[tex]\boxed{\sf \sum _{n=1}^{20}\:4\left(\frac{8}{9}\right)^{n-1}}[/tex]
Identify the following:
First Term (a) = 4(8/9)¹⁻¹ = 4Common ratio (r) = 8/9Total Terms (n) = 20Formula Required:
[tex]\rightarrow \quad \sf S_n = \dfrac{a(r^n - 1)}{r-1}[/tex]
Insert values identified:[tex]\rightarrow \sf S_{20} = \dfrac{4(\dfrac{8}{9}^{20} - 1)}{\dfrac{8}{9} -1} \quad\overset{simplify}{\longrightarrow} \quad \dfrac{4\left(9^{20}-8^{20}\right)}{3^{38}} \quad \xrightarrow{\text{In \ Decimals} }\quad 32.58609013[/tex]
Peter has 5 times as much Money as Bala.
They have $1674 in total.
How much more money has Peter than bala
Answer:
Bala = 279$
Peter = 1395$
Step-by-step explanation:
Peter has 5 times as much Money as Bala.
They have $1674 in total.
How much more money has Peter than bala
Bala has 1 unity
Peter has 5 unity
total unity = 6
Find 1 unity
1674 : 6 = 279
Bala = 279
Peter = 5 * 279 = 1395
If = 152°, what is m∠ABC? 152° 38° 76° 104°
The value of ABC when AC is given as 152 will be 76°.
How to calculate the angle?It should be noted that the angles that are opposite to equal sides are equal and that the angle sum property of triangle is 180°.
In this case, (2 × ABC) = 152°
2ABC = 152°
ABC = 152°/2
ABC = 76°
In conclusion, the correct option is C.
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Which factor pair of 36 has a sum that is - 20?
The factor pair of 36 whose sum is -20 are -2 and -18.
What are Factors?Factors of a number or an algebraic expression are the numbers or expressions which divides the given number evenly.
For example, 10 = 2 × 5
So we can say that 2 and 5 are factors of 10.
Let x and y be the two factors of the number 36.
Then we have,
x × y = 36
Write the factors of the number 36 as the product.
36 = 1 × 36, sum = 1 + 36 = 37
36 = -1 × -36, sum = -1 - 36 = -37
36 = 2 × 18, sum = 2 + 18 = 20
36 = -2 × -18, sum = -2 - 18 = -20
Hence the factor pair of 36 whose sum is -20 are -2 and -18.
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HELP ASAP!!
I need this answer quickly it’s due in 15 minutes!
TY!!
Answer:
mean for data set 1 is 41
data set 1 MAD is 16.4
data set 2 MAD is 16.8
mean for data set 2 is 38
Step-by-step explanation:
Finding the mean:
Data set 1:formula: sum of the data set / total number of terms
sum of the data set: 18 + 29 + 35 + 58 + 65 = 205
total number of terms: there is 5 numbers in the data set
mean = 205 / 5
mean = 41
MAD (Mean Absolute Value):
step 1: Find the mean of the data (above)
step 2: Find the distance between each data and mean.
18, 29, 35, 58, 65
Distance between 18 and 41 is 23 (41 - 18 = 23)
Distance between 29 and 41 is 12 (41 - 29 = 12)
Distance between 35 and 41 is 6 (41 - 35 = 6)
Distance between 58 and 41 is -17 (41 - 58 = -17)
Distance between 65 and 41 is -24 (41 - 65 = -24)
step 3: take the absolute value of any negative numbers
|-17| and |-24| is 17 and 24
step 4: add all the distances
23 + 12 + 6 + 17 + 24 = 82
step 5: divided it by the number of data
82 / 5 = 16.4
Data set 2:
formula: sum of the data set / total number of terms
sum of the data set: 19 + 26 + 27 + 45 + 73 = 190
total number of terms: there is 5 numbers in the data set
mean = 190 / 5
mean = 38
MAD (Mean Absolute Value):
step 1: Find the mean of the data (above)
step 2: Find the distance between each data and mean.
19, 26, 27, 45, 73
Distance between 19 and 38 is 19 (38 - 19 = 19)
Distance between 26 and 38 is 12 (38 - 26 = 12)
Distance between 27 and 38 is 11 (38 - 27 = 11)
Distance between 45 and 38 is -7 (38 - 45 = -7)
Distance between 73 and 38 is -35 (38 - 73 = -35)
step 3: take the absolute value of any negative numbers
|-7| and |-35| is 7 and 35
step 4: add all the distances
19 + 11 + 12 + 7 + 35 = 84
step 5: divided it by the number of data
84 / 5 = 16.8
Let me know if you have any questions !
If Cyrus knows that △ABC∼△EDC and AB¯¯¯¯¯¯¯¯∥ED¯¯¯¯¯¯¯¯, how can he prove that line m passing through AB¯¯¯¯¯¯¯¯ has the same slope as line l passing through ED¯¯¯¯¯¯¯¯?
As AB and ED are parallel, they have the same slope. This means that since lines that are colllinear with parallel segments are parallel, lines l and m are parallel.
AB is tangent to circle O at B. The diagram is not drawn to scale. If AB =15 in and AO =20, what is the length of the radius (r)? Round the answer to the nearest tenth.
The length of the radius (r) to the nearest tenth is 13.2
What is Pythagoras theorem?The theorem states that the square of the longest side is equal to the sum of the square of other two sides.
In order to determine the radius of the circle, we will use the theorem above to have:
AO² = AB² +r²
Given
AB = 15
AO = 20
Substitute
20² = 15² +r²
r² = 400 - 225
r² = 175
r = 13.2
Hence the length of the radius (r) to the nearest tenth is 13.2
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HELP MEEEEEEEEEEEEEEEE
Answer:
[tex]x = 3[/tex]
Step-by-step explanation:
[tex]3x + 18 = 11x - 6 [/tex]
[tex]24 = 8x[/tex]
[tex]x = 3[/tex]
A bottle contains 20 blue bags and 15 red bags. If two bags are picked at random one after the other with replacement, what is the probability that the first bag is blue and then red?
Answer:
12÷49Step-by-step explanation:
The total number of bags in the bottle = 20 + 15 = 35
Then
the probability that the first bag is blue = 20/35
If we replace the first bag :
the probability that the second (picked) bag is blue = 15/35
Conclusion:
If two bags are picked at random one after the other with replacement
Then
the probability that the first bag is blue and then red is :
(20÷35)×(15÷35)
= (4÷7)×(3÷7)
= 12÷49
= 0.244897959184
find the height of a a cuboid if it's length is 10m , breadth is 5m and LSA is 180m² .
NONSENSE = REPORT
[tex]\huge\sf\underline{Answer}[/tex]
Let's find out ~
Given :-
Length ( l ) = 10m Breadth ( b ) = 5m LSA = 180m²Solution :-
[tex]\sf\rightarrow \:LSA \: of \: cuboid \: = 2h \: ( \: l + b \: )[/tex]
[tex]\sf\rightarrow \: 180 = 2h \: (10 + 5)[/tex]
[tex]\sf\rightarrow180 = 2h \: \times 15[/tex]
[tex]\sf\rightarrow 180 = 30h \: [/tex]
[tex]\sf\rightarrow \: 30h \: = 180[/tex]
[tex]\sf\rightarrow \: h = \frac{180}{30} [/tex]
[tex]\sf\rightarrow \: 6[/tex]
Thus , the height of cuboid is 6m
A stack of 30 science flashcards includes a review card for each of the following: 10 insects, 8 trees, 8 flowers, and 4 birds.
What is the probability of randomly selecting a tree or a flower?
Express the Probability as a reduced fraction
Using it's concept, it is found that the probability of randomly selecting a tree or a flower is given by:
[tex]p = \frac{8}{15}[/tex]
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, out of 30 cards, 8 + 8 = 16 are trees or flowers, hence the probability is given by:
[tex]p = \frac{16}{30} = \frac{8}{15}[/tex]
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How does the diagram show that the slope between any
two points on a line is the same?
OA)
It does not show this because the triangles are not
the same size.
OB)
The triangles have the same vertical heights and
horizontal lengths.
OC)
The distance between A and B is the same as the
distance between B and C.
OD)
The triangles are similar so the ratios of their vertical
heights to their horizontal lengths are equivalent.
The diagram shows that the triangles on the graph had similar ratios, as such their vertical heights to their horizontal are equivalent.
Option D is correct.
What is the slope of a graph?The slope of a graph determines the steepness of the graph and it is the difference between two points on the y-coordinate(rise) and the difference between two points on the x-coordinate(run).
[tex]\mathbf{slope = \dfrac{rise}{run}}[/tex]
[tex]\mathbf{slope = \dfrac{\Delta y}{\Delta x}}[/tex]
[tex]\mathbf{slope = \dfrac{ y_2-y_1}{x_2-x_1}}[/tex]
From the diagram attached, we can see that the triangles on the graph had similar ratios, as such their vertical heights(y-coordinates) to their horizontal (x-coordinates) are equivalent.
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Help me(I will give brainliest if correct)
Anser choices are:
A. -4/3
B. -3/4
C. 10-17
D. 17/10
Answer:
the answer is -3/4 c
Step-by-step explanation:
it's down 3 over 4
Identify the domain of the function shown in the graph.
Based on the function shown on the graph, we can find the domain to be C. x ≥ 0.
What is the function's domain?The domain refers to where all the values of x and y for the function fall within the graph.
As seen from the graph, there is no negative value of x and the lowest value of x is 0.
The domain for x is therefore:
x ≥ 0.
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Just give me answer
By applying the equation of dilation, the coordinates of the vertices of the triangle ABC are A'(x, y) = (-12, 0), B'(x, y) = (0, -9) and C'(x, y) = (-12, -9).
How to find the image of a triangle
A dilation is a type of rigid transformation. Rigid transformations are transformations applied to geometric loci such that Euclidean distances are conserved.
There is a triangle and its image must be a triangle, the new triangle is found by transforming the three vertices of the prior one following this formula:
A'(x, y) = P(x, y) + k · [A(x, y) - P(x, y)] (1)
Where:
P(x, y) - Center of reflection.A(x, y) - Original vertexA'(x, y) - New vertexk - Dilation factorIf we know that P(x, y) = (0, 0), A(x, y) = (-4, 0), B(x, y) = (0, -3) and C(x, y) = (-4, -3), then the new vertices of the triangle are, respectively:
Point A
A'(x, y) = (0, 0) + 3 · [(-4, 0) - (0, 0)]
A'(x, y) = (-12, 0)
Point B
B'(x, y) = (0, 0) + 3 · [(0, -3) - (0, 0)]
B'(x, y) = (0, -9)
Point C
C'(x, y) = (0, 0) + 3 · [(-4, -3) - (0, 0)]
C'(x, y) = (-12, -9)
Lastly, we draw the two triangles, which are presented in the image attached below.
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Find the area of AAOB
9√3 un²
3√3 un²
4.5√3 un
Answer:
Step-by-step explanation:
The area of the equilateral triangle is [tex]\frac{\sqrt{3}}{4}(6)^{2}=\boxed{9\sqrt{3}}[/tex]
Answer fast pls i need help
Answer:
12X3/-a=`12
Step-by-step explanation:
12x3=36
36xa/+=12
A helicopter flies 125 miles west and 20 miles north and lands.
The helicopter flies back on a direct course.
What is its bearing?
8
At a party there are 90 people.
48 are women and 42 are men.
Some women leave.
Some men arrive.
The ratio of women to men is now
10:11
Are there now more than 90 people at the party?
Tick one box.
Yes
No
Show working to support your answer.
Cannot tell
[2 marks
Answer:
No, there are less than 90 people at the party.
Step-by-step explanation:
This is because the number of women cannot go above 48 as it says "Some women leave".
-> This means that the ratio 10:11 actually states that there are 40(or less) women and 44(or less) men in the party now which is less
than 90 overall, so the answer is No.
:)
A certain car model comes in four different colors (black, white, blue, and silver) and can either have automatic or manual transmission. The company that makes the car took a random sample of 384384384 cars that were sold and checked their color and transmission. Here are the results:
The expected count for the cell corresponding to the white car in the sampling will be 204.
How to calculate the value?From the information given, the certain car model comes in four different colors, and can either have automatic or manual transmission.
The expected count for the cell corresponding to the white car will be:
= 96 × 204/384
= 51
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QUICKLY!!
Which of the following formulas is used to calculate the probability of mutually exclusive events
Answer:
P(AUB)=P(A)+P(B)
Step-by-step explanation:
I found it somewhereI don't know?Trust me:)
14. The two-way table shows whether the 576
students at Jim's school rode the bus or in a car to
school. Of the 6th graders, find the relative frequency
of those who rode in a car to the nearest percent.
Using it's concept, it is found that the relative frequency of 6th graders who rode a car is given by:
D. 55%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
The number of 6th graders is given by:
N6 = 576 - (219 + 189) = 168.
The number of 6th graders who rode a car is:
N6C = 168 - 75 = 93
Hence the relative frequency is given by:
r = 93/168 = 55%.
Hence option D is correct.
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what is the slope-intercept form of the equation of the line with the following points? (-3,5), (6,3)
Answer:
Y=-0.22X+6.33
Step-by-step explanation:
Y-yo=m(X-x0)
punto A=(-3,5)
punto B=(6,3)
ecuacion de la recta: Y-yo=m(X-x0)
m=Pendiente=[tex]\frac{5-3}{(-3-6)} =\frac{2}{-9}[/tex]
sea B(6,3) xo=6 y yo=3
reemplazando:
Y-6=[tex]\frac{-2}{9}[/tex](X-3)
Y-6=-0.22X+0.33
Y=-0.22X+6.33
brian runs 7 kilometers each day.write an equation that models the total kilometers,k,brian runs over,d, days
Answer:
k = 7d
Step-by-step explanation:
y = mx + b
slope (m): 7 kilometers each day
x: Brian runs over d days
y - intercept (b): when x = 0, y = 0 since it will be day 0
y: total kilometers, k
Answer:
k = 7d
Step-by-step explanation:
The standard form of an equation is :
y = mx + b
Here, the variables for y and x are k and d respectively.
===============================================================
It is given that Brian runs 7 kilometers each day. Hence, that is our rate of change, m. The value of b will be 0 as he starts from 0 km.
============================================================
So, the equation is :
k = 7d
75 points! pls help me! find the lateral area, total surface area, and volume?
Answer:
8
Step-by-step explanation:
8 is the answers I think
Answer:
To find the lateral area, total surface area, and volume of a geometric shape, I need to know the specific shape you are referring to. Could you please provide more details about the shape you are interested in? For example, is it a cube, cylinder, sphere, or some other shape? Once I have this information, I can provide you with the calculations for the lateral area, total surface area, and volume of that particular shape.Which graph does not represent a function of x?
Se dispone de un recipiente de 24 litros de capacidad y de tres medidas, A, B y C.
Se sabe que el volumen de A es el doble del de B, que las tres medidas llenan el
depósito y que las dos primeras lo llenan hasta la mitad. ¿Qué capacidad tiene cada
medida?
(Necesito saber el sistema de ecuaciones)
Teniendo en cuenta la definición de sistema de ecuaciones lineales, cada medida tiene una capacidad de A= 8 L, B= 4 L y C= 12 L.
Qué es un sistema de ecuacionesUn sistema de ecuaciones lineales es un conjunto de dos o más ecuaciones de primer grado, en el cual se relacionan dos o más incógnitas.
Resolver un sistema de ecuaciones consiste en encontrar el valor de cada incógnita para que se cumplan todas las ecuaciones del sistema. Es decir, se debe buscar los valores de las incógnitas, con los cuales al reemplazar, deben dar la solución planteada en ambas ecuaciones.
Capacidad de cada medidaEn este caso, se dispone de un recipiente de 24 litros de capacidad y de tres medidas, A, B y C.
Se sabe que el volumen de A es el doble del de B → A=2B
Las tres medidas llenan el depósito → A+ B +C= 24 L
Las dos primeras medidas llenan hasta la mitad del recipiente → A +B= 24 L÷2 → A +B= 12 L
Entonces, el sistema de ecuaciones a resolver es el formado por las tres ecuaciones anteriormente mencionadas.
Existiendo diversos métodos para resolver un sistema de ecuaciones, se decide resolver mediante el método de sustitución, que consiste en despejar una de las dos variables en una de las ecuaciones del sistema y sustituir su valor en la otra ecuación.
En este caso, reemplazando la primer ecuación en la tercera ecuación se obtiene:
2B +B= 12 L
3B= 12 L
B= 12 L÷3
B= 4 L
Reemplazando este valor en la primer ecuación se obtiene:
A=2B
A=2×4 L
A= 8 L
Finalmente, para obtener el valor de C se reemplaza el valor de A y B en la segunda ecuación:
A + B + C= 24 L
8 L + 4 L + C= 24 L
12 L + C= 24 L
C= 24 L - 12 L
C= 12 L
Finalmente, cada medida tiene una capacidad de A= 8 L, B= 4 L y C= 12 L.
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Brad took 5 kicks and made 4 goals: 4/5
Sydney will take 10 shots and she wants to make an equivalent fraction of the goals. How many goals must She make?
4/5 x ?/? = ?/10
Answer: 8/10
Step-by-step explanation: so you have to multiply 5 times x u till you get 10 so you’ll multiply it 2 times and since you multiplied the left 5 times two you have to multiply the 4 by 2 also to keep everything equal so the final answer is 8/10
Can someone help me with this problem?
The length of the rope Kurt started with is 13 1/3 inches
Calculating lengthsFrom the question, we are to determine the total length of the rope
From the given information,
The first piece was 4 4/5 inches long
and
The second piece was 8 1/2 inches long
Then,
The length of the rope Kurt started with will be
4 4/5 + 8 1/2
[tex]4\frac{4}{5} + 8\frac{1}{2}[/tex]
First, convert the fractions into improper fractions
[tex]\frac{24}{5} + \frac{17}{2}[/tex]
The Lowest common multiple (LCM) of the denominators is 10.
Then, we get
[tex]\frac{(2\times 24) + (5 \times 17)}{10}[/tex]
= [tex]\frac{48 + 85}{10}[/tex]
= [tex]\frac{133}{10}[/tex]
= [tex]13 \frac{1}{3}[/tex]
Hence, the length of the rope Kurt started with is 13 1/3 inches.
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PLEASE HELP!! 50 POINTS!!!!!
Answer:
3\2 is the marked
y cos x,=2
3\2=0.5
x=0.5*2=3.0
=3.0*2=6.0
The ideal weight (in stones) of people of varying heights is given in the table below. Draw a scatter plot for the data. Height (feet/inches) 5 ft 0” 5 ft 1” 5 ft 2” 5 ft 3” 5 ft 4” 5 ft 5” Weight (stones) 9.1 9.5 9.8 10 10.4 10.8 a. A graph has height on the x-axis, and weight on the y-axis, from 9 to 10.8 in increments of 0.2. Points are at (5, 9.1), (5 foot 1 inch, 9.5), (5 foot 2 inches, 9.8), (5 foot 3 inches, 10), (5 foot 4 inches, 10.4), (5 foot 5 inches, 10.8). c. A graph has height on the x-axis, and weight on the y-axis, from 9 to 10.8 in increments of 0.2. Points are at (5, 9.2), (5 foot 1 inch, 9.5), (5 foot 2 inches, 9.8), (5 foot 3 inches, 10), (5 foot 4 inches, 10.3), (5 foot 5 inches, 10.8). b. A graph has height on the x-axis, and weight on the y-axis, from 9 to 10.8 in increments of 0.2. Points are at (5, 9.5), (5 foot 1 inch, 9.8), (5 foot 2 inches, 10), (5 foot 3 inches, 10), (5 foot 4 inches, 10.4), (5 foot 5 inches, 10.8). d. A graph has height on the x-axis, and weight on the y-axis, from 9 to 10.8 in increments of 0.2. Points are at (5, 9), (5 foot 1 inch, 9.5), (5 foot 1 inch, 9.8), (5 foot 3 inches, 10), (5 foot 4 inches, 10.4), (5 foot 5 inches, 10.8). Please select the best answer from the choices provided
The scatter plot for the data will be A. A graph has height on the x-axis, and weight on the y-axis, from 9 to 10.8 in increments of 0.2. Points are at (5, 9.1), (5 foot 1 inch, 9.5), (5 foot 2 inches, 9.8), (5 foot 3 inches, 10), (5 foot 4 inches, 10.4), (5 foot 5 inches, 10.8).
What is a scatter plot?A scatter plot is a set of points plotted on horizontal and vertical axes that show the extent of correlation between the variables.
In this case, the scatter plot for the data will be a graph has height on the x-axis, and weight on the y-axis, from 9 to 10.8 in increments of 0.2. Points are at (5, 9.1), (5 foot 1 inch, 9.5), (5 foot 2 inches, 9.8), (5 foot 3 inches, 10), (5 foot 4 inches, 10.4), (5 foot 5 inches, 10.8).
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