A local business has an area reserved behind the store for a parking lot that is 78 meters long by 19 meters wide. The stalls of the lot are at 90° angles to a required aisle that bisects the lot. The aisle is 8 meters by 78 meters.

An area reserved for a parking lot is 78 meters long by 19 meters wide. 2 stalls and an aisle are in the reserved area. The aisle is 78 meters long and 8 meters wide.

Use the layout of the parking lot to answer the questions.

What is the total area available for cars to park?

m2.

If the parking spaces are compact, they have an area of 12.5 m2. How many compact parking spaces will fit in the lot?

.

If the parking spaces are not compact, they will be 3 meters by 5.5 meters. How many noncompact parking spaces will fit in the lot?

.

All possible lengths of segment AB wil be 27 < AB < 81.Option b is correct

A triangle is a three-sided polygon. It is one of the most fundamental geometric forms.

Any two triangle sides' lengths added together are longer than the third side's length.

The triangular inequality theorem is applied in three ways;

1.

AC+BC > AB

27+54 > AB

81 > AB

2.

27+AB > 54

AB> 54-27

AB > -27

3.

54+AB > 27

AB > 27-54

AB > -27

All possible lengths of segment AB wil be 27 < AB < 81.

Hence option b is correct

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Answer:

27 < AB < 81

Step-by-step explanation:

The answer above is correct.

Answer:

a fraction

Step-by-step explanation:

this will produce a fraction, for example:

3^-1 = 1/3

and (-2)^-3 = -1/8

The number of watches that just be sold is 90 and the profit is -356400.

From the information given, the equation is given as:

P = −50x² + 550x − 900

P = -5x² + 55x - 90

= -5x² + 45x + 10x - 90

= -5x(x - 9) + 10(x - 9)

= (-5x + 10)(x - 9)

x - 9 = 0

x = 0 + 9 = 9

The watches that must be sold will be (9 × 10) = 90

The profit will be:

P = −50x² + 550x − 900

P = -50(90)² + 550(90) - 900

P = -405000 + 49500 - 900

P = -356400

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The volume of the rectangular prism is 3359232 cubic centimeters

The length of the cube is given as:

Length, l = 12 cm

The volume of a cube is:

[tex]V = l^3[/tex]

So, we have:

[tex]V = 12^3[/tex]

Evaluate

V = 1728

The volume of 1944 cubes is then calculated as:

Volume = 1728 * 1944

Evaluate

Volume = 3359232

Hence, the volume of the rectangular prism is 3359232 cubic centimeters

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There are exactly 1,944 of the 12 cm, or 0.5 foot cubes inside a rectangular prism.  What is the volume of the rectangular prism in cubic centimeters?

Answer:

88 square units

Step-by-step explanation:

     a  and b are the length of the parallel sides.

      a = IL = 15

      b = JK = 7

      h = height between the parallel lines = 8

[tex]\sf \boxed{\bf Area \ of \ trapezium = \dfrac{(a +b)*h}{2}}[/tex]

                                   [tex]\sf =\dfrac{(15+7)*8}{2}\\\\=\dfrac{22*8}{2}\\\\= 11*8\\\\= 88 \ square \ units[/tex]

-10 belongs to the set of negative integers and rational numbers and also belongs to the set of real numbers.

Answer:

40 Including membership Price

35 Just for Pizza

Step-by-step explanation:

$5 for Membership for the month (Not sure if the final answer includes this or not)
1.75 x 20 = $35 for Pizza

Answer:

The Framers are offering a better price and are cheaper by $1.35

Step-by-step explanation:

I've been framed price:

50% off of 115 = 0.5*115 = 57.5

10% off of sale price = 0.9*57.5 = $51.75

the Framers price:

30% off of 120 = 0.7*120 = 84

40% off of sale price = 0.6*84 = $50.40

Difference: 51.75-50.40 = $1.35

Answer:

D

Step-by-step explanation:

on a graph, look at the points (-3,0) (-1,0) and (2,0). Then, see if the line passes through those points. You will see that graph D passes through all those points. If you're confused on how to turn the (x,y) format into points on a graph, remember that the first point tells you how left/right you want to be, and the second point tells you how up/down you want to be.

Answer: Probability = 44%

Step-by-step explanation:

To find the probability of finding 2 black balls in a row, we first need to find the probability of finding 1 black ball at a time.

To do that, we need to divide the amount of total black balls by the number of total balls.

Black balls = 6

Total balls = 3 + 6 = 9

6 divided by 9 = 0.(6)

If you multiply 0,(6) by 100%, it will give you 66% (rounded) of getting a black ball.

Now, to find the chances of getting 2 black balls in a row, we need to multiply [tex]\frac{6}{9}[/tex] by [tex]\frac{6}{9}[/tex]. What we are doing is squaring the chances of getting one black ball, by the number of times we want to get it.

That is equal to 0,(4)

Multiply 0,(4) by 100%, and it will give you 44%(rounded) chances to get a black ball 2 times in a row.

Probability = 44%

Hope I Helped!

Using the arc length formula, the length of ST in the circle is: 15 units.

Arc length of a circle = ∅/360 × 2πr.

In the image given, we have:

∅ = m∠TSU = 72º

Arc length TU = 6π

r = ST

Plug in the values

6π = 72/360 × 2π(ST)

6π = 0.2 × 2π(ST)

6π/2π = 0.2 × ST

3 = 0.2(ST)

3/0.2 = ST

ST = 15 units.

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Since there are no patterns for the rate of change of the function, it is quadratic.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input.

When this rate is constant, the function is said to be linear, while if the rate increases in a proportional way, the function is exponential.

In this problem, no patterns of linearity or of exponentiality can be established, hence the function is quadratic.

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Answer:

50 points

Step-by-step explanation:

Let the total points scored by the team = x

30% of x = 15 points

     [tex]\sf \dfrac{30}{100}*x = 15\\\\[/tex]

              [tex]\sf x = 15* \dfrac{100}{30}\\\\ x = 50[/tex]

The team scored 50 points.

Answer:

[tex]y = 4 \cos(4\pi \: t + \frac{\pi}{4} ) [/tex]

[tex]y = a\cos(w\: t + \alpha ) [/tex]

[tex]w = 4\pi[/tex]

[tex]2\pi \: f = 4\pi[/tex]

[tex]f = 2[/tex]

Answer:

[tex]\displaystyle 2[/tex]

Step-by-step explanation:

[tex]\displaystyle y = Acos(Bx - C) + D[/tex]

When working with a trigonometric equation like this, always remember the information below:

[tex]\displaystyle Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A|[/tex]

So, the first procedure is to find the period of this graph, and when calculated, you should arrive at this:

[tex]\displaystyle \boxed{\frac{1}{2}} = \frac{2}{4\pi}\pi[/tex]

You will then plug this into the frequency formula, [tex]\displaystyle T^{-1} = F.[/tex] Look below:

[tex]\displaystyle \frac{1}{2}^{-1} = F \\ \\ \boxed{2 = F}[/tex]

Therefore, the frequency of motion is two hertz.

I am delighted to assist you at any time.

The given quadrilateral is a rectangle because 2 pairs of sides are equal in length.

We are given the coordinates of the quadrilateral as;

W(0, 5), X(-3, 2), Y(0, -4), Z(3, 2).

Now, the formula for distance between two coordinates is;

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Thus;

WX = √[(-3 - 0)² + (2 - 5)²]

WX = 3√2

XY = √[(0 + 3)² + (-4 - 2)²]

XY = 3√5

YZ = √[(2 + 4)² + (3 - 0)²]

YZ = 3√5

ZW = √[(0 - 3)² + (2 - 5)²]

ZW = 3√2

Thus, we can conclude that the given quadrilateral is a rectangle because 2 pairs of sides are equal in length.

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Answer :

Step-by-step explanation:

To find the value of 'a' we will use the tangent-chord theorem,

"Angle formed by the chord and a tangent to the circle measure the half of the intercepted minor arc"

Angle 'a' is formed between the chord and the tangent.

Measure of the intercepted arc = (2 × 52)°

Therefore, measure of the angle 'a' = \frac{104}{2}

2

104

a = 52°

Therefore, Option (A) will be the correct option.

Both sides of the equation are not equal, therefore, Massa was wrong.

For an equation to be correct, the values on both sides of the equation must be equal and balance.

Given the expression, 540 ÷ 6 = 9, 540 divided by 6 is 90. 90 is not equal to 9.

Thus, the value on the both sides are not balanced, therefore, Massa is incorrect.

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The amount of waste is 22 oz

The weights of the 3 rainbow trouts are:

3 Ib 5 oz, 2 Ib 12 oz, and 3 Ib 8 oz.

The total weight is:

Total = 3 Ib 5 oz + 2 Ib 12 oz + 3 Ib 8 oz

Evaluate the sum

Total = 8 Ib 25 oz

The amount she was left with is 8 Ib 2 oz

Subtract this amount from the total

Waste = 8 Ib 25 oz - 8 Ib 2 oz

Evaluate

Waste = 22 oz

Hence, the amount of waste is 22 oz

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Vial contains 0.96g powder.

Proportion is used to show how quantities and amounts are related to each other. The amount that quantities change in relation to each other is governed by proportion rules.

A direct and inverse proportion are used to show how the quantities and amount are related to each other. They are also mentioned as directly proportional or inversely proportional. The symbol used to denote the proportionality is ‘∝‘.  For example, if we say, a is proportional to b, then it is represented as “a ∝ b” and if we say, a is inversely proportional to b, then it is denoted as ‘a∝1/b’

The given question is the example of direct variation.

Powder volume ∝ Liquid volume

∴ We can apply cross multiplication method

Let powder volume be x

1g→ 10ml

x→ 9.6ml

cross multiplying

1 x 9.6 = 10 x [tex]x[/tex]

x = 0.96 g

Thus Vial contains 0.96g powder.

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There are 9240 ways to select a committee to develop a discrete math course if the committee is to consist of three faculty from the math department and four from the computer science department.

It is given that there are 9 faculty members in the math department and 11 in the computer science department.

[tex]C^{9} _{3} * C^{11} _{4}[/tex]

[tex]= \frac{9!}{(9-3)!3!} * \frac{11!}{(11-4)!4!}\\= 28 * 330\\= 9240[/tex]

Therefore, there are 9240 ways to select the committee.

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Answer: x=-1 and y=-2

Answer:

40 total students

Explanation:

Total students: 100%

Let the number of total students be x.

Solving stepwise:

7.5% : 100% --> 3 : x

[tex]\rightarrow \sf \dfrac{7.5}{100} = \dfrac{3}{x}[/tex]

[tex]\rightarrow \sf 7.5x = 3(100)[/tex]

[tex]\rightarrow \sf 7.5x = 300[/tex]

[tex]\rightarrow \sf x =40[/tex]

The probability of picking a red counter is therefore; 8/25.

Since the ratio of red to green is 2 :3 and there are 24 green counters, it follows that the number of red counters is;

x = (2/3)× 24 = 16 red.

The total of red and green is; 16 +24 = 40 which constitutes 80% of the total counters.

The total number of counters is therefore; 40/0.8 = 50 counters.

The probability of picking a red counter is therefore; 16/50 = 8/25.

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Answer:

the answer is x= 3/4 I think

El cuadrado completo es:

[tex]\left[\begin{array}{ccc}0.048&0.056&0.016\\0.008&0.04&0.072\\0.064&0.024&0.032\end{array}\right][/tex]

Tenemos el cuadrado:

[tex]\left[\begin{array}{ccc}0.048&a&0.016\\b&c&0.072\\0.064&e&f\end{array}\right][/tex]

Y queremos encontrar los valores de las letras, tal que cada suma de columna, fila y de cada diagonal de 0.12,

Entonces tenemos:

0.048 + b + 0.064 = 0.12

b = 0.12 - 0.048 - 0.064 = 0.008

0.016 + 0.072 + f = 0.12

f = 0.12 - 0.016 - 0.072 = 0.032

Tambien las diagonales deben dar 0.12, entonces:

0.064 + c + 0.016 = 0.12

c = 0.12 - 0.016 - 0.064 = 0.04

Reemplazando esos valores obtenemos:

[tex]\left[\begin{array}{ccc}0.048&a&0.016\\0.008&0.04&0.072\\0.064&e&0.032\end{array}\right][/tex]

Ahora las filas tambien deben dar 0.12:

0.048 + a + 0.016 = 0.12

a = 0.12 - 0.048 - 0.016 = 0.056

0.064 + e + 0.032 = 0.12

e = 0.12 - 0.064 - 0.032 = 0.024

El cuadrado completo es:

[tex]\left[\begin{array}{ccc}0.048&0.056&0.016\\0.008&0.04&0.072\\0.064&0.024&0.032\end{array}\right][/tex]

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The value of 'x' that would make Line segment T V is parallel to Line segment Q S is 10. Option C

It is important to note that for line TV to be parallel to line QS, the sides of the triangle must be divided equally.

Thus, we have

RT/TQ = RV/VS

RT = x + 10

TQ = x - 3

RV = x + 10

VS = x

Substitute the value

[tex]\frac{x + 4}{x-3} = \frac{x + 10}{x}[/tex]
Cross multiply

(x+ 4) × x = (x + 10) × (x-3)

x² + 4x =  x² -3x + 10x -30

Divide through by x²

4x = -3x + 10x - 30

Collect like terms

4x + 3x - 10x = - 30

-3x = -30

x = -30/ -3

x = 10

Thus, the value of 'x' that would make Line segment T V is parallel to Line segment Q S is 10 Option C

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The surface area of the cylinder is 244. 92 inches²

surface area of a cylinder = 2πr(r + h)

where

Therefore,

r = 6 / 2 = 3 inches

h = 10 inches

surface area of a cylinder =  2 × 3.14 × 3(3 + 10)

surface area of a cylinder = 18.84(13)

surface area of a cylinder = 244.92

surface area of a cylinder = 244. 92 inches²

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Answer:

2nd option

Step-by-step explanation:

the quadrilateral has 1 pair of parallel sides and is therefore a trapezoid.

• each lower base angle is supplementary to the upper base angle on the same side, that is

∠ 1 + ∠ 2 = 180° , so

x + x + 50 = 180

2x + 50 = 180 ( subtract 50 from both sides )

2x = 130 ( divide both sides by 2 )

x = 65

then

∠ 1 = x = 65°

∠ 2 = x + 50 = 65 + 50 = 115°

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The correct option is A, BC < MN.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

As per the given conditions, the angle that will be opposite to ∠A is BC and  ∠L is MN.

Now since the measure of ∠L is more than the measure of ∠A, therefore, the side MN will be greater than BC.

Hence, the correct option is A, BC < MN.

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Answer: Option 1 or A. BC<MN

Step-by-step explanation: Trust Me!

The answer is correct on Edge.  The proof is in the pic below.

Goodluck everyone! :)

Given AC = LN and BA = ML, which statement must be true?

A. BC < MN

Answer: 8/15, 15/8

Step-by-step explanation:

By the Pythagorean theorem, the length of the unknown side is

[tex]\sqrt{17^{2}-8^{2}}=15[/tex]

So, the tangents of the acute angles are [tex]\boxed{\frac{8}{15}, \frac{15}{8}}[/tex]