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:
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(6x^2+5x-3)+(x^2-9) find the sum please
Answer:
7x^2+5x-12
Step-by-step explanation:
(6x^2+5x-3)+(x^2-9)
Combine like terms
(6x^2+ x^2+5x-3-9)
7x^2+5x-12
There were 49 questions in the exam and Peter answered 45 questions correctly. Find the percent of error.
A. 8.16%
B. 8.2%
C. 8.5%
D. 8.8%
Answer:
A
Step-by-step explanation:
49-45 = 4 wrong
4/49 = 0.08163
= 8.16%
Answer:
A) 8.16
Step-by-step explanation:
1) Subtract 49-45
2) Divide 4/49 and multiply by 100
3) Then multiply by 100
Hope this helped
There are 5,426 people seated at tables. Each table seats 8 people.
How many tables are full?
How many people are sitting at a table that is not full?
How many tables are needed for all 5,426 people?
Answer:
678
2
679
Step-by-step explanation:
Number of people: 5426
Capacity of table: 8
How many tables are full?
Number of full tables= 5426/8= 678.25 so full part is 678How many people are sitting at a table that is not full?
0.25 table= 8*0.25= 2 people are sitting at a table that is not fullor
5426 - 678*8= 2 peopleHow many tables are needed for all 5,426 people?
678+1= 679 tablesuse factoring to solve
x^2-2x-35=0
Answer:
I'm sorry I don't have an answer but for all future math work you should download photomath on your phone it's rly good
Answer:
The solution set of the quadratic equation is
x = {7, -5}
Step-by-step explanation:
Given the quadratic equation
[tex]$ x^2 - 2x -35 = 0 $[/tex]
We need to factor this equation
So you need two numbers such that
a + b = -2
and
a×b = -35
How about -7 and 5?
-7 + 5 = -2
-2 = -2
and
-7×5 = -35
-35 = -35
(x - 7)(x + 5) = 0
(x - 7) = 0
x = 7
and
(x + 5) = 0
x = -5
Therefore, the solution set of the quadratic equation is
x = {7, -5}
Verification:
Plug 7 into the quadratic equation
[tex]x^2 - 2x -35 = 0 \\\\(7)^2 - 2(7) -35 = 0 \\\\49 - 14 - 35 = 0 \\\\49 - 49 = 0\\\\0 = 0[/tex]
Plug -5 into the quadratic equation
[tex]x^2 - 2x -35 = 0 \\\\(-5)^2 - 2(-5) -35 = 0 \\\\25 + 10 - 35 = 0 \\\\35 - 35 = 0\\\\0 = 0[/tex]
Use the data in the table to answer the question. Citations are "speeding tickets." You may fill in the table to help you answer the question. Original data Line of "best guess" Line of best fit Mph greater than speed limit Number of citations Outputs Residuals Outputs Residuals 5 3 7.5 6 10 10 15 5 20 6 Use a calculator or online resource to find the line of best fit. Note that values have been rounded. y = 0.7 x - 5.2 y = 0.7 x + 5.2 y = 0.07 x + 5.2 y = 0.07 x - 5.2
Answer: ŷ = 0.07X + 5.2
Step-by-step explanation:
Given the following :
Number of citations 5 - 7.5 - 10 - 15 - 20
Outputs Residuals 3 - - 6 - - 10 - 5 - - 6
Using the online regression calculator :
Line of best fit is represented by the equation:
ŷ = 0.06897X + 5.2069
ŷ = 0.07X + 5.2
From the line equation:
y = mx + c
With 0.07 = slope of gradient(m)
Intercept (c) = 5.2 (point where the line of best fit intersect the y_axis
x and y are values of x and y respectively
The volume of a sphere is 45001 m3. Find the length of the radius
of the great circle.
Answer:
[tex]\large \boxed{\text{22.07 m}}[/tex]
Step-by-step explanation:
The formula for the volume (V) of a sphere is:
V = ⁴/₃πr³
We can use this equation to calculate the radius (r).
[tex]\begin{array}{rcl}45001 & = & \dfrac{4}{3} \pi r^{3}\\\\33750 & = &\pi r^{3}\\10740 & = &r^{3}\\r & = & \textbf{22.07 m}\\\end{array}\\\text{The radius of the great circle is $\large \boxed{\textbf{22.07 m}}$}[/tex]
how are trapizods and recangles the same
Answer:
Yes, but no
Step-by-step explanation:
So the trapezoid is a quadrilateral because it has four sides. ... A rectangle can also be termed as trapezoid as its one pair of opposite is parallel and equal. On the other hand a trapezoid may not have all its internal four angles as right angles but a rectangle must have all its angles as right angles.
Hope this helps you
Write a sequence with at least 5 terms that forms a pattern. Identify the rule.
please its due in an hour!!!!!!!!!!!!!
The pattern is attached in the image provided with the work.
I have started off listing 4 terms and then 3 blanks
so we can study the pattern and find the next few terms.
Here, notice that the difference between -5 and 1/2 and -5 is +1/2.
The difference between -5 and -4 and 1/2 is +1/2
and the difference between -4 and 1/2 and -4 is +1/2.
Continuing the same pattern, -4 + 1/2 will be equal to -3 and 1/2.
-3 and 1/2 + 1/2 will be equal -3
and -3 + 1/2 will be equal to -2 and 1/5.
If angle ABC measures 40 degrees, what does angle ADC measure
Answer:
what shape is ABCD?
Answer:
Step-by-step explanation: 60%
How do you make x the subject for (A) please?
Answer:
x = y / (4x+11)
Step-by-step explanation:
y = 4x^2 + 11x
4x^2 + 11x - y = 0
4x^2 + 11x = y
x(4x + 11) = y
x = y / (4x+11)
Find the area of the shape shown below.
24
25
8
units?
HELP
Answer:
hope this is correct
Answer:
108
Step-by-step explanation:
I need these so i don't fail.
1.Given the points (−2,5)and (6,−1)the midpoint is? 2.Given the points (9,−4)and (−5,2)the midpoint is ? 3.Given the points (−2,−5)and (−6,7)the midpoint is?
I need the midpoints.
Answer:
1) (2,2)
2) (2,-1)
3) (-4,1)
Step-by-step explanation:
Five state officials are listed to the right. a. List the 10 possible samples (without replacement) of size 3 that can be obtained from the population of five officials. Governor (Upper G) Lieutenant Governor (Upper L) Secretary of State (Upper S) Representative (Upper R) Press Secretary (Upper P) b. If a simple random sampling procedure is used to obtain a sample of three officials, what are the chances that it is the first sample on your list in part (a)? the second sample? the tenth sample? a. List all 10 possible samples (without replacement) of size 3. Use the letter abbreviation for each official.
Answer:
All possible are:
(G,L,S)
(G,L,R)
(G,L,P)
(G,S,R)
(G,S,P)
(G,R,P)
(L,S,R)
(L,S,P)
(S,R,P)
{L,R,P)
Probability of 1st/2nd/10th sample = 1/10
Step-by-step explanation:
All the possible combinations of the 3 size samples from a 5 size population have been listed without repetition.
Total Numbers of Samples = 10
To find the probability of finding the first sample from random sampling procedure,
Probability = Number of desired outcomes/ Total number of outcomes
Where Number of desired outcome is 1 and total number of outcomes is 10.
Probability = 1/10
Similarly, to find 2nd sample or 10th sample, the number of desired outcomes is same i.e 1, hecne the probability remains the same i.e 1/10
Possible samples:
(G,L), (G,S), (G,A), (G,P), (L,S), (S,A), (A,P), (L,P), (S,P), (A,L).
a) Given:
Population size [tex]N=5[/tex].
Sample size [tex]n=2[/tex]
Possible sample (without replacement)
[tex]\Rightarrow 5C_{2}=\frac{5!}{2!\times 3!}[/tex]
[tex]=\frac{5\times 4}{2}[/tex]
[tex]=10[/tex]
[tex]10 samples:-[/tex]
Governor, Lieutenant Governor, secretary of state, Attorney General, Press (P)
Possible samples:
(G,L), (G,S), (G,A), (G,P), (L,S), (S,A), (A,P), (L,P), (S,P), (A,L).
b) Event: [tex]E\to[/tex]choosing sample second and tenth.
[tex]E=\left\{\left ( G,S \right ),\left ( A,L \right ) \right\}\\n\left ( E \right )=2\\n(S) =10[/tex]
The Probability of that it is the first sample.
Second and tenth sample[tex]=\frac{n\left ( E \right )}{n(S)}[/tex]
[tex]=\frac{2}{10}[/tex]
[tex]=\frac{1}{5}[/tex]
Learn More: https://brainly.com/question/5123318
a rectangular inflatable swimming pool is 2 [tex]\frac{4}{5}[/tex] yards long, 2 yards wide, and [tex]\frac{3}{5}[/tex] yard tall. What is the volume of the pool? Round to the nearest tenth
Answer:
3.4 yd^3
Step-by-step explanation:
The volume is
V = l*w*h
V = 2 4/5 * 2 * 3/5
Changing the mixed number to an improper fraction
2 4/5 = ( 5*2+4)/5 = 14/5
V = 14/5 * 2 * 3/5
= 84/25
Changing back to a mixed number
3*25 = 75 with 9 left over
3 9/25
3.36 yd^3
To the nearest tenth
3.4 yd^3
Answer: 3.4 yards cubed, after rounding.
Step-by-step explanation:
To find the volume of a rectangular prism, use the following formula:
[tex]V = wlh[/tex], where w is the width, l is the length, and h is the height
Substitute the values given to you into the formula:
[tex]V = 2 * \frac{3}{5} * 2\frac{4}{5}[/tex]
Simplify the mixed number by multiplying both the numerator and denominator of 2/1 by 5 to get 10/5 and add it to the fraction to get 14/5.
[tex]V = \frac{2}{1} * \frac{3}{5} * \frac{14}{5}[/tex]
Now, multiply the numerators and denominators of the fractions and simplify:
[tex]V = \frac{2 * 3 * 14}{5 * 5}\\\\V = \frac{84}{25}\\\\\\V = 3.36[/tex]
The volume is 3.36 yards cubed. Round to the nearest tenth to get 3.4 yards cubed.
What is the perimeter of the triangle?
Answer:
To find the perimeter of the triangle, you need to add up the three sides of the triangle
/\
1 /__\ 5
9
1+5+9
_________________________________
Hey!!
The formula to find perimeter of triangle is a+b+c
For example:
If a triangle has the sides of 5,4 and 3 respectively,then to find the perimeter of triangle,we have to use the formula a+b+c which equals to 12.
Hope it helps
Good luck on your assignment
___________________________________
Which ratios is equivalent to 12 over 2 ?
Answer: 12:2, 6:1, 24:4
Step-by-step explanation:
Simplify 16-3(8-3)2÷5
Answer:
10/1 = 10
Step-by-step explanation:
1) Subtract: 8 - 3 = 5
2) Multiple: 3 * the result of step No. 1 = 3 * 5 = 15
3) Multiple: the result of step No. 2 * 2 = 15 * 2 = 30
4) Divide: the result of step No. 3 : 5 = 30 : 5 = 6
5) Subtract: 16 - the result of step No. 4 = 16 - 6 = 10
Solve.
a + 1 = Vb + 1 for b.
Answer:
b = a² + 2a
Step-by-step explanation:
a + 1 = √(b + 1)
(a + 1)² = b + 1 (Square both sides)
a² + 2a + 1 = b + 1 (Expand left side)
a² + 2a = b (Subtract 1)
umm what are the answers for :
21% of 36570
12.2% of 640
87.5% of 860
37.5% of 3200
awwwww pls help meh!!! i need to know asap...please..try help!!...thank u sooo much!!
lu yall..pls help!!!
Step-by-step explanation:
21% of 36570
21/100 x 36570 = 7679.7
12.2% of 640
12.2/100 x 640 = 78.08
87.5% of 860
87.5/100 x 860 = 752.5
37.5% of 3200
37.5/100 x 3200 = 1200
Graph the inequality
-9 < y + 5x < 14
Answer:
Step-by-step explanation:
2x-4=2
what is x=
plz help
Answer:
3
Step-by-step explanation:
2x=2+4
2x=6
x=3
#RAVEN
(1). An Aeroplane leaves an airport, flies due North for 2 hrs at 500km/h. It then flies on a bearing of 053 degree at 300km/h for 90 mins. How far is the plane from the airport correct to 1 dp *(2). Find the bearing of the plane from the Airport correct to 1 dp. *(3). If it takes the Aeroplane 150 mins to fly back to the airport. Find the average speed of the aeroplane for the whole flight correct to 1dp. *
Answer:
1. 1320.7 km
2. 015.8 degrees.
3. 461.8 km/h.
Step-by-step explanation:
(1) the distance from the airport is approximately 1096.5 km.
(2) the bearing of the plane from the airport is approximately 24.4 degrees.
(3) the average speed of the airplane for the whole flight is approximately 580 km/h.
(1) To find the distance the plane is from the airport, we can break down the two legs of the journey into their respective distances and use the Pythagorean theorem.
For the first leg of the journey, the plane flies due North for 2 hours at a speed of 500 km/h. Therefore, the distance covered is:
Distance = Speed * Time = 500 km/h * 2 h = 1000 km
For the second leg of the journey, the plane flies at a bearing of 053 degrees at a speed of 300 km/h for 90 minutes (1.5 hours). We can calculate the distance covered using the formula:
Distance = Speed * Time = 300 km/h * 1.5 h = 450 km
Using the Pythagorean theorem, the distance from the airport is the hypotenuse of a right triangle with sides of 1000 km and 450 km:
Distance from the airport = √(1000² + 450²) ≈ 1096.5 km (rounded to 1 decimal place)
Therefore, the distance from the airport is approximately 1096.5 km.
(2) To find the bearing of the plane from the airport, we need to determine the angle between the plane's position and the north direction. We can use the inverse tangent function (arctan) to find this angle.
The angle can be calculated as:
Angle = arctan(opposite/adjacent) = arctan(450/1000) ≈ 24.4 degrees (rounded to 1 decimal place)
Therefore, the bearing of the plane from the airport is approximately 24.4 degrees.
(3) To find the average speed of the airplane for the whole flight, we can calculate the total distance traveled divided by the total time taken.
The total distance traveled is the sum of the distances from the first and second legs of the journey:
Total Distance = 1000 km + 450 km = 1450 km
The total time taken is the sum of the time taken for each leg:
Total Time = 2 hours + 1.5 hours + 2.5 hours (150 minutes is equal to 2.5 hours)
Average Speed = Total Distance / Total Time = 1450 km / 2.5 h ≈ 580 km/h (rounded to 1 decimal place)
Therefore, the average speed of the airplane for the whole flight is approximately 580 km/h.
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Un cazador se encuentra en la parte mas alta de un arbol. Para averiguar a que altura se encuentra, deja caer una bola, observando que demora 4 segundos. Encuentra el alto del arbol (g=10m/s2)
Answer:
80 m
Step-by-step explanation:
La velocidad inicial de la pelota es 0 m/s.
La altura del árbol es s.
El tiempo necesario es de 4 segundos.
Podemos aplicar una de las ecuaciones de movimiento de Newton:
[tex]s = ut + \frac{1}{2}gt^2[/tex]
donde u = velocidad inicial
t = tiempo empleado
g = aceleración debido a la gravedad
Por lo tanto:
[tex]s = 0 * 4 + (1/2 * 10 * 4^2)\\\\s = 0 + 80 \\\\s = 80 m[/tex]
El árbol tiene 80 metros de altura.
X2=
a. 48
b. 16
c. 12
Answer:
16
Step-by-step explanation:
x^2 = whole * part
x^2 = (6+2) * 2
x^2 = 8*2
x^2 = 16
Answer:
16
Step-by-step explanation:
Hope this helps.
If you find answers that say 48 for this same problem, they are incorrect. Please disregard them.
is x^2 + y^2 = 5 a function
Answer:
No it is not a function.
Step-by-step explanation:
Answer:
No. This is NOT a function.
Step-by-step explanation:
Find the equation of the line that is perpendicular to y = -3/4x+1 and contains the point (9,12).
Answer:
[tex]y = \frac{4}{3} x[/tex]
Step-by-step explanation:
Perpendicular = m1*m2 = -1
[tex]-\frac{3}{4}*\frac{4}{3} = -1[/tex]
[tex]y = \frac{4}{3} x +b[/tex]
[tex]12 = \frac{4}{3}(9)+b\\12 = 12 + b\\b = 0\\y = \frac{4}{3} x+0\\y = \frac{4}{3} x[/tex]
The equation of the line perpendicular to the given line is [tex]y=\frac{4}{3}x[/tex].
Given that, the equation of a line [tex]y=\frac{-3}{4}x+1[/tex] and the coordinate point (9, 12).
What is the slope of perpendicular lines?Slope of a perpendicular line can be computed from the slope of a given line. The product of the slope of a given line and the slope of the perpendicular line is equal to -1. If the slope of a line is m1 and the slope of the perpendicular line is m2, then we have m1.m2 = -1.
From the given equation of a line slope m1=-3/4
The slope perpendicular to equation of line m2 = -1/m1 = 4/3
Now, substitute m=4/3 and (9, 12) in y=mx+c and solve for c.
That is, [tex]12=\frac{4}{3} \times 9 +c[/tex]
⇒ c=0
Put c=0 and m=4/3 in y=mx+c, we get
[tex]y=\frac{4}{3}x[/tex]
Therefore, the equation of the line perpendicular to the given line is [tex]y=\frac{4}{3}x[/tex].
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Factorise polynomials 15^2p-7p
Answer:
p ( 15p - 7)
Step-by-step explanation:
15 p^2 - 7p
The only common term is p so factor out p
p ( 15p - 7)
____________________________
15p^2-7p
take the common,
Ans: p(15p-7)
hope it helps
Good luck on your assignment
__________________________
expand and simplify the equation
Answer:
7x+12
Step-by-step explanation:
5(3x+2) - 2(4x-1)
Distribute
15x + 10 -8x+2
Combine like terms
7x +12
what are the steps I need to do to get the answer?
Answer:
B. 10.9
Step-by-step explanation:
Area of triangle= 1/2*24*h
∠N=90° ⇒ Area of triangle= 1/2*MN*ON
MN²= h²+(24-7)²
ON²= h²+7²
24h=MN*ON24h= √h²+(24-7)²*√h²+7²(24h)²=(h²+17²)(h²+7²)h²=k576k=k²+289k+49k+289*49k²-238k+14161=0k=119h²=119h=√119= 10.9Find the equation of this line
the Answer is:
3/4x + 1/4
Answer:
y=3/4 x + 1/4
Step-by-step explanation:
y=mx+b
(5,4) first point
(-3,-2) second one
m=y2-y1/x2-x1 =-2-4/-3-5=-6/-8=-3/-4=3/4
find b when x=5 and y= 4
y=mx+b
4=3/4 (5) +b
4-15/4 =b
4 b=16-15
b=1/4
