_1+ya_2+za_3=b[/tex]

from here we got :

x+5z = 2

-2x+y-6z = -1

2y + 8z = 6

after solving the above equation we get the solution as

{x,y,x} = {2,3,0} is a solution to the above equation so b is a linear combination of [tex]a_1,a_2,a_3[/tex]

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Complete question:

determine if b is a linear combination of [tex]a_1,a_2,a_3[/tex]

[tex]a_1[/tex] = [tex]\left[\begin{array}{ccc}1\\-2\\0\end{array}\right][/tex]      , [tex]a_2 = \left[\begin{array}{ccc}0\\1\\2\end{array}\right][/tex]   , [tex]a_3 = \left[\begin{array}{ccc}5\\-6\\8\end{array}\right][/tex] ,  b= [tex]\left[\begin{array}{ccc}2\\-1\\6\end{array}\right][/tex]

Answer:

1,547

Step-by-step explanation:

15' x 20' = 300 square feet

2,275 / 300 = $7.583 per square foot

12 x 17 = 204 square feet

204 x 7.583 = 1,547

Answer:

Step-by-step explanation:

for every 24 apples there is 12 bananas

so if you dived it by 2 it will be 12 apples 6 bananas

so it will always be half amount of bananas

The number of basketballs that were donated is equal to 28 basketballs.

In Mathematics, a proportion can be defined as an equation which is typically used to represent the equality of two (2) ratios.

This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities as follows;

7:6 = x:24

7/6 = x/24

Cross-multiplying, we have the following:

6x = 7 × 24

6x = 168

x = 168/6

x = 28 basketballs.

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Answer:

$0.50

50 cents per ounce.

Step-by-step explanation:

To get the unit price, you take the cost of the package divided by the parts it has. Since Marissa has a package of yogurt that costs $3.50 and there are seven ounces in the package we have this equation:

($3.50)/(7 ounces)= $0.50 = 50 cents = the second answer available.

Answer: 9.25

For this equation you will need to use division. 74min. divided by 8mi.

To double check your answer is correct you have to multiply. 9.25min times 8mi.

The water stream's parabola has the equation y = 48 - (x2)/(20*sqrt(3)), with the vertex at (0, 48) and the point of impact at (10sqrt(3), 0).

The equation of the parabola created by the water stream has a vertex at (0, 48), which is where the pipe ends. It is a quadratic equation. The pipe serves as the middle of the parabola's base, which is symmetrical and has a vertex at that location. The vertex form of a parabola can be used to determine the equation of the parabola, which is y = 48 - (x2)/(20*sqrt(3)). The parabola opens downward, with the highest point at (0, 48) and the lowest point at (10sqrt(3), 0), where the water stream hits the ground, according to the equation. The parabola's vertex and point of impact with the ground are described by the equation for the water's journey.

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Answer:

308/9

Step-by-step explanation:

Answer: 34 + 4/9 x 1/2 = 34 + 2/9 = 36/9.

Decimal Form: 34 + 4/9 x 1/2 in decimal form is 34.22222222.

Step-by-step explanation:

The best prediction possible for the number of times you will pick a marble that is not orange, is 7 times.

The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.

Given:

There are 4 pink marbles and 3 orange marbles.

The probability of not picking orange marbles,

= 4/(3 + 4)

= 4/7

If you do this 7 times,

the best prediction possible for the number of times you will pick a marble that is not orange,

= 4/7 x 7

= 4 times

Therefore, number of times is 4.

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The complete question:

There are 4 pink marbles and 3 orange marbles.

You select a marble without looking and then put it back. If you do this 7 times, what is the best prediction possible for the number of times you will pick a marble that is not orange?

Answer:

460

Step-by-step explanation:

Let b = base speed and w = wind power.

Here's what we know:

b + w = 490

b - w = 430

From here, we can use the elimination method. If we treat each variable and constant as columns, we do the following:

b + b = 2b

w - w = 0

490 + 430 = 920

Leaving us with:

2b = 920

Divide by 2:

2b / 2 = b

920 / 2 = 460

So b = 460 mph

Answer:

14

Step-by-step explanation:

First we can find Wednesdays inventory by doing 16-5, giving us 11

We can do the same thing for Saturday. Doing -2+20 because the change was positive 20, not negative. That brings Saturdays inventory to 18

They said Saturdays change was -4

So taking the 18 and subtracting 4 gets you Sundays inventory of 14

Using trial and improvement the numbers that should replace A and B is 20 and 34.

If you are unable to solve a problem using standard algebraic techniques, try using the trial and improvement approach. If you want to get a C in math, you must comprehend this question because it typically is worth 3 marks.

According to the topic

6 = A * 2 - B = 2A - B

SZ = A - S - B = SA - B {Find the relationship}

:: 3A = 36 - 8 = 28

/ A = 28/3 = 9

; B = 2A - 8 = 18 - 8 = 10

the rule expression. 14n-10

: n = 3 , 10 . 3 - 10  = 20

n = 4  11 . 4 -  10 = 34

Using trial and improvement the numbers that should replace A and B is 20 and 34.

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The inequality of the statement is x ≤ 30

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

The bus has a maximum capacity of 30 passengers

Represent the bus capacity with x

This means that the value of x cannot exceed 30

The term cannot exceed implies less than or equal to

So, we have

x ≤ 30

Hence, the inequality is x ≤ 30

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For the solution that satisfies, sketch the solution curve and estimate the following y(0)=0: y(1)≈0.75, y(-1)≈0.5; Y(0)=4: Y(0.5)≈-0.5, Y(-1)≈0.75; Y(0)=-1: Y(1)≈-1.5, Y(-1)≈-1.5.

(a) To sketch the solution curve for the given slope field, beginning at the point (0, 0) and following the arrows, draw a curved line that gradually moves from left to right, gradually increasing in value and then slowly decreasing. The estimated value of y(1) is 0.75 and y(-1) is 0.5.

(b) To sketch the For the solution that satisfies, sketch the solution curve and estimate the following y(0)=0: y(1)≈0.75, y(-1)≈0.5; Y(0)=4: Y(0.5)≈-0.5, Y(-1)≈0.75; Y(0)=-1: Y(1)≈-1.5, Y(-1)≈-1.5. curve for the given slope field, beginning at the point (0, 4) and following the arrows, draw a curved line that gradually moves from right to left, gradually decreasing in value and then slowly increasing. The estimated value of Y(0.5) is -0.5 and Y(-1) is 0.75.

(c) To sketch the solution curve for the given slope field, beginning at the point (0, -1) and following the arrows, draw a curved line that gradually moves from left to right, gradually increasing in value and then slowly decreasing. The estimated value of Y(1) is and y(-1) is -1.5.

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The new image of the rectangle after a translation of two units to the left is of option D

Suppose the graph is drawn on the coordinate plane.

Let the shifting be (x,y) → (x+a, y+b)

Then, add 'a' to all x coordinates of the graph's points. Add 'b' to all y coordinates of the graph's points.

The resultant set of new points will be plotted.

Given;

A rectangle area on graph with coordinates (1,0), (6,0),(6,2), (1,2)

Now after the shift of 2 unit left, the x coordinates will be affected;

=(1-2,0), (6-2,0),(6-2,2), (1-2,2)

=(-1,0), (4,0),(4,2), (-1,2)

Therefore, the coordinates of shifted graph will be (-1,0), (4,0),(4,2), (-1,2)

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The total distance that rob ran and walked for 60 minutes is; 8820 meters

The parameter for the constant speed is that Rob runs at a speed of 3.4 meters per second for one half hour.​ Thus;

V1 = 3.4 m/s

t1 = 1.5 hours =

30 * 60 = 1,800 seconds.

The distance he runs at that speed and time is;

S1 = V1 * t1

= 3.4 * 1,800

= 6,120 meters

He walks at V2 = 1.5 m/s for t2 = 1,800 seconds.

The distance he walks;

S2 = V2 * t2

= 1.5 * 1,800

= 2,700 meters

The total distance he runs and walks;

S = S1 + S2

= 6120 + 2700

= 8820 meters

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This formula states that each term in the sequence is equal to the previous term plus 3.

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Answer: To graph y = f(x) = -(x+4)²+1 and y = 1/f(x) on the same axes, you can follow these steps:

Plot the y-intercept of y = f(x) which is (0,-1)

For y = f(x), the parabola opens downward since the coefficient of x² is -1, thus the vertex is at (-4,1)

Plot the x-intercepts of y = f(x) which are x = 4 and x = -8

The parabola of y = f(x) is symmetric about the y-axis, so the graph will be reflected about the y-axis.

For y = 1/f(x), the x-intercepts will be the same as y = f(x) and the y-intercept is (0,1)

To graph y = 1/f(x), we can start by plotting the x-intercepts and the y-intercept, and then connecting the points.

Label the x-intercepts, y-intercepts, and vertex for both graphs

Shade the regions above the parabola of y = f(x) and below the graph of y = 1/f(x)

Note: It is important to remember that the graph of y = 1/f(x) is a reflection of the graph of y = f(x) across the x-axis, so the y-intercept of y = 1/f(x) is (0,1)

Step-by-step explanation:

The equation on the interval [0, 2π).x is 4π / 3 ,5π / -2

Intervals are expressed using parentheses or rectangular brackets, and a comma is used to separate two integers. The two numbers are referred to as the interval's endpoints. The least element or lower bound is shown by the number on the left. The biggest element or upper bound is shown by the number on the right.

As a result, when x = 4 and 5 4, f (x) has its maximum value of 1, which is 1.

A range of numbers between two specified numbers that include all real numbers in that range is known as an interval.

2sinx+ [tex]\sqrt{}[/tex]3 =0

⇒sinx= [tex]\sqrt{}[/tex] 3− 2

⇒x=nπ+(−1) ^-n  4π /3 (∵sin3 4π  = [tex]\sqrt{}[/tex]3/-2 )

X =?]π5TT

x = 4π / 3 ,5π / -2

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Answer:

16

Step-by-step explanation:

It's the number where the line crosses the y-axis

Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1). Therefore, option B is the correct answer.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Given that, three softball players discussed their batting averages after a game.

Probability:

Player 1: 4/7 =0.57

Player 2: 5/8 =0.625

Player 3: 3/6 =0.5

Therefore, option B is the correct answer.

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The range of this set of data is 30 ≤ y ≤ 80.

In Mathematics, a range is the set of all real numbers that connects with the elements of a domain.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown above, we can reasonably and logically deduce the following domain and range:

Domain = 0 ≤ x ≤ 24 or [0, 24].

Range = 30 ≤ y ≤ 80 or [30, 80].

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As per the interpolation method, the proportion of orders that are processed in less than 240 seconds is 0.17

The interpolation method is defined as a method of deriving a simple function from the given discrete data set such that the function passes through the provided data points.

Here we have given that at a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately normal with mean 276 seconds and standard deviation 38 seconds.

And the proportion of orders that are processed in less than 240 seconds is calculated as,

Here we know that 1 standard deviation below mean = 16% = M - d

Then we apply the value on it, then we get,

=> 276 s - 38 s = 238 s

Here we know that the mean of distribution is,

=> 50% which is equal to 276 s

And the proportion less than 240 s is consider that x%, then by using the interpolation method it can be calculated as,

=> (240 - 238) / (276 - 238) = (x - 16) / (50 - 16)

When we simplify this one then we get,

=> 1/19 = x - 16 / 34

Which can be rewritten as,

=> 19(x - 16)  = 34

=> 19x - 304 = 34

=> 19x = 338

=> x = 17.78%.

Therefore the closest to the proportion of orders that are processed in less than 240 seconds is 17% that is equal to the value of 0.17.

Hence the correct option is (A).

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The expression models the total cost for a visitor to go on n rides (c) is 4.00+1.50n

What is Expressions?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.

total cost for a visitor to go on n rides (c) = 4.00+1.50n

Admission fee = 4.00

Cost of each ride = 1.50

Now the cost of each ride is doubled.

New cost of each ride = 2×1.50 = 3.00

New cost model (C') for n rides = 4.00+ 3n

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1. Optimal strategy for solving this problem would be to feel for the socks, and grab two socks of the same color at random, as they have a 50% chance of being a match.

2. The total number of different ways they could be combined in pairs, assuming all 20 socks are different colors, is calculated by using the formula (nCr) = n! / (r! * (n-r)!)

So, the total number of different ways they could be combined in pairs would be (20*19)/2 = 190.

3. The total number of different ways they could be combined in pairs would be 10, as there are 10 black and 10 white socks, and they can only be paired with one another.

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