A rectangular piece of metal is 15 in longer than it is wide. squares with sides 3 in long are cut from the four
corners and the flaps are folded upward to form an open box. if the volume of the box is 1782 in2, what were the
original dimensions of the piece of metal?

Answer:

1647

Step-by-step explanation:

Given the following information:

Length of traffic = 8 miles

Average Length of vehicles on the road :

Cars = 14.5 feets

Trucks = 21 feets

18 Wheeler tractor = 73 Feets

% distribution of the different vehicles :

Cars = 70% = 0.7

Trucks = 20% = 0.2

18 wheeler tractor = 10% = 0.1

Distance between vehicles = 4feets

Number of vehicles stuck in the traffic :

Let number of vehicles = v

Summation of (number of vehicles * length of each vehicle) + distance between each vehicle = Length of traffic

Total distance between each vehicle = 4(v-1)

(0.7v * 14.5) + (0.2v * 21) + (0.1v * 73) + 4(v - 1) = 8 miles

1 mile = 5280

8 miles = (5280 * 8) = 42,240

10.15v + 4.2v + 7.3v + 4v - 4 = 42240

25.65v = 42240 + 4

25.65v = 42244

v =42244 / 25.65

v = 1646.939

v = 1647.

Answer:

177

Step-by-step explanation:

An integer is a negative or positive whole number. any number greater or equal to 5 you round up the the nearest whole number

Hope this helps.

"decimals are not included in the set of integers." with this information you can infer that you need to round to the nearest whole number, therefore 176.912 would be round to 177 because the decimal in the tenth place is 5 or above (9) so you round UP.

By critically observing the graph shown above, the set of ordered pairs include the following:

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

An ordered pair can be defined as a pair of two elements that are typically written in a fixed order within parentheses as (x, y), which represents the x-axis (abscissa) and the y-axis (ordinate) on a coordinate plane.

By critically observing the graph shown above, we can logically deduce that the set of ordered pairs include the following:

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The total goal distance Sarah run is 7/8.

The distance covered by Sarah is found to be more than Tori.

A number's exponent indicates what many times a number has been multiplied by itself. For instance,  2×2×2×2 can be composed as 2⁴.

If a fraction does have a negative exponent, we take its reciprocal to make this same exponent positive.

If a fraction does have a negative exponent, we take its reciprocal to create the exponent positive.

Some properties of exponents are-

Now, as pet the given question;

Tori has covered 2⁻³ of the total distance;

Thus, it can be written as;

= 1/2³

= 1/8

Lets consider the total distance covered by both of them is 1.

Then, the distance covered by Sarah will be;

= 1 - 1/8

= 7/8

Thus, the distance covered by Sarah is 7/8.

As, 7/8 > 1/8

Therefore, the distance covered by Sarah is more than Tori.

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Answer:

[tex]\textsf{1.} \quad s=\dfrac{8r}{9}[/tex]

[tex]\textsf{2.} \quad s=4[/tex]

[tex]\textsf{1.} \quad x=y(w+z)[/tex]

[tex]\textsf{2.} \quad x=10[/tex]

Step-by-step explanation:

Question 1

1.  Solve for s:

[tex]\implies 2r = \dfrac{5s}{2}-\dfrac{s}{4}[/tex]

[tex]\implies 2r = s\left(\dfrac{5}{2}-\dfrac{1}{4}\right)[/tex]

[tex]\implies 2r = s\left(\dfrac{10}{4}-\dfrac{1}{4}\right)[/tex]

[tex]\implies 2r = s\left(\dfrac{9}{4}\right)[/tex]

[tex]\implies 4(2r) = 9s[/tex]

[tex]\implies 8r = 9s[/tex]

[tex]\implies s=\dfrac{8r}{9}[/tex]

2.  When r = ⁹/₂ :

[tex]\implies s=\dfrac{8\left(\frac{9}{2}\right)}{9}[/tex]

[tex]\implies \dfrac{8}{9} \times \dfrac{9}{2}[/tex]

[tex]\implies \dfrac{8 \times9}{9 \times2}[/tex]

[tex]\implies s=\dfrac{72}{18}[/tex]

[tex]\implies s=4[/tex]

Question 2

1.  Solve for x:

[tex]\implies w=\dfrac{x}{y}-z[/tex]

[tex]\implies w+z=\dfrac{x}{y}[/tex]

[tex]\implies y(w+z)=x[/tex]

[tex]\implies x=y(w+z)[/tex]

2.  When x = -8,  y = -5,  z = 6:

[tex]\implies x=-5(6+(-8))[/tex]

[tex]\implies x=-5(6-8)[/tex]

[tex]\implies x=-5(-2)[/tex]

[tex]\implies x=10[/tex]

Answer:18.2055

Step-by-step explanation:−6.87(−2.65)=−6.87*−2.65=18.2055

Interval and ratio scales of data measurement are associated with quantitative data.

Data measurement:- Data measurement is the way in which data can be subcategorized to analyze the data properly. Data can be classified into two types-

Thus we can conclude that, Interval and ratio scales of data measurement are associated with quantitative data.

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Answer:

see below

Step-by-step explanation:

angle e is a vertical angle(each of the pairs of opposite angles made by two intersecting lines.) of 114 so e=114 and angle d is the vertical angle of 22 so d=22. and finally angles d+f+e=180

114+22+?=180

?=180-114-22

?=180-136

?=44

e=144

d=22

f=44

Answer: $48.17

Step-by-step explanation:$148.68-$24.32=  $124.36

$124.36-$37.53=  $86.83

$135 -$86.83=$48.17

So he needs forty-eight dollars and 17 cents.                                            

Answer:

Step-by-step explanation:

y=csc(x)      x∈ [-2,2]

[tex]A.\\\displaystyle\\Increasing: \ [-2,-\frac{\pi }{2})U(\frac{\pi }{2},2]\\\\Decreasing:\ (-\frac{\pi }{2},0)U(0,\frac{\pi }{2} ) \\\\B.\\\\Relative\ min:\ 1\\\\Relative \ max:\ -1[/tex]

                                           Watching the graph:

Answer:

[tex]\textsf{Increasing}:\left[-2,-\dfrac{\pi}{2}\right) \textsf{ and }\left(\dfrac{\pi}{2},2\right][/tex]

[tex]\textsf{Decreasing}:\left(-\dfrac{\pi}{2}, 0\right) \textsf{ and }\left(0, \dfrac{\pi}{2}\right)[/tex]

[tex]\textsf{Relative min}: \left(\dfrac{\pi}{2},1 \right)[/tex]

[tex]\textsf{Relative max}: \left(-\dfrac{\pi}{2},-1 \right)[/tex]

Step-by-step explanation:

Part A

Given function:

[tex]f(x)=\csc (x), \quad -2\leq x\leq 2[/tex]

[tex]\csc(x)=\dfrac{1}{\sin(x)}[/tex]

Therefore, the function f(x) is undefined when sin(x) = 0, leading to vertical asymptotes at the value of x where sin(x) = 0.

[tex]\sin(x) = 0 \textsf{ at }x = 0\pm 2 \pi n, \pi \pm 2 \pi n[/tex]

Therefore, f(x) has a vertical asymptotes at x = -2π, -π, 0, π, 2π etc.

Where the graph of the sine function increases, the graph of the cosecant function decreases.

Where the graph of the sine function decreases, the graph of the cosecant function increases.  

The sine function increases on the intervals:

[tex]\left(-\dfrac{\pi}{2}\pm 2 \pi n, \dfrac{\pi}{2}\pm 2 \pi n\right)[/tex]

and decreases on the intervals:

[tex]\left(\dfrac{\pi}{2}\pm 2 \pi n, \dfrac{3\pi}{2}\pm 2 \pi n\right)[/tex]

Therefore, for the interval -2 ≤ x ≤ 2, the cosecant function f(x):

Increases on the intervals:

[tex]\left[-2,-\dfrac{\pi}{2}\right) \textsf{ and }\left(\dfrac{\pi}{2},2\right][/tex]

Decreases on the intervals:

[tex]\left(-\dfrac{\pi}{2}, 0\right) \textsf{ and }\left(0, \dfrac{\pi}{2}\right)[/tex]

Part B

The relative minimums of the graph of the sine function are the relative maximums of the graph of the cosecant function.

The relative maximums of the graph of the sine function are the relative minimums of the graph of the cosecant function.

The sine function has a range of -1 ≤ sin(x) ≤ 1.

Therefore, its minimum points are when sin(x) = -1 and its maximum points are when sin(x) = 1.

[tex]\sin(x)=-1 \implies x=\dfrac{3\pi}{2}\pm 2 \pi n \implies \textsf{Minimum points}: \left(\dfrac{3\pi}{2}\pm 2 \pi n ,-1 \right)[/tex]

[tex]\sin(x)=1 \implies x=\dfrac{\pi}{2}\pm 2 \pi n \implies \textsf{Maximum points}: \left(\dfrac{\pi}{2}\pm 2 \pi n,1 \right)[/tex]

Therefore, the minimum and maximum points of the cosecant function in the given interval -2 ≤ x ≤ 2 are:

[tex]\textsf{Relative min}: \left(\dfrac{\pi}{2},1 \right)[/tex]

[tex]\textsf{Relative max}: \left(-\dfrac{\pi}{2},-1 \right)[/tex]

Note in the attached graph:

The another point is  (2,23) of the function y(x).

What does regression analysis mean?

The given Regression is -

y (X) = 30 - 3. 5 x .......................(1)

now   when x = 0 , y(x) = 30    ..........................(1)

thus ,   y- intercept  = 30

one point is    ( 0 , 30 )

Again taking   x = 0  we get

             y(x) =   30 - 3. 5  x 2    by (1)

               y(X) = 23

Thus the another point is  (2,23).

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Answer:

C. y = 2x + 2

Step-by-step explanation:

There are 2 points on the line (0,2) and (-3,-4)

from (-3,-4) to (0,2), rise over run is 6/3 so slope is 2

You can calculate it too

m = (y2-y1)/(x2-x1)

m = (-4 - 2)/(-3 - 0) = -6/-3 = 2

Using m = 2, x = 0, y = 2

y = mx + b

2 = 2(0) + b

b = 2

therefore

y = 2x + 2

The mean and the median value of the given data set is 12.62 and 6.

According to the statement

We have to find that the mean and the median of the following data.

So, For this purpose, we know that the

The mean is found by adding all of the numbers together and dividing by the number of items in the set.

And

The median is the middle number in a sorted, ascending or descending list of numbers

From the given information:

The data set are:

1,20,1, 49, 16, 5, 3, 6

Then

According mean definition,

Mean = 1+20+1+ 49+ 16+ 5+ 3+6/8

Mean = 101/8

Mean = 12.625

Then

The data set is 1,3,5,6,16,20,49.

Median = 8 terms /2

Median = 4th term

Median = 6.

So, The mean and the median value of the given data set is 12.62 and 6.

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Answer: Rotation

Step-by-step explanation:

All rhombus are parallelograms, parallelogram have exactly two pairs of parallel lines, therefore all rhombus have exactly two pairs of parallel lines, so option A is correct.

A unique kind of quadrilateral created by parallel lines is called a parallelogram. A parallelogram can have any angle between its neighboring sides, but for it to be a parallelogram, its opposite sides must be parallel.

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. Every rhombus is a parallelogram because its opposite sides are all parallel. But all parallelograms cannot be rhombus as a rhombus have all sides equal.

Both a square and a rhombus have equal numbers of sides. The square's diagonals are also perpendicular to one another and divide the opposing angles. A square is a rhombus as a result.

Thus, all rhombus are parallelograms as they have one pair of parallel sides.

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Ella's bait and tackle shop sells 230,385 in April and May.

Based on the given conditions, formulate:

Bait and tackle sold in 128,278 live worms in April

Bait and tackle sold in 102,278 live worms in May

So the total number of Bait and tackles sold in April and May =

                                                                                             =128,107+102,278

                                                                                              = 230,385

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Answer:

x = 35° , y = 125°

Step-by-step explanation:

y and 55° lie on the straight line and sum to 180° , that is

y + 55° = 180° ( subtract 55° from both sides )

y = 55°

x and 55° form a right angle and sum to 90° , that is

x + 55° = 90° ( subtract 55° from both sides )

x = 35°

Answer:

20

Step-by-step explanation:

the line equals 180 degrees total.

so subtract the angle we already know from the total...

180- 100=80

then, make an equation with the last two variables since we know both of them added together should equal 80

80=x +3x

Combine like terms

80=4x

Divide by 4

20=x

Answer:

Step-by-step explanation:

Let x represent the number of weeks a population of the bacteria increases. Then, we have the number of bacteria is molded by the expression of 900*3^x. By, the given expression and when we assigned a value of x=2. Then we have 900*3² .

Answer:

174

Step-by-step explanation:

absolute value means the distance from zero.  Distance is always measured with a positive number.  If you asked me how far I lived from my work, I would never say -12 miles away.  If I was going or coming to work, the distance would be the same 12 miles.

134 + 4 + 35 = 174

An equivalent expression for 4 times d raised to the negative third power all over quantity 22 times d raised to the ninth power is 2d⁻³/11d⁻⁹

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

An exponent can be defined as a mathematical operation that is used to raise a quantity to the power of another and it is generally written as bⁿ.

Translating the word problem into an algebraic expression, we have;

4 times d raised to the negative third power = (4 × d)⁻³ = 4d⁻³

22 times d raised to the ninth power = (22 × d)⁻⁹ = 22d⁻⁹

Next, we would write the equation as a quotient:

Expression = 4d⁻³/22d⁻⁹

Expression = 2d⁻³/11d⁻⁹

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Answer:

- 6x² + 8x

Step-by-step explanation:

- 2x(3x - 4) ← multiply each term in the parenthesis by - 2x

= - 6x² + 8x

Answer:

Step-by-step explanation:

Mistake in step 3 the (2x+1) and the (x-1) both cancel out but the other binomials (x + 3) and (x - 3) are different so don't cancel out.

Step 3 should be 3(x-3) / 4(x+3)

3 should not be an excluded value.

By isolating the variable, we will see that the solution of the linear equation is v = -9

Here we have the following linear equation:

v/9 - 7 = -8

Where we can see that the variable is v. To solve this, we need to perform operations in both sides of the linear equation in a way such that the variable is isolated in one of the sides.

Adding 7 in both sides we get:

v/9 - 7 + 7 = -8 + 7

v/9 = -1

Now we multiply both sides by 9:

(v/9)*9 = -1*9 = -9

v = -9

We conclude that the solution of the linear equation is v = -9.

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Answer:

-2 <= y <= 4

Step-by-step explanation:

-3 <= 2y + 1 <= 9

-4 <= 2y <= 8

-2 <= y <= 4

Answer:

-2 <= y <= 4

Step-by-step explanation:

-3 <= 2y + 1 <= 9

-4 <= 2y <= 8

-2 <= y <= 4