Final answer:
The explicit formula for the geometric sequence 120, 60, 30, 15, ... is an n = 120 times [tex](0.5)^{n-1}[/tex], where an is the nth term of the sequence.
Explanation:
The sequence given, 120, 60, 30, 15,..., is an example of a geometric sequence where each term is obtained by multiplying the previous one by a constant called the common ratio. For this sequence, the first term a is 120, and the common ratio r is 0.5 since each term is half the preceding one.
An explicit formula for a geometric sequence can be expressed as:
an = a times [tex]r^{n-1}[/tex]
Where a is the first term, r is the common ratio, and n is the term number. Applying this to the given sequence, the explicit formula is:
an = 120 times [tex](0.5)^{n-1}[/tex]
This formula represents the nth term of the sequence, showing how each term can be calculated directly from its position in the sequence.
The names of nine boys and six girls from your class are put into a hat. What is the probability that the first two names chosen will both be girls?
Final answer:
The probability that the first two names chosen will both be girls from a hat that contains the names of nine boys and six girls is 1/7.
Explanation:
The question involves determining the probability of selecting two girls' names from a hat that contains the names of nine boys and six girls. We are dealing with a situation of probability without replacement, which means that once a name is drawn, it is not put back into the hat.
To calculate the probability of the first name drawn being a girl, we have 6 girls out of the total 15 students, which gives us a probability of 6/15. If a girl's name is drawn first, there will then be 5 girls' names left and 14 names total. So, the probability of the second name drawn being a girl as well is then 5/14.
To find the overall probability of both events happening, we multiply the two probabilities together: (6/15)
x (5/14) = 30/210 = 1/7. Therefore, the probability that the first two names chosen will both be girls is 1/7.
Jana predicts that the population, y, will grow according to y = 12 log(x + 1) + 10, where x is the time in minutes. How much greater does Kirk’s model predict the population will be after 60 minutes than Jana’s model?
Answer:
Greater by about 50 bacteria
Step-by-step explanation:
Greater by about 50 bacteria
Answer:
Greater by about 50 bacteria
Step-by-step explanation:
Jorge is comparing two data sets. He uses the mean and mean absolute deviation to compare the center and variability of the data sets. If the measures of center and variability accurately describe the sets, which best describes both data sets?
a. not symmetrical without outliers
b. not symmetrical or containing outliers
c. symmetrical and containing outliers
d. symmetrical without outliers
Answer:
C. Symmetrical without outliers
Step-by-step explanation:
It's talking about BOTH and how they compare. :)
Answer:
C
Step-by-step explanation:
Sorry i'm late
Anyway i wish you have a good day!
:)
Which equation shows the correct use of the Distributive Property? −4(3/2x−1/2)=−15
A. 6x + 4 = –15
B. 2x – 12 = –15
C. –6x – 2 = –15
D. –6x + 2 = –15
Answer:
D
Step-by-step explanation:
Based on the side lengths alone, could the triangles be similar? Triangle R S T. Side R S is 3 centimeters, side S T is 6 centimeters, and side R T is 6.4 centimeters. Triangle W X U. Side W X is 16 centimeters, side X U is 7.5 centimeters, and side W U is 15 centimeters. No, the sides are not proportional. Yes, the sides are in the ratio 2:5. Yes, the sides are in the ratio 4:5. Yes, the sides are in the ratio 1:5.
Answer:
Yes, the sides are in the ratio 2:5.
Step-by-step explanation:
All sides divided by each congruent side are = to .4 and 2/5 is = to 4/10
The sides of triangles are not proportional, thus the triangle is not similar triangle.
What is triangle?Triangle is "a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees".
What is similar triangles?
If the ratio of the "sides of the triangles ΔABC and ΔDEF are equal then the triangles are similar triangles".
According to the question,
In ΔRST and ΔWXU are similar triangle if ∠R = ∠W; ∠S = ∠W; ∠T=∠U
then [tex]\frac{RS}{WX} = \frac{ST}{XU}[/tex] .
In ΔRST, side RS is 3 centimeters, side ST is 6 centimeters, and side RT is 6.4 centimeters. In ΔWXU, Side WX is 16 centimeters, side XU is 7.5 centimeters, and side WU is 15 centimeters.
[tex]\frac{3}{16} = \frac{6}{7.5} = \frac{6.4}{15}[/tex]
Hence, the sides are not proportional then the triangle is not similar triangle.
Learn more about similar triangles here
https://brainly.com/question/27609371
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Imani’s rent increased from $560 per month to $600 per month. Her friend, Ariana, had her rent increase from $825 to 875. Who had the larger percent increase in their rent
And explain why
Answer:
Ariana
Step-by-step explanation:
560 is 93.33 percent of 600 and 825 is 94.29 percent of 875.
The required, Imani has a larger percent increase in their rent.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
here,
Imani’s rent increased from $560 per month to $600 per month.
percentage increase in Imani’s rent = 600 - 560 / 560 × 100%
= 7.14%
Ariana's rent increased from $825 per month to $875 per month.
percentage increase in Ariana's rent = 875 - 825 / 875 × 100%
= 5.71%
Thus, the required, Imani has a larger percent increase in their rent.
Learn more about percentages here:
brainly.com/question/13450942
#SPJ5
Mr. Goodwin received a paycheck for $1200. He deposited the money into a
bank account. The account has an interest rate of 6% compounded
continuously. This is the first and last deposit Mr. Goodwin makes into this
account. How much money will be in the account in 15 years?
Answer: There will be $2951.52 money in the account in 15 years
Step-by-step explanation:
Given: Principal ; P = $1200
Interest rate;r = 6% compounded continuously
Time; t = 15 years
As we know the compounded continuously formula is given by
[tex]A= Pe^{rt}[/tex] where A is amount , P is principal , r is rate, t is time and e be the mathematical constant.
So according to question we have
[tex]A= 1200 e^{0.06 \times 15} = 1200 e^{0.9} \approx 2951.52[/tex]
Hence, there will be $2951.52 money in the account in 15 years
find the exact length of the third side
Answer:
≈7.48, exact would be 7.48331477355
Step-by-step explanation:
Pythagorean Theorem
c is the hypotenuse (longest side)
a and b are interchangeable
a^2 + b^2 = c^2
3^2 + 7^2 = c^2
(9 + 47 = 56)
56= c^2
[tex]\sqrt{56}[/tex] = c
7.48 ≈ c
hope this helps :)
1 1/3 x 6/7 (the 1 in the front is a whole)
Look at the attached picture
Hope it will be helpful to you
Answer:
well it would be 9 over 14 hope this helps
Step-by-step explanation:
solve for a 7a - 2b =5a + b
Answer:
a = 3/2 b
Step-by-step explanation:
7a - 2b =5a + b
Subtract 5a from each side
7a-5a - 2b =5a-5a + b
2a -2b = b
Add 2b to each side
2a-2b+2b = b+2b
2a = 3b
Divide each side by 2
2a/2 = 3b/2
a = 3/2 b
can someone help me out plz?
2. There are 14 rollercoasters at the amusement park. There are 2 rollercoasters made of steel, 6 of them are made of steel and have loops, 4 of them have loops but aren't made of steel and there are 2 rollercoasters with no loops and aren't made of steel.
4. 60% of rollercoasters with loops are made of steel. 40% of rollercoaster with loops are not made of steel. 50% of rollercoasters made of steel have no loops and 50% of rollercoasters not made of steel don't have loops.
6. 75% of rollercoasters are made of steel either have loops or no loops.
25% of rollercoasters not made of steel either have loops or no loops.
This was quite a lot to do, I'm pretty sure the relative frequency graph number 3 had me a bit confused.
Which ratio is equivalent to the ratio 30:48?
Answer: 5:8
Step-by-step explanation:
By reducing both sides equally, the ending answer is 5:8
(There can be many answers to your question but the one i told you is the most reduced one)
Answer:
10 : 13
Step-by-step explanation:you can find equivalent ratios by dividing or multiplying both the ratios by the same number.
eg 30 : 48 can be divided by 3 which gives 10:16
Hope it is clear,Thank you
8x-72=2x-36
I need the answer
Answer: [tex]x=6[/tex]
Subtract 2x from both sides
[tex]8x-72-2x=2x-36-2x\\6x-72=-36[/tex]
Add 72 to both sides
[tex]6x-72+72=-36+72\\6x=36[/tex]
Divide both sides by 6
[tex]6x/6=36/6\\x=6[/tex]
Answer:
x=6
Step-by-step explanation:
first thing first you always need to get x alone and since you have an X on both side we need to move one of them to the same side as the other one.
8x-72=2x-36
add 72 on both sides ( the opposite of subtracting is adding)
8x=2x-36+72
8x=2x+36
then we subtract 2x on both sides to get X alone
8x-2x=36
6x=36
then we divide 36 by 6 to get our answer for x
X= 6
and that's your answer, hope this helped
Estimate how many minutes Jessica must practice basketball free throws if she has to shoot a total of 50 successful free throws, and he
average is 3 successful free throws a minute.
A.3
B.17
C.47
D.53
E.150
Answer:
17
Step-by-step explanation:
average per minute is 3, and you need 50, so 3x?=50
to know "?" we change how the question is, so it ends 50/3=?
50/3= 16.6666666667 and the closest is 17
Directions: Simplify each expression by combining like terms
1.) -y+9z-16y-25z
2.) 6x +3y-y+2+2
3.) 9b + 5(b - 4) + 15
4.) -4(3x + 5) + 10x + 1
5.) 0.5(y + 4) + 18y - 9
6.) -0.7r+9(-r-15)
Answers:
1.) -y+9z-16y-25z = -17y-16z
2.) 6x +3y-y+2+2 = 6x+2y+4
3.) 9b + 5(b - 4) + 15 = 14b-5
4.) -4(3x + 5) + 10x + 1 = -2x-19
5.) 0.5(y + 4) + 18y - 9 = 18.5y-7
6.) -0.7r+9(-r-15) = -9.7r-135
PLEASE ANSWER MY QUESTION IT IS URGENT I AM BEING TIMED
Write each fraction as a percentage. Include a fraction in the hundredths place if needed.
Example: 12 3/4%
First question: 1/2
second question: 1/4
Answer: The 1st one is 0.5%
The 2nd one is 0.25%
Step-by-step explanation:
Christine purchased a prepaid phone card for $30. Long distance calls cost 18 cents a minute using this card. Christine used her card only once to make a long distance call. If the remaining credit on her card is $27.84, how many minutes did her call last?
Answer:
The answer is 12 minutes.
Step-by-step explanation:
It is given that the cost of one minute is $0.18. Firstly, you have to substract the remaing credits from her original credits :
$30 - $27.84 = $2.16
We have found out that she uses $2.16 for her long distance call. Next, you have to divide 18 cents from the uses in order to find out how many minutes she use :
[tex]1 \: min = 0.18dollar[/tex]
[tex]x \: mins = 2.16dollars[/tex]
[tex]x = 2.16 \div 0.18[/tex]
[tex]x = 12 \: mins[/tex]
An ice cream cone has a diameter of 6 inches and a height of 7 inches. What number can be used to complete the volume
statement for the ice cream cone?
Volume
Answer:
The volume of ice cream cone is 66 cubic inch.
Step-by-step explanation:
Diameter of ice cream cone is 6 inches
Height of the cone is 7 inches
The volume of a cone shaped object is given by :
[tex]V=\dfrac{1}{3}\pi r^2h[/tex]
Substituting all the values in above formula as:
[tex]V=\dfrac{1}{3}\times \dfrac{22}{7}\times 3^2\times 7\\\\V=66\ \text{inches}^3[/tex]
So, the volume of ice cream cone is 66 cubic inch.
Answer:
66
Step-by-step explanation:
Solve for the volume of the cylinder.
(Use picture below)
The set of points in a plane that are equidistant from a given point from a ————
Answer:
The set of points in a plane that are equidistant from a given point create a circle.
Hope this helps!
:)
Pip and Sara win some money and share it in the ratio 7:3. Pip gets £36 more than Sara. How much did they get altogether?
Answer:
I think its 90 but im not sure.
Step-by-step explanation:
Final answer:
To find the total amount won by Pip and Sara, a ratio problem was solved by establishing an equation from the given ratio 7:3 and the fact that Pip gets £36 more than Sara, resulting in a total amount of £90.
Explanation:
The question involves solving a problem based on a ratio and determining the total amount of money shared by Pip and Sara. The ratio in which Pip and Sara share the money is 7:3, and since Pip gets £36 more than Sara, we can set up equations to find the individual and total amounts.
Let's denote Sara's share as S, hence Pip's share will be S + £36.
According to the ratio given, Pip's share to Sara's share is 7 to 3, so we can write the equation:
7S = 3(S + 36)
7S = 3S + 108
4S = 108
S = 27
So Pip's share is £27 + £36 = £63.
Adding both shares, the total amount is £63 + £27 = £90.
Therefore, Pip and Sara got £90 altogether.
1) During skating practice, Sasha landed 7 out of 12 jumps. What is the experimental
probability that she will land her next jump?
Answer:
14 maybe
Step-by-step explanation:
B. Mercury, Venus, and Earth are the three planets closest to the sun. Would their combined distance from
the sun be greater or less than the distance from the sun to Neptune? Show your work and justify your
answer.
Answer:
Mercury Venus and earth together would be greater than the distance from Neptune to the sun neptune is 2.759 billion miles away from the sun and the three others combined are 196.18 million miles away from the sun.
PLEASE HELP!!!!!!! PLEASE!!
Find the indicated limit, if it exists. (2 points)
limit of f of x as x approaches negative 10 where f of x equals negative 4 minus x when x is less than negative 10, 6 when x equals negative 10, and x plus 16 when x is greater than negative 10
6
0
16
The limit does not exist.
Answer:
limit does not exist
Step-by-step explanation:
From the left: f(x) = x + 10 (for x < 8), as x --> 8, f(x) --> 18
From the right: f(x) = 10 - x (for x >= 8), as x --> 8, f(x) --> 2
Since the limits on either side do not converge to the same point, the limit does not exist
whats the radius of a sphere if its volume is 1928pi
Answer:
Cube root of 1446
Step-by-step explanation:
The formula for the volume of a sphere is [tex]\frac{4}{3} \pi r^3[/tex]. Therefore, if we divide 1928pi by 4/3pi and then take the cube root, you will find the radius. In this case, 1928pi/(4pi/3)=1446, meaning that the radius is the cube root of 1446. Hope this helps!
The formula for the volume of a sphere is 4/3 the product of π and the cube of the radius of the sphere.
Therefore, if we're working backwards, we can start by multiplying 1928 by 4/3.
1928 x (4/3) = 2570.66666667
From there, we can find the cube root to find our radius.
(cube root) of 2570.6666667 = 13.698781
Therefore, the radius of the circle is 13.698781, or about 13.7.
Hope this helps! :)
What is the value of x
Answer:
x= ?
Step-by-step explanation:
Answer:
depends on the equation u didnt give us
Step-by-step explanation:
After decoding the clues on the map, they found out that they needed to go to the
Island of Mysteries which was 120 miles away. To get there, they could either
take a plane for $600 or a boat for $254. How much money can they save if they
took a boat to the island?
Answer:
$346.00
Step-by-step explanation:
We know that the price to take a plane to the Island of Mysteries is $600 and the price to take a boat is $254.
To find how much money they will save if they were to take a boat, you would subtract the cost of the boat ride from the plane ride to find the difference.
$600 - $254 = $346.00
HELP HELP. Look at the factors of 50 and 75.
Factors of 50: 1, 2, 5, 10, 25, 50
Factors of 75: 1, 3, 5, 15, 25, 75
The GCF of 50 and 75 is ______
Answer:
25
Step-by-step explanation:
25 bc it is the largest number than can go both into 50 and 75
Answer:
GCF =25
Step-by-step explanation:
The prime factorization of 50 is: 2 x 5 x 5.
The prime factorization of 75 is: 3 x 5 x 5.
The prime factors in multiplicities 50 and 75 have in common are 5 x 5.
5 x 5 is the GCF of 50 and 75.
I hope this helps!! :]
A ramp with a one-meter distance from edge to edge reaches a height of 0.643 meters. What is the value of the acute angle?
a. 300
C. 600
b. 400
d. none of the above
Answer:
The value of the acute angle is 40°Step-by-step explanation:
Given a ramp with a one-meter distance from edge to edge and reaches a height of 0.643 meters, the equivalent set up will form a right angled triangle where the length of the ramp will be the hypotenuse of the triangle and its height will be the opposite side of the triangle facing the acute angle directly.
To get the value of the acute angle, we will use the trigonometry ratio known as SOH, CAH, TOA.
Given length of ramp = hypotenuse = 1m
Height =Opposite side = 0.643m
Using SOH;
sin[tex]\theta\\[/tex] = [tex]\frac{opp}{hyp}[/tex]
sin[tex]\theta[/tex] = 0.643/1
sin[tex]\theta[/tex] = 0.643
[tex]\theta[/tex] =sin⁻¹0.643
[tex]\theta[/tex] = 40°
The value of the acute angle is 40°
plz help!!!!!!!! It’s timed
Answer:
first option is the answer
hope it helps.you
sorry for giving wrong answer last time
Answer:
y^3
Step-by-step explanation:
sqrt(y^3) * sqrt(y^3)
We know that sqrt(a) sqrt(b) = sqrt(ab)
sqrt(y^6)
y^3 since we know that y≥0