An auditorium with 30 rows of seats has 10 seats in the first row. Each successive row has one more seat than the previous row. If students taking an exam are permitted to sit in any row, but not next to another student in that row, what is the maximum number of students that can be seated for an exam

Answer:

[tex]\sf 1\dfrac{2}{5} \ cm[/tex]

Step-by-step explanation:

    If two sides of the triangle are equal, then the triangle is called isosceles triangle.

Let the two equal sides = x cm

Perimeter of the triangle = [tex]\sf 4\dfrac{2}{15}[/tex] cm

[tex]\sf x + x + \dfrac{4}{3}=4\dfrac{2}{15}\\\\[/tex]

      [tex]\sf 2x +\dfrac{4}{3}=\dfrac{62}{15}[/tex]

             [tex]\sf 2x = \dfrac{62}{15}-\dfrac{4}{3} \ [\text{\bf LCM of 15 , 3 = 15}]\\\\2x = \dfrac{62}{15}-\dfrac{4*5}{3*5}\\\\2x = \dfrac{62}{15}-\dfrac{20}{15}\\\\2x = \dfrac{42}{15} \ [\text{\bf Divide both sides by 2}]\\\\ x = \dfrac{42}{15*2}\\\\ x = \dfrac{7}{5}\\\\ x = 1\dfrac{2}{5}[/tex]

[tex]\sf \boxed{\text{Equal sides of isosceles triangle = $1\dfrac{2}{5}$ cm}}[/tex]

Answer:

x = 19.1

Step-by-step explanation:

Because this is a right triangle, we can use trigonometry.

Thus, we must use either sine (opposite / hypotenuse), cosine (adjacent / hypotenuse), or tangent (opposite / adjacent).

If we use 33 as the reference angle, the side measuring 16 is the adjacent side and x is the hypotenuse.

Thus, we can use cosine:

[tex]cos 33=\frac{16}{x} \\x*cos33=16\\x=19.0778=19.1[/tex]

46.5 is higher than 5.2

Note that:

The larger the magnitude(value) of the heights given the larger the heights

Units are not added to the values representing each height

By carefully considering the heights given:

5.2 is a lesser value than 46.5

Since 46.6 > 5.2, we can conclude that 46.5 is higher than 5.2

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In the graph, the constant of proportionality is 40

From the question, we are to determine the constant of proportionality

The constant of proportionality = [tex]\frac{y}{x}[/tex]

From the graph, a point on the line is (1, 40)

That is,

When x = 1 and y = 40

Thus,

The constant of proportionality = [tex]\frac{40}{1}[/tex]

Constant of proportionality = 40

Hence, the constant of proportionality is 40

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Answer:

40

Step-by-step explanation:

The constant of proportionality is 40/1 which equals 40.

Direct Variation; k=3 best describes the function on the graph

Option A)

Direct variation is a linear function defined by an equation of the form y = kx when x is not equal to zero. Inverse variation is a nonlinear function defined by an equation of the form xy = k when x is not equal to zero and k is a nonzero real number constant. In direct variation, as one number increases, so does the other. This is also called direct proportion: they're the same thing. An example of this is relationship between age and height. As the age in years of a child increases, the height will also increase. In inverse variation, it's exactly the opposite: as one number increases, the other decreases. This is also called inverse proportion. An example would be the relationship between time spent goofing off in class and your grade on the midterm. The more you goof off, the lower your score on the test

The given equation is a Straight line with equation y = 3x.

Thus the given graph is direct Variation graph with k=3.

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Answer:

1+2√2

a = 1 b= 2

See the attached page, I've shown the calculation over there.

The coordinates of the focus and the equation of the directrix is option B: focus: (0, one-half); directrix: y = negative one-half.

Since we were given Parabola x² = 2 y

Then one has to compare and and so it will be  x² = 4 a y

                                                                               4 a = 2

Make a the subject of the formula:

a = 2/4

= 1/2

Therefore,   Focus ( 0,a) = (0, 1/2 )

To solve for directrix:

Note that the equation of the directrix is:

y = -a or y +a=0

Then the equation of the directrix is:

y = - 1/2 or

y = + 1/2 = 0

Then the equation of the directrix will be 2 y +1 =0.

Therefore, The coordinates of the focus and the equation of the directrix is option B: focus: (0, one-half); directrix: y = negative one-half.

See full question below

A parabola can be represented by the equation x2 = 2y. What are the coordinates of the focus and the equation of the directrix? focus: (0,8); directrix: y = –8 focus: (0, one-half); directrix: y = negative one-half focus: (8,0); directrix: x = –8 focus: (one-half, 0); directrix: x = negative one-half

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The reason that completes the proof for step 6 is (a) Definition of median

From the graph, point R' to be the midpoint of points M' and O'

Also, points P' and Q' are the midpoints of lines M'N' and N'O', respectively

This means that the three points are the median of the sides of the triangle

The line drawn through the three medians meet at point S

Hence, the reason that completes the proof for step 6 is (a) Definition of median

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Answer: median

Step-by-step explanation:

The total volume of the cubes in factored form is  (4p + 2q^2)(16p^2 -  8pq^2 + 4q^4)

The volume of a figure or a three dimensional shape is the amount of space inside the figure or the three dimensional shape

The two cubes are stacked upon one another, so they form a composite figure.

The side lengths of the cubes are given as

Cube 1 = 4p

Cube 2 = 2q^2

The volume of each cube is calculated as:

Volume = Side length^3

So, the total volume is

Total = (4p)^3 + (2q^2)^3

Evaluate the exponents

Total = 64p^3 + 8q^6

Using the sum of cubes, we have the factored form to be

Total = (4p + 2q^2)(16p^2 -  8pq^2 + 4q^4)

Hence, the total volume of the cubes in factored form is  (4p + 2q^2)(16p^2 -  8pq^2 + 4q^4)

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Complete question

A cube with side length 4p is stacked on another cube with side length 2q^2. What is the total volume of the cubes in factored form?

Answer: 480

Step-by-step explanation:

20(12)(2) = 480

Answer:

You add the numerator

multiply the denominator and substract

then you can divide the expression.

Step-by-step explanation:

According to BODMAS

division comes before multiplication, addition and subtraction.

but in some cases like this, it's difficult to follow that procedure

Multiplicative rule's probability is a rule which states that the when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities

According to the statement

we have to explain about the those law which is used when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities

So, For this purpose we know that the

According to multiplicative rule of probability ,

If A and B are two independent events in a probability experiment, then the probability that both events occur simultaneously is: P(A and B)=P(A)⋅P(B) In case of dependent events , the probability that both events occur simultaneously is: P(A and B)=P(A)⋅P(B | A)

and we see that these conditions are fulfilled by the definition of the multiplicative rule.

So, Multiplicative rule is a rule which states that the when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities

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Answer:

Step-by-step explanation:

hello :

P(A ∩ B)=P(A)×P(B)=1/2×1/3 = 1/6

Answer: D

Step-by-step explanation:

As the circumference of a circle is 360 degrees, this means arc BC is 64 degrees.

So, we can conclude that arc AB measures 180-64=116 degrees.

Thus, angle AOB is also 116 degrees.

Answer:

D) 116°

Step-by-step explanation:

If arcBAC measure 296°,

And arcAC measure 180°,

You can get arcAB measure 116°,

Because the arc equals the measure of the central angle,

<AOB=116°

Hope this helps <3

1) [tex]\overline{AB} \cong \overline{CD}[/tex], [tex]\overline{AD} \cong \overline{CB}[/tex], [tex]\overline{AX} \perp \overline{BD}[/tex], [tex]\overline{CY} \perp\overline{BD}[/tex] (given)

2) [tex]\overline{BD} \cong \overline{BD}[/tex] (reflexive property)

3) [tex]\triangle ABD \cong \triangle ACDB[/tex] (SSS)

4) [tex]\angle ADB \cong \angle CBY[/tex] (CPCTC)

5) [tex]\angle CYB[/tex] and [tex]\angle AXD[/tex] are right angles (perpendicular lines form right angles)

6) [tex]\triangle CYB[/tex] and [tex]\triangle AXD[/tex] are right triangles (a triangle with a right angle is a right triangle)

7) [tex]\triangle AXD \cong \triangle CYB[/tex] (HA)

8) [tex]\overline{AX} \cong \overline{CY}[/tex] (CPCTC)

The 41th term of the arithmetic sequence is 66.

Arithmetic sequences are those that contain these patterns. The difference between successive terms in an arithmetic series is constant. Because the difference between consecutive words is always two, the sequence 3, 5, 7, and 9 is an example of arithmetic.

[tex]a_{n}=a_{1}+(n-1)d[/tex]

[tex]a_n[/tex] =   the nᵗʰ term in the sequence.

[tex]a_1[/tex] =  the first term in the sequence.

d    =   the common difference between terms.

Finding arithmetic sequence for the nth term:

aₙ = a₁ + (n-1)d

d = the common difference

a₇ = a₁ + (7-1)d

34 = 5 + 6d

29 = 6d

d = 29/6

Now ,

Finding the  41st term of the arithmetic sequence.

a₄₁ = a₁ + (n-1)d

   = 5 + (41-1)d

   = 5 + 40d

   = 5 + 40(29/6)

   = (198)* 1/3

  =  66

The 41th term of the arithmetic sequence is 66.

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The new loan amount is $113,797

What is compound interest?

Compound interest is the interest imposed on a loan or deposit amount. It is the most commonly used concept in our daily existence. The compound interest for an amount depends on both Principal and interest gained over periods. This is the main difference between compound and simple interest.

We can find new loan amount as shown below:

Total amount of loan=4*6,970+4*11,320

=27,880+45,280

=$73,160

Now, we will find new loan amount using compound interest formula.

Amount=[tex]P(1+\frac{r}{n})^{nt}[/tex]

P=$73,160

n=12

t=1 year

r=4.5%=0.045

Putting in formula

Amount[tex]=73,160(1+\frac{0.045}{12})^{12}[/tex]

=$113,797.039

Rounding to nearest dollar

=$ 113,797

Hence, new loan amount after one-year grace period is $113.797.

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there are two correct options:

We know that:

f(x) = 3x + 1

Now, if we look at the graph of f(x), we can see that the y-intercept is at y = -5, and for each increase in one unit in the x-variable, there is an increase of 3 units in the y-variable.

Then the equation of g(x) is:

g(x) = 3*x - 5

Then g(x) is a translation downwards of 6 units, such that:

g(x) = f(x) - 6 = (3x + 1) - 6 = 3x - 5

And we also could write it as a horizontal translation of 2 units to the right:

g(x) = f(x - 2) = 3*(x - 2) + 1 = 3*x - 3*2 + 1 = 3x - 5

So there are two correct options:

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The value of s is 45 and the value of BC is 434

The given parameters are:

AB = 9s + 29

DC = 10s - 16

Opposite sides of rhombus are equal.

So, we have:

9s + 29 = 10s - 16

Evaluate the like terms

s = 45

Substitute s = 45 in AB = 9s + 29

AB = 9 * 45 + 29

Evaluate

AB = 434

This means that

BC = AB = 434

Hence, the value of s is 45 and the value of BC is 434

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Answer:

Step-by-step explanation:

hello :

The graph of y =-3x+4 is the line

Answer:

By 3.

Step-by-step explanation:

-12-3=-15

Hope this helps!

Answer:

-12 exceeds -15 by 3

Step-by-step explanation:

To find out by how much a exceeds b, subtract a - b.

For example, by how much does 8 exceed 6?

Here, a = 8 and b = 6.

a - b = 8 - 6 = 2

2 is correct since we know that 8 is 2 greater than 6.

Now we do this problem.

By how much does -12 exceed -15?

a = -12; b = -15

a - b = -12 - (-15) = -12 + 15 = 3

Answer: -12 exceeds -15 by 3

The volume of the cone based on the figure illustrated wil be 196cm³.

The information is incomplete and the complete question wast found online. An overview will be given.

Let's assume that the height is 4cm and the radius of the cone is 7cm. The volume of the cone will be:

= 1/3πr²h

= 1/3 × 3.14 × 7² × 4

= 196cm³

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Answer:

33600 m²

Step-by-step explanation:

The top and bottom horizontal sides are parallel, so this is a trapezoid with bases DC and AB. The height is BC.

area of trapezoid = (a + b)h/2

where a and b are the lengths of the bases, and h is the height.

We need to find the height, BC.

Drop a perpendicular from point A to segment DC. Call the point of intersection E. E is a point on segment DC.

DE + EC = DC

EC = AB = 360 m

DC = 600 m

DE + 360 m = 600 m

DE = 240 m

Use right triangle ADE to find AE. Then BC = AE.

DE² + AE² = AD²

DE² + 240² = 250²

DE² = 62500 - 57600

DE² = 4900

DE = √4900

DE = 70

BC = 70 = h

area = (a + b)h/2

area = (600 m + 360 m)(70 m)/2

area = 33600 m²

Answer:

33,600 m^2.

Step-by-step explanation:

This is a trapezium, so

Area = (h/2)(a + b)

=  (h/2) ( 360 + 600)

= 960h / 2

= 480h,

We find the value of h using Pythagoras:

250^2 = h^2  + (600-360)^2

h^2 =  250^2 - 240^2 = 4900

h = 70.

So the Area = 70 * 480

= 33,600 m^2

Answer:

[tex]0 = {x}^{2} + 14x + 46[/tex]

[tex] \boxed{ {x}^{2} - 14x - 46 = 0}[/tex]

[tex]x1.2 = \frac{ - b ±  \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

[tex]x1.2 = \frac{ - 14  ± \sqrt{ { - 14}^{2} - 4(1 \times 46) } }{2 (1)} [/tex]

[tex]x1.2 = \frac{ - 14 ±  \sqrt{196 - 184} }{2} [/tex]

[tex]x1.2 = \frac{ - 14 ± \sqrt{12}  }{2} [/tex]

[tex]x1.2 = \frac{ \cancel{ - 14} ±  \sqrt{12} }{ \cancel{2} } [/tex]

[tex]x1.2 = - 7 ±  \sqrt{12} [/tex]

[tex]x1.2 = - 7 ±  \sqrt{4 \times 3} [/tex]

[tex] \boxed{ \bold{ - 7 ± 2 \sqrt{3}}} [/tex]

Answer:

its a I hope it's helps you

A system equations that can be used to determine after how many months the boys will owe the same amount is

60 x = $ 1000

20 y = $ 600

In mathematics, a system of equations, also known as a system of simultaneous or systems of equations, is a finite system of equations for which we have sought common solutions. A system of equations can be classified in a similar way to simple equations. A system of equations finds application in our everyday life in modeling problems where unknown values can be represented in the form of variables.

In algebra, a system of equations contains two or more equations and looks for common solutions to the equations. "A system of linear equations is a set of equations that are satisfied by the same set of variables."

We need to find a system equations that can be used to determine after how many months the boys will owe the same amount

Let lan take x months to pay $ 1000 to his parents

In 1 month Ian pays $60

In x months Ian pays =

60 x= $ 1000

Let Ken take y months to pay $ 600 to his parents

In 1 month Ian pays $20

In y months Ian pays =

20 y= $ 600

Hence 60 x= $ 1000 and 20 y= $ 600 are the system of equations

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The value of f⁻¹(f(58)) is 58 and the value of the function f(f(5)) is 11

As a general rule, we have:

f⁻¹(f(x)) = x

Substitute 58 for x

So, we have:

f⁻¹(f(58)) = 58

Hence, the value of f⁻¹(f(58)) is 58

Also, we have:

f(f(5))

From the table, we have:

f(5) = 9

So, we have:

f(f(5)) = f(9)

From the table, we have:

f(9) = 11

So, we have:

f(f(5)) = 11

Hence, the value of the function f(f(5)) is 11

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The type of correlation relationship that exists between the number of fire stations in a city and the number of parks is: accidental correlation relationship.

Accidental relationship is a type of correlation relationship whereby there is a strong correlation between two variables without a logical explanation for such relationship. It is often regarded as coincidental.

Therefore, the type of correlation relationship that exists between the number of fire stations in a city and the number of parks is: accidental correlation relationship.

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The ratio of the area of the smaller rectangle to the area of the larger rectangle is 1:16

Area of a rectangle

The formula for calculating the area of a rectangle is expressed as:

A = length * width

For the large triangle

Area = 16 * 12

Area of large triangle = 192 square units

For the smaller rectangle

Area = 4 * 3

Area. of small rectangle = 12 square units

Ratio = 12/192 = 1:16

Hence the ratio of the area of the smaller rectangle to the area of the larger rectangle is 1:16

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The width of the deck is 6.5 feet.

The perimeter of a two-dimensional shape is the total length of the outline. To find the perimeter of a rectangle, we add the lengths of all four sides. Since opposite sides of a rectangle are always equal, we need to find the dimensions of length and width to find the perimeter of a rectangle. We can write the perimeter of the rectangle as twice the sum of its length and width. The perimeter is a linear measure and has units as meters, centimeters, inches, feet, etc.

Assuming the deck is rectangle

Perimeter = 2(length + width)

33ft = 2 (10 + width)

16.5 = 10 + width

width = 6.5 ft

Thus the width of the deck is 6.5 feet.

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The rate of change of area when radius = 4feet is 75.36 feet²/min.

Area definition, any particular extent of space or surface.

Area of circle = πr²

Let the area of the circle be πr²

dr/dt = 3feet/min (GIVEN)

Differentiating both sides with respect to time:

A = πr²

dA/dt =  π(2r).(dr/dt)

dA/dt = (2 * 3.14 * r).(dr/dt)

The rate of change of area when radius = 4feet

dA/dt  = (2 * 3.14 * 4).(3)

dA/dt = 75.36

Hence, the rate of change of area is 75.36feet²/min.

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