Answer:
a: 3
b. 6973568802
Step-by-step explanation:
a₁ = 6 , r = 3 , a₂₀ =?
Result:
a₂₀ = 6973568802
Explanation:
To find a₂₀ we use the formula
aₙ = a₁ · r ^ⁿ⁻¹
In this example we have a₁ = 6 , r = 3 , n = 20. After substituting these values to above
formula, we obtain:
aₙ = a₁ · r ^ⁿ⁻¹
a₂₀ = 6 · 3 ^²⁰⁻¹
a₂₀ = 6 · 1162261467
a₂₀ = 6973568802
A trapezoid has a base length of 22 cm and a mid-segment length of 23 cm. What is the length of the other
base?
24 cm
26 cm
22 cm
28 cm
Answer:
24 cm
Step-by-step explanation:
Let the length of other base be x cm
Therefore, by mid segment formula of a trapezoid, we have:
[tex]23 = \frac{1}{2} (x + 22) \\ \\ 23 \times 2 = x + 22 \\ 46 = x + 22 \\ 46 - 22 = x \\ x = 24 \: cm[/tex]
a:b=7.2 how many times larger is a than b?
Answer:
A = 3.5x larger
Step-by-step explanation:
7 ÷ 2 = 3.5
Hope this helped! :)
Answer:
a is 3.5 times larger than b
Step-by-step explanation:
If a:b is 7:2 and 7/2 = 3.5, then a is 3.5 times larger than b
There are only green pens and red pens in a box. there are 3 more red pens than green pens in the box. sheila is going to take at random two pens from the box the probability that sheila will take two pens of the same color is 17/35 work out two different numbers of green pens that could be in the box
Answer: 6 or 9
Step-by-step explanation:
Given the following :
Let the number of green pens = x
Number of red pens = x + 3
Probability of picking same color = 17/35
Taking two pens at random; probability of picking two pens of same color.
Probability of picking red on first pick then red on second pick ; or picking blue on first pick then blue on second pick
Probability = (Required outcome / Total possible outcomes)
Total number of pens = x + x + 3 = 2x + 3
Probability of picking red then red:
P(red first) = (x+3)/2x+3
P(red second) = x+3-1 / 2x+3-1 = (x+2)/2x+2)
Therefore, probability of red then red =
(x+3)/(2x+3) × (x+2)/2x+2)
= (x+3)(x+2) / (2x+3)(2x+2)
Probability of green then green:
P(first green) = x/(2x+3)
P(second green) = (x-1) / (2x+3-1) = (x-1) / (2x+2)
P(green then green) = x(x-1)/(2x+3)(2x+2)
Therefore,
[(x+3)(x+2) / (2x+3)(2x+2)] + [x(x-1)/(2x+3)(2x+2)] = 17/35
(x+3)(x+2)+x(x-1) / (2x+3)(2x+2) = 17/35
Cross multiply :
35(x+3)(x+2)+x(x-1) = 17(2x+3)(2x+2)
35(2x^2 + 4x + 6) = 17(4x^2 + 10x + 6)
70x^2 + 140x + 210 = 68x^2 + 170x + 102
70x^2 - 68x^2 + 140x - 170x + 210 - 102 = 0
2x^2 - 30x + 108 = 0
Now we have a quadratic equation which can be factoeized used using any known factorization method.
Factorizing this, we get
(x-6) = 0 or (x-9) = 0
x = 6 or x = 9
Find the length of the side labeled x. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth.
Answer:
42.1
Explanation step-by-step:
Working out the lenght of the blue-dashed line:
SOH
47 is the Hypotenuse.
the blue line is the adjacent.
adjacent= Cos(30) x47
adjacent= 40.7
Working out x :
40.7 is the opposite this time.
x is the adjacent.
x = 40.7/ Tan(44)
x = 42.1
If Manuel does a job in 150 hours and with the help of Shantel they can do it together in 50 hours, how long would it take Shantel to do it alone? _______ hours
What is the domain of this function?
{x|x >0}
{x|x <8)
{x|0
{xlx < 0x8}
Answer:
x≥0, or x=[0,∞)
Step-by-step explanation:
Domain is values of x.
x≥0, or x=[0,∞)
Find the length of side a
Answer:
a = 8.
Step-by-step explanation:
a^2 + b^2 = c^2
b = 6; c = 10
a^2 + 6^2 = 10^2
a^2 + 36 = 100
a^2 = 64
a = plus or minus 8
Since side lengths can't be negative, a = 8.
Hope this helps!
I need help fast please
Answer:
The answer is D
: An Australian man on holiday in Germany finds that his wallet
contains 700 AUD. If he changes the money at a bank how
many euros will he receive?
Answer:
700 AUD ⇒ 430.72 euros
Hope this helps.
Un ascensor sube desde el primer piso al quinto piso, baja al segundo, sube al octavo. Si cada piso tiene 3 metros de altura, ¿cuántos metros recorrió el ascensor?
Answer:
El ascensor recorrió unos 39 metros
Step-by-step explanation:
Segun la pregunta cada cada piso tiene 3 metros de altura, por lo tanto para calcular los metros que recorrió el ascensor tenemos que hacer el siguiente calculo:
metros desde el primer piso al quinto piso=3 metros*4=12 metros
metros desde el quinto piso al segundo piso=3 metros*3=9 metros
metros desde el segundo piso al octavo piso=3 metros*6=18 metros
Por lo tanto los metros que recorrió el ascensor=12 metros+9 metros+18 metros
metros que recorrió el ascensor=39 metros
El ascensor recorrió unos 39 metros
I need help on this problem plz
Answer:
needddd
Step-by-step explanation:
1 + 2a + 3 + 4a + 5 + 6a + ...... + 97 + 98a + 99 + 100a = 0 What does a equal?
Answer:
a = -50/51
Step-by-step explanation:
1 + 2a + 3 + 4a + 5 + 6a + ...... + 97 + 98a + 99 + 100a = 0
1 + 3 + 5 + ... + 99 + 2a + 4a + ... + 98a + 100a = 0 Eq. 1
99 + 97 + 95 + ... + 1 + 98a + 96a + ... + 4a + 2a = 0 Eq. 2
Add Eq. 1 and Eq. 2
100 + 100 + ... + 100 + 102a + 102a + ... 102a = 0
50(100)/2 + 50(102a)/2 = 0
2500 + 2550a = 0
2550a = -2500
a = -2500/2550
a = -250/255
a = -50/51
What two numbers multiply to 1/4 and add to -1?
Answer:Are there any options?
Step-by-step explanation:
Two or more expressions with an Equal sign is called as Equation. Two numbers are x =-1/2 and y=-1/2 whose product is 1/4 and which add to -1.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
We need to find two numbers whose product is 1/4 and add to -1.
Let the two numbers are x and y.
By given,
Two numbers multiply to 1/4
xy=1/4
Two numbers add to -1
x+y=-1
Let x=-y-1
Substitute in equation 1.
(-y-1)y=1/4
-y²-y-1/4=0
Multiply negative on both sides
y²+y+1/4=0
Use quadratic formula
b=1,c=1/4,a=1
y=-1±√1-1/2=-1/2
Now substitute y in x+y=-1
x-1/2=-1
x=-1+1/2
x=-1/2
Hence the two numbers are x =-1/2 and y=-1/2 whose product is 1/4 and which add to -1.
To learn more on Equation:
https://brainly.com/question/10413253
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1. The perimeter of the given triangle PQR is
cm
P
7cm
3cm
R
4cm
O 16
28
26
65
Answer:
No, it is not possible to construct a triangle with lengths of its sides as 4 cm, 3 cm and 7 cm because here we see that sum of the lengths of two sides is equal to third side i.e., 4+3 = 7. As we know that, the sum of any two sides of a triangle is greater than its third side, so given statement is not correct.
Step-by-step explanation:
HELP WITH MATH PLS!!!
Answer:
Option A, y=8
Step-by-step explanation:
If you graph each of the equations, you will find that y=8 is the only line that crosses through the point (-3,8)
Also,
If you notice the given point, the y-coordinate is 8 indicating that the point lies on the line that has y as 8
Hope that helps!!
based on the function h(t), what will be the account value five years after the account is opened?
Answer:
Option B
Step-by-step explanation:
f(t) = 5000
g(t) = 250t
h(t) = f(t) + g(t) = 5000 + 250t
After 5 years, the amount of money in the account is:
h(t = 5) = 5000 + 250(5) = 5000 + 1250 = 6250$
Which of the two functions below has the largest maximum y-value?
f(x) = -3x^4-14
g(x) = -x^3 + 2
Answer:
B. g(x)
Step-by-step explanation:
If you graph both equations in a graphing calc, you should see that the maximum y-value of f(x) is -14 (it's a parabola facing down) while the maximum y-value of g(x) is infinite.
PLZ HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
1²+3
Step-by-step explanation:
I'm not to sure I hope this helped.
What is the answer please help! make sure to explain. thanks!! Mrs. Anderton is giving a test in her third-period class. She has decided to record the amount of time that each student takes to finish the test (in minutes) and compare that to the grade each student receives on the test (out of 100). A plot of her results is below. Which of the following does this situation represent? A. both a relation and a function B. a function only C. neither a relation nor a function D. a relation only
Answer:
A
achievements
Step-by-step explanation:
What is the explicit formula for the sequence {3, 8, 13, 18, ...}?
an = 3 – 5(n − 1)
O an = 3 +5,-1
An = 3 + 5(n − 1)
an = 3 + an-1
Re-write the quadratic function below in Standard Form
y = 7(x - 1)(x – 6)
Answer:
7x^2-49x+42
Step-by-step explanation:
X*x=x^2 X*-6=-6x -1x*x=-1x -1*-6=6
7(x^2-6x-1x+6)
The answer
Twice the difference of a number and 5 is equal to three times the sum of the number and 2. Find the number.
Answer:
The number is - 16Step-by-step explanation:
Let the number be x
Twice the difference of a number and 5 is written as
2( x - 5)
three times the sum of the number and 2 is written as
3( x + 2)
Equate them
We have
2(x - 5) = 3(x + 2)
Expand
2x - 10 = 3x + 6
Group like terms
2x - 3x = 16 + 10
- x = 16
Multiply through by - 1
x = - 16
Hope this helps you
In a school auditorium, the number of chairs in a row is the same as the number of rows of chairs. There are 7033 students in the school. If we know that less than 31 chairs were empty, how many chairs were empty after all the students sat down?
Same number of rows to chairs in a row would form a square.
Use the total number of students as the area
Find the number or rows by taking the square root of student:
The square root of 7033 is 83.86
Round up to 84
Total seats would be rows x seats per row:
84 x 84 = 7,056 total seats
7056 seats - 7033 students = 23 empty seats
20 points help w part b
Answer:
8:07 am
Step-by-step explanation:
It takes 9 minutes to walk from his house to the bus station. It then takes 92 minutes for the bus to travel from Birmingham to Coventry. After arriving, he takes 12 minutes to reach his workplace. This takes a total of 113 minutes.
9 + 92 + 12 = 113
Convert 113 minutes to hours and minutes.
113 - 60 = 53
1 hr and 53 min
He has to be at work by 10. Subtract the time it takes to get to his work by the time he has to get there.
10 - 1 hr = 9
9 - 53 min = 8:07
The latest time he can leave is 8:07.
If the number of bacteria in a colony doubles every 10 hours and there is currently a population of 300 bacteria, what will the population be 20 hours from now?
Answer:
1200 bacteria
Step-by-step explanation:
20 hours divided by 10 hours = 2, so it will be doubled two times.
300 times 2 for the first doubling = 600
600 times 2 for the second doubling = 1200
Plz help fast Question 1(Multiple Choice Worth 5 points) (8.01 LC) Two lines, A and B, are represented by the equations given below: Line A: x + y = 6 Line B: x + y = 4 Which statement is true about the solution to the set of equations? There are infinitely many solutions. There is no solution. It is (6, 4). It is (4, 6).
Answer:
(B) There is no solution.
Step-by-step explanation:
Given the two lines A and B where:
[tex]L$ine A: x + y = 6 \implies y=6-x\\$Line B: x + y = 4 \implies y=4-x\\$Therefore:$\\6-x=4-x\\-x+x=4-6\\0=-2\\$Since, $ 0\neq -2,$ there is no solution.[/tex]
The correct option is B.
Answer:
A
Step-by-step explanation:
Just took test, can I have Brainliest.
A top view of two walls of a room is represented by the x and y-axis, with units in meters. A ball is rolled from the point (0,15). It hits the adjacent wall at (20,0). Find the absolute value function that models the path of the ball. Determine when the ball passes within 3 meters of the wall represented by the x-axis.
Answer:
The absolute value function that models the path of the ball is
[tex]f(x) = \left | -\frac{3}{4}\cdot x + 15 \right |[/tex]
The coordinates when the ball passes within 3 meters of the wall is [tex]\left (3, 12\tfrac{3}{4} \right )[/tex]
Step-by-step explanation:
Given that the ball rolls without other external influences, we have;
(y - 0) = (x - 15)
The slope, m is give by the relation;
m = (y₂ - y₁)/(x₂ - x₁)
m = (15 - 0)/(0-20) = -3/4
The equation of the path of the ball in slope and intercept form is presented as follows;
y = m·x + c
15 = -3/4 ×0 + c = 15
c = 15
The absolute value function that models the path of the ball is then;
[tex]f(x) = \left | -\frac{3}{4}\cdot x + 15 \right |[/tex]
The vale of the function when x = 3 is given by the relation
[tex]f(x) = \left | -\dfrac{3}{4}\times 3 + 15 \right | = \dfrac{51}{4}[/tex]
Therefore, we have the coordinates as [tex]\left (3, 12\tfrac{3}{4} \right )[/tex].
A Rosa le gusta jugar con su primo Eduardo utilizando números. Rosa le planteó encontrar dos números que sumados den 15 y que el doble de uno de ellos sea igual al otro más 3 unidades, ¿De qué números se trata?
Answer:
Los números son 6 y 9
Step-by-step explanation:
Este problema se puede resolver por medio de un sistema de ecuaciones.
El primer número será x y el segundo número será y.
Sabemos que los dos números suman 15, por lo tanto esto se puede escribir como:
[tex]x+y=15[/tex]
Por otro lado sabemos que el doble de uno de ellos es igual al otro más 3 unidades, esto lo podemos escribir de la siguiente manera:
[tex]2x=y+3[/tex] (el doble del primero es igual al segundo más 3)
Reescribiendo esta segunda ecuación tenemos:
[tex]2x-y=3[/tex]
Por lo tanto, nuestras dos ecuaciones son:
[tex]x+y=15\\2x-y=3[/tex]
Resolviendo el sistema por el método de reducción observamos que, si sumamos ambas ecuaciones, las y se cancelan y quedamos con:
[tex]3x=18\\x=6[/tex]
Ahora, sustituimos este valor en la primera ecuación para obtener el valor de y:
[tex]x+y=15\\6+y=15\\y=15-6\\y=9[/tex]
Por lo tanto, los números son 6 y 9
Por medio de un sistema de ecuaciones, hay qué los números son 6 y 9.
Los números son desconocidos, por lo tanto, llaremos un de x, otro de y.Los números sumados den 15, o sea:
[tex]x + y = 15[/tex]
El doble de uno de ellos sea igual al otro más 3 unidades, o sea:
[tex]2x = y + 3[/tex]
[tex]y = 2x - 3[/tex]
Reemplazando en la primera ecuación:
[tex]x + y = 15[/tex]
[tex]x + 2x - 3 = 15[/tex]
[tex]3x = 18[/tex]
[tex]x = \frac{18}{3}[/tex]
[tex]x = 6[/tex]
[tex]y = 2x - 3 = 2(6) - 3 = 12 - 3 = 9[/tex]
Los números son 6 y 9.
Un problema similar es dado en https://brainly.com/question/24646137
Clinical literature reports that the duration of a typical cold is roughly 18 days. Researchers wanted to know if people tend to underestimate the duration of a typical cold, on average. They surveyed a random sample of 352 healthy adults in Georgia and asked them how long they think that a typical cold lasts. The researchers reported a 95% confidence interval of 6.9 to 8.2 days for the mean expected duration of typical cold. The researchers reported that the answers to this question were strongly right-skewed. The 95% confidence interval (6.9, 8.2) they obtained is
Answer:
The 95% confidence interval (6.9, 8.2) they obtained means that "We are 95% confident that the population mean duration is between 6.9 and 8.2 days".
Option B from the complete Question.
Step-by-step explanation:
Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Critical value will be obtained using the t-distribution if there is no information provided for the population standard deviation and it is obtained from the z-tables if the population standard deviation is known or the sample size is large enough that the sample properties can be approximated to be the same as the population properties.
Standard error of the mean = σₓ = (σ/√n)
σ = standard deviation of the sample
n = sample size
Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
So, the confidence interval (6.9, 8.2) obtained in the question means that "We are 95% confident that the population mean duration is between 6.9 and 8.2 days".
Hope this Helps!!!
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 2−x and y = 4x + 3 intersect are the solutions of the equation 2−x = 4x + 3. (4 points) Part B: Make tables to find the solution to 2−x = 4x + 3. Take the integer values of x only between −3 and 3. (4 points) Part C: How can you solve the equation 2−x = 4x + 3 graphically? (2 points) PLez Answer 50 points
Answer:
Step-by-step explanation:
Part A:
We have two lines: y = 2 - x and y = 4x + 3 . Given two equations that are both required to be true. The answer is the points where the lines cross, this means we have to make the equations equal to each other. It will look like this:
2 - x = 4x + 3
Part B:
In order to solve the equation we need to put the like terms together. So we will add x on each side.
2 - x = 4x + 3
+x +x
So now we get:
2 = 5x + 3
Now that x is on one side and is positive we will move 3 on the left side by subtracting it from each side.
2 = 5x + 3
-3 -3
So now we get:
-1 = 5x
Now that the like terms have been combined we need to find out what x alone is so we divide 5 on each side:
[tex]\frac{-1}{5}[/tex] = [tex]\frac{5x}{5}[/tex]
No we see that:
x = [tex]-\frac{1}{5}[/tex]