the display manager at a museum is setting up a rectangular area for a exhibit. The exhibit must be atleast 400 square feet, and its perimeter must be 82 feet. What are the possible widths of the exhibit area?

The area of the complex shape is 35.1 square meters.

A unique kind of quadrilateral called a parallelogram has two opposite sides that are parallel to one another. The opposite sides and angles of a parallelogram have equal lengths and measurements.

The given shape is a parallelogram.

Since the opposite sides of a parallelogram are equal, the base of the parallelogram is 27m.

The area of the parallelogram is given by the following formula:

[tex]A = b *h[/tex]

Where, b is the base and h is the height of the parallelogram.

Substitute the value of b = 27m and h = 1.3m:

A = (27)(1.3)

A= 35.1 square meters.

Hence the area of the complex shape is 35.1 square meters.

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Answer:

The result is 13.3452

It depends on what your teacher wants you to round to.

To the whole number, it would be 13.

To the tenth, it would be 13.3

To the hundredth, it would be 13.35.

To the thousandth, it would be 13.345.

Hope this helps.

Answer:

13.3452, multiply both the numbers,
an estimation would be about 13 since 1.98 is close to 2 and 6.74 is close to 7, but since they aren’t quite there, a 13 would make sense to guess

Answer:

268 ounces

Step-by-step explanation:

13.40 in pennis is 1,340 pennies. If 10 pennies weigh 2 ounces then each penny weighs .2 ounces. So then all you have to do is 1,340×.2 which is 268. So, a bunch of pennies worth $13.40 weigh 268 ounces. :)

Answer:

268 ounces

Step-by-step explanation:

$13.40 = 1340 penny, so, 1340/10*2 is 268

The amount of time I spent tutoring from the tape diagram is 4 hours.

Let x represent one rectangle. Therefore from the tape diagram:

Amount of hours I spent tutoring = x + x = 2x

Amount of hours my friend spent tutoring = x + x + x + x = 4x

Since both me and my friend spent a total of 12 hours, hence:

2x + 4x = 12

6x = 12

Dividing through by 6:

x = 2 hours

Amount of hours I spent tutoring = 2x = 2(2) = 4 hours

The amount of time I tutor is 4 hours.

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The lines are not parallel and the slope of the lines is 3 and intercept is 1

Two lines are parallel if their slopes are equal and they have different y-intercepts. In other words, perpendicular slopes are negative reciprocals of each other.

In the two equations

2y = 6x+ 3

divide both sides by 2

y = 3x+1

This means that the slope of the line is 3.

And also in equation y = 3x+1. The slope of the line here is also 3.

Though both lines have the same slope but they have thesame y-intercept which is 1. Therefore the two lines are not parallel.

The slope of the equations is 3 and the intercept is 1

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On solving the provided question we can say that - probability of P(A B) = P(A) + P(B) - P(A B)= 70%

A branch of mathematics known as probability measures the possibility of an event happening or a proposition being true. The probability of an occurrence is a number between 0 and 1, where roughly 0 denotes the event's improbability and 1 denotes certainty. A probability is a numerical representation of the possibility or probability that a specific event will take place. Probabilities can alternatively be stated as percentages ranging from 0% to 100%, or as percentages from 0 to 1. the proportion between the number of events in a comprehensive collection of equally likely outcomes that lead to a certain occurrence and the entire number of outcomes.

P(A)= 60%, P(B) = 30%

P(A B) = 20%

P(A B) = P(A) + P(B) - P(A B)= 70%

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The system of equations are A = 8x³ and B = 2x³ and difference of the two equations is C = 6x³

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the difference of the two expressions be C

Let the first equation be represented as A

Now , the value of A = ( 2x )³

On simplifying the equation , we get

A = ( 2x )³   be equation (1)

A = ( 2 )³ ( x )³

A = 8x³

And , let the second equation be represented as B

The value of B = 2x³   be equation (2)

Now , dividing equation (1) by equation (2) , we get

A/B  be equation (3)

Substituting the values in the equation , we get

A/B = 8x³/2x³

A/B = 8/2

A/B = 4

Multiply by B on both sides of the equations , we get

A = 4B

So , 8x³ = 4 ( 2x³ )

The difference between the two expressions C = 8x³ - 2x³ = 6x³

Therefore , the value of C is 6x³

Hence , the system of equations are solved

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The simplification of the expression, D, in terms of k and h for 8 cylinders is D =  πk²h/2.

The displacement if the bore is 4 inches, the stroke is 3.4 inches, and the engine has four cylinders is 179.9 cubic inch

An engine has n cylinders, the displacement is D = pi(bore/2)² • stroke • n, where the bore is the diameter of the cylinder and stroke is the length of the piston's travel.

If bore = k/2 and stroke = h, simplify the expression, D, in terms of k and h for 8 cylinders:

D = pi(bore/2)² • stroke • n

D = π(k/2/2)²• h • 8

D =  π(k/4)²• h • 8

D =  π(k²/16)• h • 8

D =  πk²h/2

If the bore is 4 inches, the stroke is 3.4 inches, and the engine has four cylinders, the displacement will be:

D = pi(bore/2)² • stroke • n

D = π(4/2)² × 3.4 × 4

D = π(2)² × 3.4 × 4

D = 4π × 3.4 × 4

D = 179.9 cubic inch

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Complete Question

The engine displacement of an automobile is the volume through which the piston moves from high to low position. If an engine has n cylinders, the displacement is D = pi(bore/2)^2 • stroke • n, where the bore is the diameter of the cylinder and stroke is the length of the piston's travel.

If bore = k/2 and stroke = h, simplify the expression, D, in terms of k and h for 8 cylinders.

If the bore is 4 inches, the stroke is 3.4 inches, and the engine has four cylinders, what is the displacement? Round your answer to the nearest tenth of a cubic inch.

The positive solution for the number is 6 as the expression will result to a quadratic equation.

A quadratic equation is a second-order polynomial equation in a single variable x in the form ax² + bx + c = 0. with a ≠ 0.

We Shall represent the unknown number with the letter x so that we have:

x² - 18 = 3x

x² - 3x - 18 = 0 {a quadratic equation}

x² + 3x - 6x - 18 = 0 {expand the middle term}

x(x + 3) -6(x + 3) = 0 {factor out x + 3}

(x - 6)(x + 3) = 0

x - 6 = 0 or x + 3 = 0

x = 6 or x = -3

we have two solutions for the quadratic equation and 6 is the positive solution

Therefore, the positive solution for the quadratic equation is 6

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The answer is 16/5=3.2

explanation

1.2(0.4-0.9)/(-6) +3.1

simplify the expression:

1.2(0.4-0.9)/-6+3.1

simplified the answer

16/5=3.2

expanded 16/5

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Answer:

  9x -4y = -44

Step-by-step explanation:

You want the equation of the line through (-4, 2) and perpendicular to the line through (-4, 6) and (5, 2).

The equation of a line through (h, k) and perpendicular to the line through (x1, y1) and (x2, y2) can be written as ...

  (x2 -x1)(x -h) +(y2 -y1)(y -k) = 0

Using the given points, this becomes ...

  (5 -(-4))(x -(-4)) +(2 -6)(y -2) = 0

  9(x +4) -4(y -2) = 0

Expanding this gives the general form equation:

  9x -4y +44 = 0

Subtracting the constant gives the standard form equation:

  9x -4y = -44

well, we know that Bridgette has 2500 bucks, now her dad gave her 20% of 3000, well heck, what's 20% of 3000 anyway?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of 3000}}{\left( \cfrac{20}{100} \right)3000}\implies 600~\hfill \underset{\textit{yeap, she has enough}}{\stackrel{2500~~ + ~~600}{\text{\LARGE 3100}}}[/tex]

A cylindrical tank is half-full of oil. The cylinder has a base radius of 100 cm. The height of the cylinder is 250 cm than the oil present in the tank is 3926.990 lit.

Given :

The volume of the half cylinder is given by:

[tex]Volume= \frac{1}{2} (\pi r^{2} ) X h\\\\Volume=\frac{1}{2} X(\pi X(100)^{2} ) X 250[/tex]

[tex]Volume = Volume = 3926990.82 cm^{3}[/tex]

[tex]Volume = 3926.990 lit.[/tex]

So, 3926.990 lit. of oil are present in the cylindrical tank.

Answer:

Arithmetic progression

Next 3 terms are 15, 18 and 21.

Step-by-step explanation:

The sequence is an arithmetic progression (AP)

Looking at the first few terms of the sequence,

there is an addition of 3 from the current term to the next term.

(Value of addition of 3 is a constant)

Hence,

First blank: 12 + 3 = 15

Second blank: 15 + 3 = 18

Third blank: 18 + 3 = 21

Here are the shapes and dimensions of each garden space:

Rose Bush: rectangular, 3x + 1 and 2x + 7

Iris Orchid: rectangular, 4x + 2 and x + 5

Sonny Flower: square, 4x + 2

To find the area of each garden space, you will need to use the formula for the area of a rectangle (length x width) or the area of a square (side length x side length). Here is how you would find the area of each space:

Rose Bush: (3x + 1) * (2x + 7) = 6x^2 + 7x + 2x + 7 = 6x^2 + 9x + 7

Iris Orchid: (4x + 2) * (x + 5) = 4x^2 + 9x + 2x + 10 = 4x^2 + 11x + 10

Sonny Flower: (4x + 2) * (4x + 2) = 16x^2 + 32x + 16x + 4 = 16x^2 + 48x + 4

Therefore, the area of the garden space for Rose Bush is 6x^2 + 9x + 7, the area of the garden space for Iris Orchid is 4x^2 + 11x + 10, and the area of the garden space for Sonny Flower is 16x^2 + 48x + 4.

Answer:

In the exact form, it would be 2/3.

(Hope it works!)

Step-by-step explanation:

No,  Avery is not interpreting the probability correctly because 0.40 represents probability in the long run over many visits to the site. Therefore, option 'D' is the correct answer.

Probability refers to the possibility that an event will occur. It assesses the certainty of the event. Such as in the scenario given where the probability of a randomly selected visitor to a certain website participating in an online survey is 0.40. Avery claims that for the next five visitors to the site, two visitors will be asked to participate in the online survey. Avery interprets the probability incorrectly it is because 0.40 refers to the probability in the long run over several visits to the site.

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The numeric value of ∠PSR is 60°

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Given:

Some measurements of angles of JKLM and PQRS are given. m∠MJK = (12x+15)°, m∠SPQ = (14x-5)°, m∠JKL = 115°,

m∠JML = (8y + 12)°, m∠PSR = = (13y-18)°.

And we know the quadrilaterals are similar.

Two quadrilaterals are similar, so their corresponding angles are equal.

JKLM and PQRS are shown, where JKLM is similar to PQRS.

So,

m∠JML = (8y + 12) = m∠PSR = = (13y-18)°.

8y + 12 = 13y -18

5y = 30

y = 6

So,

m∠PSR = (13 x 6-18)°.

m∠PSR = (60)°.

Therefore, 60° is the measure of ∠PSR.

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The blue car has an equation of y = 1/6x + 1/2

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

Cars = Blue and Red cars

For the red car, we have

y = -6x + 1/2

The equation of a line can be represented as

y = mx + c

Where

slope = m

By comparing the equations, we have:

m = -6

The blue car and the red car are perpendicular to one another

The slopes of perpendicular lines are opposite reciprocals

This means that the slope of the blue car is 1/6

i.e. m = 1/6

Recall that:

The equation of a line can be represented as

y = m(x - x1) + y1

Where

slope = m = 1/6

(x, y) = (0, 1/2)

So, we have

y = 1/6 * (x - 0) + 1/2

This gives

y = 1/6 * (x) + 1/2

Evaluate

y = 1/6x + 1/2

Hence, the equation of the blue car is y = 1/6x + 1/2

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Answer:

a = -0.05

Step-by-step explanation:

0.2a + 0.06 = -0.05

Step 1: 100 * (0.2a + 0.06 = 0.05)

20a + 6 = 5

Step 2: 20a + 6 - 6 = 5 - 6

20a = -1

Step 3: 20a / 20 = -1/20

a = -0.05

The value of 92°C to Fahrenheit will be 197.6°F.

In Mathematics, it is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. in this case, it is vital to note that they have at least two terms which have to be related by through an operator.

Since the function F(C)=1.8C+32 represents Fahrenheit, F, as a function of the temperature in Celsius,.

Therefore, 92°C to Fahrenheit will be:

= (1.8 × 92) + 32

= 197.6°F

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By factor decomposition and algebra properties, the number √180 is equal to 6√5.

In this problem we find an imperfect square root, that is, a square root whose root is an integer. However, we can simplify the expression by means of algebra properties and by redefining the number inside the root operator as a product of integers. Now we proceed to show the complete steps of the procedure:

First, decompose the number inside the root operator by factor decomposition:

√180 = √(2² · 3² · 5)

Second, simplify the resulting expression by algebra properties concerning roots:

√180 = √2² × √3² × √5

√180 = 2 × 3 × √5

√180 = 6√5

Therefore, the number √180 is equivalent by algebra properties and factor decomposition to 6√5.

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The equation of the line is y=1/3x.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

From the given graph let us take two points through which the line passes.

(-6, -2) and (6, 2)

m=2-(-2)/6-(-6)

m=4/12=1/3

The slope of the line is 1/3.

Now we have to find the y intercept

2=1/3(6)+b

2=2+b

b=0

The equation of line is y=1/3x

Hence, the equation of the line is y=1/3x.

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Answer: three angles of the triangle are 24 degrees, 84 degrees, and 72 degrees.

Step-by-step explanation:

Let's call the first angle x.

Then the second angle is x + 60.

And the third angle is 3x.

We know that the sum of the angles in a triangle is always 180 degrees.

We can use this information to set up the following equation:

x + x + 60 + 3x = 180

5x + 60 = 180

5x = 120

x = 24

So the first angle is 24 degrees.

The second angle is 24 + 60 = 84 degrees.

And the third angle is 3x = 3 * 24 = 72 degrees.

Therefore, the three angles of the triangle are 24 degrees, 84 degrees, and 72 degrees.

We can simplify the given expression to get:

-11/|-11| = -1

Here we want to rewrite the expression below:

-11/|-11|

First, remember how the absolute value works.

|x| = x  if x  ≥0

|x| = -x if x < 0.

Then we can rewrite the denominator as:

|-11| = 11

Replacing that on the expression we will get:

-11/|-11| = -11/11 = -1

That is the expression simplfied.

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The transformation sequence that Eli will use to show that the two circles J and K are similar are

The necessary transformation to map circle J onto K are

firstly dilation by a scale factor of two,: this makes the two circles equal in radius

circle J, has a radius of 3, dilation by a scale factor of 2 means 2 * 3 = 6.

hence the radius are equal and the circles similar

translation is used to position the circles same place, Circle J has its center at (3,−3)

translate 6 units left (x direction) = (3 - 6, -3) = (-3, -3)

translate 6 units up (y direction) = (-3, -3 + 6) = (-3, 3)

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Answer:

sorry but i i don't know the answer