What is the common ratio of the following sequence?
-1, 6, - 36, 216 . . .
r = -6
r = 1296
r = -1
r = 7
Answer:
r = -6
Step-by-step explanation:
-1 × -6 = 6
6 × -6 = -36
-36 × -6 = 216
Answer:
-6
Step-by-step explanation:
To find the common ratio, take the second term and divide by the first term
6/ -1 = -6
Check the third term and divide by the second term
-36/-6 = -6
And the 4th divided by the third
216/ -36 = -6
The common ratio is -6
-6x + 7y = 9
2x - 2y = 4
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8709196751
7250401594
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7258061562
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The sum of 3 numbers is 108. The first number is 8 less than the second. The third number is 3 times the first. What are the numbers?
Step-by-step explanation:
hope you can understand it properly
ANYONE A ACE OR EXPERT? PLEASE ANSWER THIS I NEED HELP
Answer:
Ace here. What do you need help with?
The values in a dataset are 3.5, 2.5, 2.5, 3.5, and 3.0. If Xbar (sample mean) = sigma X / n, what is the mean for the sample?
Answer:
[tex]\bar x = 3.0[/tex]
Step-by-step explanation:
Given
[tex]x: 3.5, 2.5, 2.5, 3.5, 3.0[/tex]
Required
The sample mean
This is calculated using:
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x = \frac{3.5+ 2.5+ 2.5+ 3.5+ 3.0}{5}[/tex]
[tex]\bar x = \frac{15.0}{5}[/tex]
[tex]\bar x = 3.0[/tex]
Arlen is planning a dinner party at which he will be able to accommodate seven guests. From past experience, he knows that each person invited to the party will accept his invitation with probability 0.5. He also knows that each person who accepts will actually attend with probability 0.8. Suppose that Arlen invites twelve people. Assuming that they behave independently of one another, what is the probability that he will end up with more guests than he can accommodate
Answer:
"0.057309921" is the correct answer.
Step-by-step explanation:
According to the question,
The coming probability will be:
= [tex]0.5\times 0.8[/tex]
= [tex]0.4[/tex]
n = 12
p = 0.4
Now,
⇒ [tex]P(X>7)=1-P(X<=7)[/tex]
Here, X = Number of guests
[tex]=1-binom.dist(7,12,0.4,1)[/tex]
[tex]=0.057309921[/tex]
Thus, the above is the correct answer.
Un número real no puede pertenecer a los racionales y a los irracionales a la vez?
Step-by-step explanation:
eso es cierto y correcto por supuesto, es tan obvio
If 4 US dollars can be exchanged for 1.75 Euros. How many Euros can be obtained for 144 US dollars?
Answer:
63 euros.
Step-by-step explanation:
4 dollars = 1.75 euros
1 dollar = 1.75 / 4 euros, so
144 dollars = (1.75/4) * 144
= 63 euros.
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Answer:
.5 or (1/2)
.5 or (1/2)
2.5 or (5/2)
Step-by-step explanation:
all you really have to do is mulitply the numbers by .5
1*.5= .5
5*.5= 2.5
the product of two consecutive positive odd integers is 2499 find the bigger integer
Step-by-step explanation:
Consecutive odd integers are integers that take on the form n, n + 2, n +4, n + 6, and so on, where n is odd.
Now, Product of two consecutive positive odd integers = 2499
=>n*(n+2) = 2499
=>n^2+2^n-2499=0
=>n^2+51^n-49^n-2499=0 =>n(n+51)-49(x+51)=0
=>(n+51)(n-49)=0
=>n=49 (n is not equal to -51 which is negative integer).
So,bigger integer =(n+2)=49+2=51.
A soccer ball is kicked from the ground at an upwards velocity of 90 feet per second. The equation h(t)=-16t^(2)+90t gives the height of the ball after t seconds. How many seconds will it take for the ball to reach its maximum height?
I need help figuring this out to help my grade
Answer: 2.81 s
Step-by-step explanation:
Given
Ball is kicked upward with velocity [tex]u=90\ ft/s[/tex]
Height of the ball is given by the function [tex]h(t)=-16t^2+90t[/tex]
Derivative of a function gives the maxima or minima at certain point
[tex]\Rightarrow \dfrac{dh}{dt}=-32t+90\\\\\Rightarrow \dfrac{dh}{dt}=0\\\\\Rightarrow -32t+90=0\\\\\Rightarrow t=\dfrac{90}{32}\\\\\Rightarrow t=2.81\ s[/tex]
Thus, it takes ball 2.81 s to reach the top.
Is the percent increase from 50 to 70 equal to thhe percent decease from 70 to 50
Answer:
No
Step-by-step explanation:
The amounts of change are the same, but the original amounts are different. The ratio for the percent increase from 50 to 70 is 20/50, or 40%. The ratio for the percent decrease from 70 to 50 is 20/70, or about 29%.
Answer:
Step-by-step explanation:
Though the difference is the same, the original value is different. Therefore they are not the same.
Percentage increase from 50 to 70
[tex]=\frac{70 - 50}{50} \times 100\\\\=\frac{20}{50} \times 100 = 40 \%[/tex]
Percentage decrease from 70 to 50
[tex]= \frac{70-50}{70} \times 100\\\\= \frac{20}{70} \times 100 = 28.57 \%[/tex]
Find the percent of increase from 380 to 510. Round to the nearest tenth of a percent, if
necessary.
Answer:
510 divided by 380 is 1.34210526316 so multiple by 10 to get 134.210526316
rounding to the tenth we get 134.2
If this sun is 66° above the horizon, find the length of the shadow cast by a building 61 feet tall. Round your answer to the nearest tenth.
Answer:
27.2 ft
Step-by-step explanation:
We solve using the Trigonometric function of tan
tan θ = Opposite/Adjacent
θ = 66°
Opposite = Height of the building = 61 ft
Adjacent = Length of the shadow = ? = x
tan 66 = 61/x
Cross Multiply
tan 66 × x = 61
x = 61 ft/tan 66
x = 27.158949804 ft
Approximately = 27.2 ft
The length of the shadow = 27.2 ft
Según la gráfica cuadrática de la expresión y= x² + 1 ¿Cuales serían las coordenadas cuando x es igual a -2,-1 y 0?
Answer:
When x = -2 P ( -2 ; 5)
When x = -1 Q ( -1 ; 2)
When x = 0 R ( 0 ; 1)
Step-by-step explanation:
y = x² + 1
When x = -2
y = ( -2)² + 1 y = 5 point P ( -2 ; 5)
When x = - 1
y = ( -1)² + 1 y = 2 point Q ( -1 ; 2 )
When x = 0
y = (0)² + 1 y = 1 point R ( 0 ; 1 )
La sombra de un árbol cuando los rayos del sol forman con la horizontal un ángulo de 36º, mide 11 metros. ¿Cuál es la altura del árbol?
Answer:
La altura del árbol es 8 metros.
Step-by-step explanation:
La sombra de un árbol, cuando los rayos del sol forman con la horizontal un ángulo de 36º, mide 11 metros. Esto se puede observar en la imagen adjunta.
La trigonometría estudia la relación entre los lados y ángulos de los triángulos. Las razones trigonométricas de un ángulo α son las razones obtenidas entre los tres lados de un triángulo rectángulo (uno de sus ángulos es recto y mide 90°).
La tangente de un ángulo es la razón entre el cateto opuesto y el cateto contiguo o cateto adyacente. En este caso se debe aplicar dicha relación trigonométrica.
[tex]tan(\alpha )=\frac{cateto opuesto}{cateto adyacente}[/tex]
En este caso, se conoce el ángulo, cuyo valor es 36°, y el cateto adyacente, cuyo valor es 11. Reemplazando:
[tex]tan(36 )=\frac{cateto opuesto}{11}[/tex]
Resolviendo:
cateto adyacente= tan(36)*11
cateto adyacente= 7.99 metros ≅ 8 metros
La altura del árbol es 8 metros.
A line that includes the points (-9, 6) and (-3, s) has a slope of -1. What is the value of s?
Answer:
s=0
Step-by-step explanation:
We have two points so we can use the slope formula
m = (y2-y1) / x2-x1)
-1 = (s-6)/(-3 - -9)
-1 = (s-6)/(-3 +9)
-1 = (s-6)/(6)
Multiply each side by 6
6*-1 = s-6
-6 = s-6
Add 6 to each side
-6+6 = s-6+6
s=0
Answer:
[tex] \large\sf \: s = 0[/tex]
Value of s is 0.
Step-by-step explanation:
Here,
A line that includes 2 two points are ( -9 ,6) and (-3, s) and has a slope of - 1.
Using slope formula
m = ( y ² - y ¹ ) / ( x ² - x ¹)
Where,
m , is the slope which is -1( y ² - y ¹ ) = ( s - 6 )( x ² - x ¹) = ( - 3 - ( - 9 ) )substitute the values into the formula
-1 = ( s - 6 ) / ( - 3 - ( - 9 ) )
-1 = ( s - 6 ) / ( - 3 + 9 )
- 1 = ( s - 6 ) / ( 6 )
multiply each side by 2
- 1 × 6 = s - 6 × 6 / 6
- 6 = s - 6
- 6 + 6 = s - 6 + 6 ..( add 6 to each side)
0 = s
4 people are going to a dinner party. Each person at the party will eat 2/3 pound of cake. If you can only buy whole pounds of cake, how many pounds should you buy?
Question
In order to save for a new car, Charles adds money each month to a savings account which earns interest that is compounded monthly. Charles has created the expression 400((1+0.0212)12⋅3−10.0212) to calculate how much money he will have in his savings account when he is ready to purchase the car.
What do the values 400, 0.02, 12, and 3 represent in the expression?
Answer:
Step-by-step explanation:
Profit and Loss question class -9
Answer:
Rs 2.25
Step-by-step explanation:
S.P. = 375 * 3.36 = 1260
C.P. = 1125. for 500 mangoes
So for 1 mango,
C.P. = Rs 2.25
Answer:
₹2.25
Step-by-step explanation:
Selling price of 1 mango = ₹3.36
Mangoes in good state = 500 - 125 = 375
Selling price of 375 mangoes = 3.36 *375 = ₹ 1260
Cost price = [tex]\frac{100}{100+profit}*SP[/tex]
[tex]= \frac{100}{100+12}*1260\\\\=\frac{100}{112}*1260\\\\= 1125[/tex]
Cost price of 500 mangoes = ₹ 1125
CP of 1 mango = 1125/500 = ₹2.25
A rectangular prism has a length of
feet
, a width of 3 feet, and a height of 5 feet. If the width of the prism is doubled, which statement is true about the new rectangular prism?
Answer:
Its volume is 2 times the original volume.
Step-by-step explanation:
It cant be the first 2 because you are making it bigger, not smaller. and it cant be the last one because you are only doubling one of the parts.
Answer:
Step-by-step explanation:
its is the second one
pls help !!! :))
17. If m_1 = 98º and mz2 = 19º,
what is mz3?
Answer:
angle 3 = 79 degree
Step-by-step explanation:
given:
angle 1 = 98 degree
angle 2 : 19 degree
angle 3 =?
angle 2 + angle 3 =angle 1 (sum of two interior angle opposite angles is equal to the exterior angle formed)
19 + angle 3 = 98
angle 3 = 98 - 19
angle 3 = 79 degree
HELP PLZZ How many and what type of solutions does 6x^2−3x+5 have?
1 rational solution
2 rational solutions
2 irrational solutions
2 nonreal solutions
Si Doña Clara lleva un tratamiento con 2 medicamentos una toma cada 8 horas y la otra toma cada 12 horas, ¿Despues de la primera toma, a las cuantas horas volverá a tomar los dos medicamentos?
Respuesta:
24 horas
Explicación paso a paso:
El primer medicamento se toma cada 8 horas.
El segundo medicamento se toma cada 12 horas.
Para Obtian el momento en que ambos medicamentos se volverán a tomar juntos:
Encontramos el mínimo común múltiplo de 8 y 12
Múltiplos de:
8 = 8, 16, 24, 32, 40, 48, 56
12 = 12, 24, 36, 48, 60
El mínimo común múltiplo de 8 y 12 es 24.
Por lo tanto, ambos medicamentos se volverán a tomar después de 24 horas.
Determine the range for the function y = (x - 3 )^2 + 4.
Answer:
Solutions are x=2 and x=−2 . At these points the function has vertical asymptotes. To address the range, let's first transform...A principal of $2700 is invested at 6.25% interest, compounded annually. How much will the investment be worth after 13 years?
Use the calculator provided and round your answer to the nearest dollar.
$
Answer:
$5938
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Compounded Interest Rate Formula: [tex]\displaystyle A = P(1 + \frac{r}{n})^{nt}[/tex]
P is principle amountr is raten is compounded ratet is timeStep-by-step explanation:
Step 1: Define
Identify variables
P = 2700
r = 6.25% = 0.0625
n = 1
t = 13
Step 2: Find Interest
Substitute in variables [Compounded Interest Rate Formula]: [tex]\displaystyle A = 2700(1 + \frac{0.0625}{1})^{1 \cdot 13}[/tex][Exponents] Multiply: [tex]\displaystyle A = 2700(1 + \frac{0.0625}{1})^{13}[/tex](Parenthesis) Divide: [tex]\displaystyle A = 2700(1 + 0.0625)^{13}[/tex](Parenthesis) Add: [tex]\displaystyle A = 2700(1.0625)^{13}[/tex]Evaluate exponents: [tex]\displaystyle A = 2700(2.19926)[/tex]Multiply: [tex]\displaystyle A = 5938[/tex]What are factors of -12 that have a sum of +1?
negative 4 minus 8 equals
Answer:
-12
hope this helps!
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*Chuckles* my GPA is in danger
Answer:
A
Step-by-step explanation:
Exponential growth is when numbers increase rapidly in an exponential fashion so for every x-value on a graph there is a larger y-value. Decay is when numbers decrease rapidly in an exponential fashion so for every x-value on a graph there is a smaller y-value. So here the one that fits the description is A.
Find the value of 1×4+2×5+3×6......n×（n+3）
Answer:
n(n+1)(n+5)/3
Step-by-step explanation:
there is no value, as we don't know n.
but we can create a summary formula/ function definition :
this is the sum for k = 1 to n of k×(k+3)
k×(k+3) = k² + 3k
so, the overall sum splits into the sum of k² for k=1 to n, and the sum of 3k for k=1 to n.
and the sum of 3k is 3 times the sum of k for k=1 to n.
Σk² for k=1 to n = [n(n+1)(2n+1)]/6
Σk for k=1 to n = n(n+1)/2
3×Σk for k=1 to n = 3×n(n+1)/2
so, we have a function formula
n(n+1)(2n+1)/6 + 3n(n+1)/2 = n(n+1)(2n+1)/6 + 9n(n+1)/6 =
= n(n+1)(2n+1+9)/6 = n(n+1)(2n+10)/6 = n(n+1)(n+5)/3
