Answer:
42 + 2/3
Step-by-step explanation:
First, to calculate the sum of an infinite geometric series, our formula is
a₁/(1-r), with a₁ being the first term of the series and r being the common ratio. Therefore, we want to find both a₁ and r.
To find r, we can first determine that 2 * r = a₄ and a₄ * r = a₅, as the ratio separates one number from the next in a geometric series. Therefore, we have
2 * r * r = a₅
2 * r² = 1/8
divide both sides by 2 to isolate the r²
r² = 1/16
square root both sides to isolate r
r =± 1/4. Note the ± because r²=1/16 regardless of whether r = 1/4 or -1/4. However, because all terms are positive, r must be positive as well, or a₄, for example, would be 2 * (-1/4) = -0.5
Therefore, r = 1/4 .
To find the first term, we know that a₁ * r = a₂, and a₂ * r = a₃. Therefore, a₁ * r² = a₃ = 2
a₁ * 1/16 = 2
divide both sides by 1/16 to isolate a₁
a₁ = 2 * 1/ (1/16)
= 2 * 16
= 32
Plugging a₁ and r into our infinite geometric series formula, we have
a₁/(1-r)
= 32 / (1-1/4)
= 32/ (3/4)
= 32/ 0.75
= 42 + 2/3
-3 , 1 , 5 , 9 , 13
find the 11th term of this sequence
show your working
Answer:
a₁₁ = 37
Step-by-step explanation:
There is a common difference between consecutive terms, that is
1 - (- 3) = 5 - 1 = 9 - 5 = 13 - 9 = 4
This indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 3 and d = 4 , then
a₁₁ = - 3 + (10 × 4) = - 3 + 40 = 37
What is the value of X?
Answer:
x=2
Step-by-step explanation:
A line that intersects a circle in two points is called a secant line, and this is the case for both line DE and AE.
For two secant lines that intersect outside of the circle, such as the ones here, we can say that
CE * DE = BE * AE
Therefore, we need to then define these lines.
CE is x+4, BE is x+1, AE = (BE + AB) = 11+x+1 = 12+x, and DE = (CE + DC) = 1+x+4 = 5+x
We then have
(x+4) * (5+x) = (x+1) * (12+x)
expand
5x + x² + 20 + 4x = 12x+x²+12+x
x²+9x + 20 = x²+13x+12
Next, we want to congregate all values to one side so we can solve for x. This can be done by subtracting both sides by (x²+13x+12) to get
-4x + 8 = 0
subtract 8 from both sides to isolate the x and its coefficient
-4x = -8
divide both sides by -4 to isolate the x
x = 2
Suppose the line y = 2.8333x - 22.4967 describes the relation between the club-head speed (in miles per hour), x and the distance a golf ball travels (in yards), y.
(a) Predict the distance a golf ball will travel if the club-head speed is 100 mph.
(b) Suppose the observed distance a golf ball traveled when the club-head speed was 100 mph was 265 yards. What is the residual?
(c) The golf ball will travel 260.8 yards. (Round to the nearest tenth as needed.)
(d) The residual is:_________ (Round to the nearest tenth as needed.)
Answer:
c) The golf ball will travel 260.8 yards.
d) Hence the residual is 4.2 yards.
Step-by-step explanation:
c) y' = 2.8333x - 22.4967
Now the golf ball will travel [tex]= 2.8333\times100 - 22.4967[/tex]= 260.8 yards
here y'= 260.8 yards.
d) The residual is : y - y' = 265 - 260.8 = 4.2 yards.
Answer:
a) [tex]y=260.8333~yd[/tex]
b) [tex]\Delta d=4.1667~yd[/tex]
c) [tex]y=260~yd[/tex]
d) [tex]\Delta y'=0.8333~yd[/tex]
Step-by-step explanation:
Given:
equation of line, [tex]y=2.8333x-22.4967[/tex]
x = club-head speed (in miles per hour)
y = the distance a golf ball travels (in yards)
a)
x = 100 mph
Then the distance travelled by the ball:
(put the given value of x in the above eq.)
[tex]y=2.8333\times 100-22.4967[/tex]
[tex]y=260.8333~yd[/tex]
b)
If the observed distance in the above case comes out to be 265 yards then the residual value will be:
[tex]\Delta d=265-260.8333[/tex]
[tex]\Delta d=4.1667~yd[/tex]
c)
From the calculated value when rounding it to the nearest tenth:
[tex]y=260~yd[/tex]
d)
The residual on rounding the calculated value to the nearest tenth:
[tex]\Delta y'=260.8333-260[/tex]
[tex]\Delta y'=0.8333~yd[/tex]
The range of cells in column D and rows 1 to 10 is represented as:
1:10 D1:D10 D:D
Answer:
how?
Step-by-step explanation:
I didnt get question
A number cube is rolled 14 times and the results are recorded in the table.
What, in simplest form, is the experimental probability that the number cube shows 4?
A. 0
B. 1/6
C. 2/7
D. 5/14
Answer:
b
Step-by-step explanation:
The experimental probability that the number cube shows 4 is 2/7.
What is an experimental probability?Experimental probability is a probability that is determined on the basis of a series of experiments.
Given that, a number cube is rolled 14 times, we need to determine the experimental probability that the number cube shows 4,
The formula to calculate the experimental probability is:
P(E) = Number of times an event occurs/Total number of times the experiment is conducted
P(E) = 4/14 = 2/7
Hence, the experimental probability that the number cube shows 4 is 2/7.
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Brooke and Lamont ran a half marathon Brooke finished in 1 hour 50 minutes Lamont finished in 100 minutes who had the faster time
Answer:
Brooke = 1 hr 50 min
Lamont = 100 min = 1 hr 40 min
Because 60 min = 1 hr
Lamont was faster
Hope this helped
i know it’s kinda all hard to see. i have many more questions like this and i can’t do graphs to save my life.. pls help !!
Answer: D
Step-by-step explanation:
Find the value of x rounded to the nearest tenth.
Answer:
The answer to the equation is C
ASAP PLEASE HELPPPPPPPPPPPPPPPPPP MEEEEEEEEEEEEEEE
Answer:
-2/5 is the answer
I hope this will help you
Answer:
-2/5
Step-by-step explanation:
Just add the top numerator together -4 + 2 = -2
please help me out (geometry)
Answer:
x = 15
Step-by-step explanation:
2x+10+4x+80=180
or, 2x+4x=180-80-10
or, 6x=90
or, x=15
Answered by GAUTHMATH
An animal shelter takes in an average of 5 animals per day. The shelter must keep its total occupancy below 300. Currently, the shelter has 165 animals. If none of the animals get adopted, which inequality represents how many more days, x, the shelter can continue to take in animals without exceeding its occupancy limit?
Answer:
5x less than 300 - 165
Step-by-step explanation:
It will take 27 days to take in animals without exceeding its occupy limit.
What is algebraic expression ?An expression which is made up of variables and constants , along with algebraic operation (addition , subtraction etc ) is called Algebraic expression.
According to the question :
165 + (x) 5 = 300
5x = 135
x = 27
Hence , it will take 27 days to occupy the limit
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Madam Chong's mass is 72 kg. After participating in a fitness programme, her mass decreases at a rate of 3 kg per month. Find the minimum number of months that Madam Chong has to participate in the programme so that her mass becomes less than 52 kg. (Give your answer to the nearest whole number.)
Solve the equation 2sin x cos x = cos x, for 0° < x≤ 90°
Answer:
2sinx.Cosx=cosx
2sin90°.cos90°=cos90°
2×1.0=0
0=0
One of the legs of a right triangle measures 9 cm and its hypotenuse measures 16 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
13.2 cm
Step-by-step explanation:
using the Pythagorean theorem, we can find the length of the other leg, since this is a right triangle. The equation is a^2 + b^2 = c^2, A and B being the legs and C being the hypotenuse. Since we are finding the other leg, we can switch the equation around to find A/B instead. (A/B being the legs). so we get: B^2 = C^2 - A^2 ; then we simplify [tex]b=\sqrt{c^2-a^2}[/tex]
We plug in the numbers given:
[tex]b = \sqrt{16^2-9^2}\\b=\sqrt{256-81}\\b=\sqrt{175} \\b= 13.229[/tex]
rounded to nearest tenth: 13.2
The measure of the other leg in the right triangle is 13.22 cm.
What is a right triangle?A triangle with one angle measuring 90° is called a right triangle.
Given that, a right triangle has a leg measuring 9 cm and its hypotenuse is 16 cm longs, we need to find the other side,
So, using the Pythagoras theorem,
16² = 9² + x²
x = √256-81
x = √175
x = 13.22
Hence, the measure of the other leg in the right triangle is 13.22 cm.
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Ecuación de la hipérbola con centro en (0;0), focos en abrir paréntesis 0 coma espacio menos raíz cuadrada de 28 cerrar paréntesis espacio y espacio abrir paréntesis 0 coma espacio raíz cuadrada de 28 cerrar paréntesis espacio ,eje conjugado = 2 raíz cuadrada de 3
Answer:
[tex]\frac{y^{2}}{25}-\frac{x^{2}}{3}=1[/tex]
Step-by-step explanation:
Para resolver este problema debemos tomar en cuenta los datos que nos dan y la ecuación de una hipérbola. Comencemos con los datos:
centro: (0,0)
focos: [tex](0,-\sqrt{28}),(0,\sqrt{28})[/tex]
eje conjugado = [tex]2\sqrt{3}[/tex]
por los focos podemos ver que la hipérbola se dirige hacia el eje y, por lo que debemos tomar la siguiente forma de la ecuación de la parábola:
[tex]\frac{y^{2}}{a^{2}}+\frac{x^{2}}{b^{2}}=1[/tex]
de los focos podemos obtener que:
[tex]c=\sqrt{28}[/tex]
y del eje conjugado podemos saber que al dividir la longitud del eje conjugado dentro de 2 obtenemos b, así que:
[tex]b=\sqrt{3}[/tex]
podemos utilizar la siguiente fórmula para obtener a:
[tex]c^{2}-a^{2}=b^{2}[/tex]
si despejamos a en la ecuación obtenemos lo siguiente:
[tex]a=\sqrt{c^{2}-b^{2}}[/tex]
ahora podemos sustituir los valores:
[tex]a=\sqrt{(\sqrt{28})^{2}-(\sqrt{3})^{2}}[/tex]
[tex]a=\sqrt{28-3}[/tex]
[tex]a=\sqrt{25}[/tex]
a=5
así que media vez conozcamos a, podemos sustituir los datos en la ecuación de la hipérbola así que obtenemos lo siguiente:
[tex]\frac{y^{2}}{a^{2}}+\frac{x^{2}}{b^{2}}=1[/tex]
[tex]\frac{y^{2}}{(5)^{2}}+\frac{x^{2}}{(\sqrt{3})^{2}}=1[/tex]
[tex]\frac{y^{2}}{25}+\frac{x^{2}}{3}=1[/tex]
si graficamos la hipérbola, queda como en el documento adjunto.
Which situation does the graph illustrate?
Answer:
eju 48, 23w6yuw43wdgn
Step-by-step explanation:
As displayed on a production possibilities curve, what will an increase in technology allow a society to do? a. Produce more, as long as the resources are also available. c. It will not affect society’s production. b. Produce less, because more resources are spent on developing technology. d. The society will spend more on the same level of production. Please select the best answer from the choices provided A
Answer:
a. Produce more, as long as the resources are also available
Step-by-step explanation:
from brainly itself
scouteo
Ace
The correct answer is A) produce more, as long as the resources are also available.
As displayed on a production possibilities curve, an increase in technology will allow a society to produce more, as long as the resources are also available.
A production possibilities graph is a valid representation of the available ways an economy is able to use the resources. In this case, an increase in technology will allow a society to produce more, as long as the resources are also available means that as long there are enough resources in the market, technology in a country helps with the production of more things to be consumed or traded.
how to find range from a distribution table.
Answer:
Range = highest value - lowest value
Explanation:
This is the required formula to find range from a distribution table.
Help pleas like please ASAP
Answer:
(x+9)(x+5)
Step-by-step explanation:
find 2 numbers that add to 14 and multiply to 45
Help Please!!!
Find the volume of the sphere
Answer:
523.6
Step-by-step explanation:
Not sure how to explain •-•
Hope it helps c:
Answer: use formula pi r^3
3.14 × 5 x 5 x 5 x 4 ÷ 3
Step-by-step explanation:
xét tính chẵn lẻ của hàm số : y = tanx + cotx
Answer:
Step-by-step explanation:
the longest side of a triangle is 80cm more than the second and 130cm more than the shortest side and its perimeter is 540cm. find its area
help help
Answer:
Area of triangle1/2b*h Now you can do
The area of the triangle is 9000 square centimeters
How to determine the area?Let the sides in order of length be represented as:
x, y and z.
So, we have:
z = 80 + y
z = 130 + x
P = 540
The perimeter is calculated as:
P = x + y + z
So, we have:
x + y + z =540
Substitute z = 130 + x
x + y + 130 + x =540
Evaluate the like terms
2x + y = 410
Substitute z = 130 + x in z = 80 + y
130 + x = 80 + y
Evaluate the like terms
x - y = -50
So, we have:
2x + y = 410
x - y = -50
Add both equations
3x = 360
Divide by 3
x = 120
Substitute x = 120 in z = 130 + x
z = 130 + 120
z = 250
Substitute z = 250 in z = 80 + y
250 = 80 + y
y = 170
So, we have:
x = 120
y = 170
z = 250
The area is then calculated as:
[tex]Area = \sqrt{s * (s -x) *(s - y) * (s -z)[/tex]
Where
s = P/2 = 540/2
s = 270
So, we have:
[tex]Area = \sqrt{270 * (270 -120) *(270 - 170) * (270 -250)[/tex]
Evaluate
Area = 9000
Hence, the area of the triangle is 9000 square centimeters
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Which statement is not correct?
options b is not correct
Answer:
B is right option
Step-by-step explanation
A reflex angle is an angle that measures greater than 180 degrees and less than 360 degrees.
If m angle ABF = (6x + 26)°, m angle EBF = (2x - 9)° , and m angle ABE = (11x - 31)° , find M angle ABF.
Answer:
122
Step-by-step explanation:
Angle ABE = angle ABF + EBF
11x - 31 = 6x + 26 + 2x - 9 add like terms
11x - 31 = 8x + 17 transfer like terms to the same side of the equation
11x - 8x = 17 + 31 add/subtract like terms
3x = 48 divide both sides by 3
x = 16 now replace x with 16 in the equation
16*6+26 = 122
Help me pleasee anyone
If 81y^2-k=9y^2-(1/2)^2 what is the value of k
Answer:
k = 1/4
Step-by-step explanation:
81y² - k = (9y)² - (1/2)²
(9y)² - k = (9y)² - (1/2)²
k = (1/2)² = 1/4
With the steps pls ……………………..
Answer: $21, 600
Step-by-step explanation:
Given:
Original cost (when the shop owner brought it) = $20,000
Profit amount = 20% of original cost
Discount rate = 10%
Solve:
First Step: Find the market price (before discount)
$20, 000 × (1 + 20%) = $24, 000Second Step: Find the discount price
$24, 000 × (1 - 10%) = $21, 600Hope this helps!! :)
Please let me know if you have any questions
What is the slope of a segment whose endpoints are labeled (-2a, 0) and (0, -2b)?
Answer:
Step-by-step explanation:
use the slope formula Faith,
point P1 (-2a,0) in the form (x1,y1)
point P2(0,-2b) in the form (x2,y2)
slope = m
m = (y2-y1) / (x2-x1)
m = (-2b - 0 ) / (0-(-2a))
m = -2b / 2a
m = - b/a
they are trying to confuse you with the "a" and "b" variables in the problem, but just use the rules you know to solve what you can :)
What is the area of the parallelogram represented by the vertices A(-6, -1), B(-2, -1), C(-1, -4) and D(-5, -4)?
Answer: 12 units²
Step-by-step explanation:
To find the area of a parallelogram, we use the formula A=l×w. To find the length and width, let's graph out the parallelogram to get a better view. Let's refer to the picture attached to see what the graph looks like. The length is 4 units while the width is 3 units. Therefore we multiply.
A=4×3=12 units²
Now, we know the area is 12 units².
Sonia received a statement on her Certificate of Deposit showing that her investment had returned $4,320 over its life. If the Certificate of Deposit pays a simple interest rate of 4.8% and her initial investment was $12,000, how long had the money been invested?
Answer:
The correct answer is -7.5 years.
Step-by-step explanation:
Given:
Principle amount = 12000
Interest = 4320
time = ?
rate = 4.8 simple interest
Solution:
We know that simple Interest I = (P*t*r)/100
then t = I*100/p*r
putting values in formula:
t = 4320*100/4.8*12000
= 432000/57,600
= 7.5 years
