40)
6 cm
4 cm
12 cm
Find the volume of the rectangular prism.
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Answer:

The total number of marbles in the set is 107 marbles

Step-by-step explanation:

The parameters given are;

Let the size of the marbles be 1 unit

The marbles are arranged to form the equilateral triangle as follows;

1st row = 1 marble

2nd row = 2 marbles and so on so that the total number of marbles for an arithmetic series as follows;

Total number of marbles, t = 1 + 2 + 3 + ... + n

Therefore;

[tex]t = \dfrac{1 + n}{2} \times n[/tex]

Since there are 2 marbles left in forming the first equilateral triangle, we have the total number of marbles in the set, t₁, is given as follows;

[tex]t_1 = \dfrac{1 + n}{2} \times n + 2[/tex]

When the same marble set are arranged into a triangle in which each side has one more marble than in the first arrangement, there where 13 marble shortage, hence, the total number of marbles is given as follows;

[tex]t_1 = \dfrac{1 + (n+1)}{2} \times (n+1) -13[/tex]

We therefore have;

[tex]t_1 = \dfrac{1 + n}{2} \times n + 2 = \dfrac{1 + (n+1)}{2} \times (n+1) -13[/tex]

Which gives;

[tex]\dfrac{n^{2}+n+4}{2}=\dfrac{n^{2}+3\cdot n-24}{2}[/tex]

Therefore;

n² + n + 4 = n² + 3·n - 24

2·n = 24 + 4 = 28

n = 14

From which we have;

[tex]t_1 = \dfrac{1 + 14}{2} \times 14 + 2 = 107[/tex]

Therefore, the total number of marbles in the set, t₁ = 107 marbles.

The number of marbles in the set would be as follows:

[tex]107[/tex] marbles

Arrangement

Given that,

After arranging the marbles in an equilateral Δ, 2 marbles would be left

The size of marble being 1 unit,

So,

The first row of the equilateral Δ will consist of 1 marble,

while

The second row comprises of 2 marbles.

The process goes so on and on.

Therefore,

Total marbles [tex]t = 1 + 2 + 3 + ... + n[/tex]

Hence,

[tex]t = (1 + n)/2[/tex] × n

Because 2 marbles are extra,

[tex]t = (1 + n)/2[/tex] × n [tex]+ 2[/tex]

In case,

The same marble set are framed into a triangle, every side would contain 1 marble exceeding the previous one where 13 marbles would be felt short.

Thus,

Total marbles = [tex]\frac{1 + (n + 1)}{2}[/tex] × [tex](n + 1) - 13[/tex]

by putting the values, we get

[tex]n^2 + n + 4 = n^2 + 3n - 24\\2n = 24 + 4 = 28\\n = 14[/tex]

∵ Total marbles [tex]= (1+ 14)/2[/tex] × [tex]14 + 2[/tex]

[tex]= 107[/tex]

Thus, 107 marbles are the correct answer.

Learn more about "Probability" here:

brainly.com/question/8069952

Answer:

3

Step-by-step explanation:

2x=2+4

2x=6

x=3

#RAVEN

The line is 7 units long. Add the two equations together and set equal to 7:

7x-1 + 2x-1 = 7

Combine like terms:

9x-2= 7

Add 2 to both sides:

9x= 9

Divide both sides by 9:

X= 1

Answer:

For 2x -1, X = 3 (2 x 3 = 6 - 1 = 5)

For 7x -1, X = 1/7 or 0.142857.

Step-by-step explanation:

Answer:

C. f = 9

Step-by-step explanation:

→Subtract 5 from both sides:

3f + 5 = 32

    - 5    - 5

_________

3f = 27

→Divide both sides by 3:

f = 9

Answer:

C f=9

Step-by-step explanation:

Trust me, I  got the answer right.

Answer:

Center = (7, - 5)

Radius = 3

Step-by-step explanation:

[tex] {x}^{2} + {y}^{2} + 14x - 10y + 65 = 0 \\ {x}^{2} + 14x + {y}^{2} - 10 + 65 = 0 \\ ( {x}^{2} + 14x + {7}^{2}) - {7}^{2} + ({y}^{2} - 10y + {5}^{2}) \\- {5}^{2} + 65 = 0 \\ (x + 7)^{2} + (y - 5)^{2} - 49 - 25 + 65 = 0 \\ (x + 7)^{2} + (y - 5)^{2} - 49 + 40= 0 \\ (x + 7)^{2} + (y - 5)^{2} - 9= 0 \\ (x + 7)^{2} + (y - 5)^{2} = 9 \\ (x + 7)^{2} + (y - 5)^{2} = {3}^{2} \\ equating \: it \: with \: \\ (x - h)^{2} + (y - k)^{2} = {r}^{2} \\ - h = 7 \implies \: h = - 7 \\ - k = - 5 \implies \: k = 5 \\ center = ( - h, \: - k) = (7, \: \: - 5) \\ \\ radius \: r = 3[/tex]

Answer:

40 pens

Step-by-step explanation:

Let the total number of pens Ron had be x.

We need to find the fraction of the pen that were blue.

3/8 of them were black and 1/4 of them were red. This means that the fraction of the pens that were blue is:

1 - (3/8 + 1/4) = 1 - 5/8 = 3/8

There were 15 blue pens. This means that 3/8 of x is 15:

3/8 * x = 15

x = 15 * 8/3 = 40 pens

Ron had 40 pens.

Answer:

233.5

Step-by-step explanation:

step 1. A=wl=8·20=160

step 2. A=wl=6·12=72

step 3. A=ab

2=3·1

2=1.5

step 4.  160+72+1.5= 233.5

First simplify the equation of parabola y=-5x^2+15x-10 in the following way:

D=(15)^2-4\cdot (-5) \cdot (-10)=225-200=25, \\  \sqrt{D}=5, \\  x_{1,2} = \dfrac{-15\pm 5}{2\cdot(-5)} = 2, 1  \\ -5x^2+15x-10=-5(x-1)(x-2), \\ y=-5(x-1)(x-2).

You can see that if x=1 or x=2, then y=0. Two points of intersection with x-axis are (1,0) and (2,0).

Answer:

P(1) = 0

Step-by-step explanation:

The  sum of 1 is impossible so that horse will never  get to move

The probability of winning is zero

Answer:

p(1) = 0

Step-by-step explanation:

The horse can't move at all (why it's a bad idea)

The probability of winning is 0

Hope this helps!

Answer:

m∠A = 24°

Step-by-step explanation:

m∠A = m∠B

3x-12 = 2x

-2x.      -2x

x-12 = 0

x = 12

3(12)-12 = 24

2(12) = 24

11 (12) = 132

132 + 24 +24 = 180

Answer:

40

Step-by-step explanation:

To find the maximum we need to find the vertex. We can do this by writing the equation in vertex notation by completing the square.

A(w) = -w(w - 80)

= -w² + 80w

= -(w² - 80w) = -(w - 40)² + 160

The vertex is then (40, 160) and since we are looking for the value of w it will be 40.

Answer:

Since it's a right angled triangle

Hypotenuse = h

h² = 7²+24²

h= √49 + 576

h = √625

h= 25

Therefore hypotenuse is 25

Hope this helps.

Answer & Step-by-step explanation:

First, we must know the Pythagorean Theorem.

a² + b² = c²

a = 24

b = 7

Now, let's plug in these numbers into the formula.

24² + 7² = c²

Simplify the exponents.

576 + 49 = c²

Add 576 and 49 together.

625 = c²

Square root the terms on both sides of the equation.

√625 = √c²

Simplify the square roots.

25 = c

The length of the hypotenuse is 25 units.

Answer:

50

Step-by-step explanation:

The sum of angles in a triangle is 180 so the answer is 180 - 90 - 40 = 50.

Also, for your first question, 2 corresponding angles of the triangles must be congruent.

Answer:

B. 50°

Step-by-step explanation:

40°+90°+y = 180°

130°+y°=180°

y° =180°-130°

y = 50° (sum of the interior angles in a triangle=180°)

Answer:

180 cm

Step-by-step explanation:

Surface Area = 2(length * width + length * height + width * height)

S.A. = 2(8 * 3 + 8 * 6 + 3 * 6)

S.A. = 180 cm.

Answer:

Probability ≈ 0.0714

Step-by-step explanation:

Consider permutation and combination;

[tex]Total Combinations - 8C4,\\8C4 = 8! / 4! * ( 8 - 4 )!,\\8 * 7 * 6 * 5 / 4!,\\\\Total Combinations = 70,\\\\Combinations of Dance Classes - 5C4,\\5C4 = 5! / 4! * ( 5 - 4 )!,\\5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1,\\\\Dance Classes = 5,\\\\Probability - 5 / 70 = 0.0714,\\Conclusion; Probability = ( About ) 0.0714[/tex]

Answer: A. 7x(2x + 5)

Step-by-step explanation:

7x * 2x = 14x^2

7x * 5 = 35x

The length of AC will be equal to 20 units for the given line.

Distance is defined as the length between the two points here we have a line AC divided into two parts having a length of AB = 4 and BC is 16.

The length of the line AC will be calculated as:-

AC  =  AB  +  BC

Ac   =  4  +  16

AC  =  20 units.

Therefore the length of AC will be equal to 20 units for the given line.

To know more about distance follow

https://brainly.com/question/2854969

#SPJ2

Answer:

[tex]5cm[/tex]

Step-by-step explanation:

[tex]r=\sqrt{\frac{V}{\pi h} } \\=\sqrt{\frac{225.5}{\pi *3} } \\=5cm[/tex]

Answer:

1st graph: m = -1/2. (m is the slope)

2nd graph: m = 3/2.

3rd graph: Midpoint = (1/2, 1/2)

Step-by-step explanation:

1st graph:

Find the slope by looking for two points on the line. Use the formula [tex]m = \frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]

We can derive the points (-3, 0) and (1, -2). Plug these into the equation above.

[tex]m= \frac{-2-0}{1-(-3)}[/tex]

Simplify this, giving you: m = -1/2.

2nd graph:

Use the same formula as stated above. From this graph, you can plug in the points (-1, 1) and (1, 4)

[tex]m = \frac{4-1}{1-(-1)}[/tex]

Simplifying gets you: m = 3/2.

3rd graph:

To find the midpoint, use the formula: [tex](\frac{x_{1}+x_{2} }{2} , \frac{y_{1} +y_{2} }{2} )[/tex]

Plug in the end-points of the graph, or (-3, 2) and (4, -1).

You get:

[tex](\frac{-3+4}{2}, \frac{2-1}{2})[/tex]

Simplify:

Midpoint = (1/2, 1/2)

Answer:

The expression for the amount of wallpaper needed is [tex]20b^{2}- 2d[/tex]

Step-by-step explanation:

The necessary dimensions of the living room we need are the length and the height. We will not be needing the width because we will not be covering the floors with any wallpaper.

We will now assign variables to represent the surface areas of some features of the rooms.

Let the length of one wall of the living room be = l cm

Let the breadth of one wall of the living room be = b cm

Let the surface area of the doors be = d [tex]cm^{2}[/tex]

From the problem, we know that  l = 5b

The area to be covered on one wall of the living room will be = length X breadth.

l X b

recall l = 5b

[tex]5b \times b = 5b^{2}[/tex]

this is the area to be covered on one wall.

For the four walls, we would have [tex]4 \times 5b^{2}= 20b^{2}[/tex]

Let us remember that the living room has two doors each covering a surface area of [tex]d cm^{2}[/tex] we will have to subtract these out since hey won't be covered.

[tex]20b^{2}- 2d[/tex]

Therefore, the expression for the amount of wallpaper needed is [tex]20b^{2}- 2d[/tex]

Answer:

Number 3

Step-by-step explanation:

It is an acute isosceles because all the angles are acute and two sides are congruent.

Answer:

Acute and isosceles

Step-by-step explanation:

All the angles are less than 90

2 sides are equal

Answer:The second term is -23

Step-by-step explanation:

Step 1- multiply

4x-5=-20

Step 2- subtract

-20 - 3=-23

Answer:

1 , 29/11

Step-by-step explanation:

3x+y = 10 ....(1)

2x² +y² = 19 ....(2)

3x+y= 10

y = 10-3x

substituting the value of y in 2nd equation

2x² + y² = 19

2x² + (10-3x)² = 19

2x² + 100 + 9x² - 60x -19 = 0

11x² - 60x +81 = 0

11x² - 33x - 27x + 81 = 0

11x( x-3) - 27(x-3) = 0

(x-3)(11x-27) = 0

x = 3, 27/11

substituting x value on first equation

x= 3 x= 27/11

y= 10-3(3) y= 10 - 81/11

= 10-9 = (110-81)/11

= 1 = 29/11

Hope it helps...

Answer:

a) 15.52mm

b) 25.8275mm

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X, or the area to the left side of the curve. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X, that is, the area to the right side of the curve.

A) What wing-span has an area of 0.1005 on it left side under the standard normal curve?

This is X when Z has a pvalue of 0.1005. So it is X when Z = -1.28.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.28 = \frac{X - 20}{3.5}[/tex]

[tex]X - 20 = -1.28*3.5[/tex]

[tex]X = 15.52[/tex]

This wing-span is 15.52mm.

B) What wing-span has an area of 0.0480 on it right side under the standard normal curve?

This is X when Z has a pvalue of 1 - 0.0480 = 0.9520. So this is X when Z = 1.665.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.665 = \frac{X - 20}{3.5}[/tex]

[tex]X - 20 = 1.665*3.5[/tex]

[tex]X = 25.8275[/tex]

This wing-span is 25.8275mm.

Answer: The length of each leg is 10 inches.

Step-by-step explanation: The triangle in question has been described as a right angled triangle, which implies that one side measures 90 degrees. It ia also described as an isosceles triangle. An isosceles triangle has two sides being equal, and also the two angles facing the two equal sides also measure the same.

If a right angled triangle is given as isosceles, then it means the hypotenuse (which is the side facing the right angle) is not one of the equal sides. The other two sides apart from the hypotenuse are the sides with equal measurement.

The area of a triangle is given as

Area of triangle = 1/2 (b*h)

Where b (the base) is one of the equal legs, and h (the vertical height) is the other leg equal to b.

Hence, the area can be re-written as follows;

Area of a triangle = 1/2 (b*h)

50 = 1/2 (b*h)

By cross multiplication, you now have

50 *2 = b*h

100 = b*h

Having already determined that b equals h,

100 = h²

Alternatively

100 = b²

Therefore, adding the square root sign to both sides of the equation, you now have

√100 = √h²

10 = h

Therefore, the length of each leg, both base and height is 10 inches

Answer:

a = 0

Step-by-step explanation:

=> 3(a+4)-5(a-2) = 22

Opening Brackets

=> 3a+12-5a+10 = 22

=> 3a-5a+12+10 = 22

=> -2a+22 = 22

Subtracting 22 to both sides

=> -2a = 0

Dividing both sides by -2

We get,

=> a = 0

Answer:

a = 0

Step-by-step explanation:

3(a+4)-5(a-2)=22

3a+12-5a+10=22

-2a+22=22

Subtract 22 from both sides

-2a=0

Multiply both sides by -1

2a= -0

2a=0

Divide both sides by 2

a=0

Hey I just realized my answer is really similar to Ujalakhan01's so sorry if it seems like I copied them.

Answer:

43.30 km^2

Step-by-step explanation:

Since the shape is a regular polygon, the sides of the triangle are equal (10km) now find the area on the triangle using herons formula

Working:

Side is 10

Perimeter= 30km

Semiperimeter (s) = 15km

Formula= √s(s-a)(s-b)(s-c)

= √15(15-10)(15-10)(15-10)

= √15*5*5*5

=5√5*15

=5√75

= 5*8.66

= 43.3 km^2

Answer:

43.3

Step-by-step explanation:

since it is a regular polygon thus it is a equilateral triangle where all sides are the same and all angles are 60

use formula 1/2 x a x b x sin C where a and b are sides and C is the angle

1/2 x 10 x 10 x sin 60 = 43.30

or method 2 is using Pythagoras theorem by drawing a perpendicular height to length 10km

h = [tex]\sqrt{10^{2} - (10/2)^{2} } = \sqrt{75} \\[/tex]

area of triangle = 1/2 x 10 x [tex]\sqrt{75}[/tex] = 43.30

.

[tex]the \: value \: of \: x \: is \: - 1. \\ the \: value \: of \: y \: is \: 4 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]

Answer:

g(-8) = -62

Step-by-step explanation:

solve for x:

8x +2 = -62 subtract 2 from each side

8x =-64 divide by 8

x =-8