Answer:
The first term of the geometric series is 1
Step-by-step explanation:
In this question, we are tasked with calculating the first term of a geometric series, given the common ratio, and the sum of the first 8 terms.
Mathematically, the sum of terms in a geometric series can be calculated as;
S = a(r^n-1)/( r-1)
where a is the first term that we are looking for
r is the common ratio which is 3 according to the question
n is the number of terms which is 8
S is the sum of the number of terms which is 3280 according to the question
Plugging these values, we have
3280 = a(3^8 -1)/(3-1)
3280 = a( 6561-1)/2
3280 = a(6560)/2
3280 = 3280a
a = 3280/3280
a = 1
Final answer:
To find the first term of a geometric series with a common ratio of 3 and a sum of the first 8 terms being 3280, we use the sum formula for a geometric series and isolate the first term 'a'. After plugging in the values and simplifying, we find that the first term 'a' is equal to 1.
Explanation:
The student is asking about the first term of a geometric series with a known common ratio and the sum of the first 8 terms. The common ratio for this series is 3, and the sum of the first 8 terms (S8) is 3280. To find the first term (a), we'll use the following formula for the sum of the first N terms of a geometric series:
S_N = a * (1 - x^N)/(1 - x),
where 'SN' is the sum of the first N terms, 'a' is the first term, 'x' is the common ratio, and 'N' is the number of terms. In this case, x=3 and S_8=3280.
Solving for 'a' gives us:
3280 = a * (1 - 3^8)/(1 - 3)
The first term (a) can now be calculated by isolating 'a' on one side of the equation.
a = 3280 / ((1 - 3^8)/(1 - 3))
a = 3280 / (1 - 6561)/(-2)
a = 3280 / (6560/2)
a = 3280 / 3280
a = 1.
Therefore, the first term of the geometric series is 1.
URGENT!!!!! Mai conducted an experiment by flipping a fair coin 200 times. The coin landed heads up 110 times. Which statement about the coin landing heads up in Mai’s experiment is correct.
A. The experimental probability of the coin landing heads up is One-half and the theoretical probability of the coin landing heads up is StartFraction 11 over 20 EndFraction.
B. The experimental probability of the coin landing heads up is StartFraction 11 over 20 EndFraction and the theoretical probability of the coin landing heads up is One-half.
C. The experimental probability of the coin landing heads up is StartFraction 11 over 20 EndFraction and the theoretical probability of the coin landing heads up is StartFraction 11 over 20 EndFraction.
D. The experimental probability of the coin landing heads up is One-half and the theoretical probability of the coin landing heads up is One-half.
Answer:
B
Step-by-step explanation:
the statement is correct
Answer:
b
Step-by-step explanation:
Help ASAP
Zero product property
1. 100-x²=0
2. 3x²-75=0
3. 0=2x²+20x+50
4. 2x²-5x-12=0
Answer:
1. x=10,-10
2. x = 5
x = -5
3. x=-5
4. x ∈ {4,- 3/2}
Step-by-step explanation:
5. (8 pts) Compute the derivative of h(x) = x^3+x^2/e^3x
and simplify your answer.
Answer:
h'(x) = (-3x^3 +2x)/e^(3x)
Step-by-step explanation:
The formula for the derivative of a quotient is ...
(u/v)' = (vu' -uv')/v²
Using u = (x^3 +x^2) and v = e^(3x), this becomes ...
h'(x) = (e^(3x)(3x^2 +2x) -(x^3 +x^2)(3)(e^(3x))/e^(6x)
h'(x) = (-3x^3 +2x)/e^(3x)
if the interest earned is $750 and the interest rate is 12.5% and the time is 4 years what is the principal
Answer:
There would be : 750 x (1 + 12.5/100)^4 = 1201.35 dollar after 4 years, with the earning is 750$ and interest rate is 12.5%.
Answer:
$1,500
Step-by-step explanation:
Interest = P × 12.5/100 × 4
750 = P × 0.5
P = 1500
The circumference of a circle is 7.7mm.
Find the length of the diameter.
Give your answer rounded to 3 SF.
PLZ HELP!!!!!!
Answer:
D = 2.45 mm
Step-by-step explanation:
D = C ÷ π
D = 7.7 ÷ 3.14
D = 2.4509
D = 2.45 mm
To find the length of the diameter of a circle when the circumference is given, divide the circumference by π.
Explanation:To find the diameter of a circle when only the circumference is given, divide the circumference by π (approximately 3.1416). The formula to find the diameter is:
Diameter = Circumference / π
In this case, the circumference is 7.7mm. So, the diameter would be:
Diameter = 7.7mm / 3.1416 ≈ 2.448mm
Therefore, the length of the diameter, rounded to 3 significant figures, is approximately 2.45mm.
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© 8 t-shirts and a hat costs £42.00
3 t-shirts and a hat costs £17.00.
How much does a t-shirt cost?
How much does a hat cost?
<
t-shirt: £
hat: £
Answer:
t-shirt: £5.00, hat: £2.00
Step-by-step explanation:
You can rewrite them into equations:
8t+h=42.
3t+h=17.
Then subtract the h from both equations using the elimination process.
8t-3t is 5t, and 42-17 is 25. The new equation is 5t=25, thus t=5. If we substitute the 5 into one of the other equations, we get h=2.
Answer:
T-shirt: £5
Hat: £2
Step-by-step explanation:
Use simultaneous equations elimination method for best results.
8t + h= 42
3t + h= 17
Subtract the two equations. h gets cancelled. 8t-3t= 5t. 42-17= 25.
5t= 25
t= 25÷5
t= £5
Substitute the value of t to give h.
8(5) + h=42
40+ h=42
h= 42-40
h= £2
Two parallel lines are cut by a transversal and angles 1 and 7 are alternate exterior angles. If angle 1 measures 120 degrees , how does angle 7 compare with angle 1?
A.Angle 7 is supplementary with angle 1
B.Angle 7 and angle 1 are congruent.
C.The angles cannot be compared.
Answer: B.Angle 7 and angle 1 are congruent.
Step-by-step explanation:
Alternate angles means that the angles are formed on the alternating sides of the transversal. The term "exterior" means that the alternate angles are formed outside the parallel lines.
Since the parallel lines are cut by a transversal and angles 1 and 7 are alternate exterior angles, it means that angles 1 and 7 are equal or congruent. This is because of the rule in geometry stating that two alternate exterior angles are congruent. Therefore, the correct option would be
B. Angle 7 and angle 1 are congruent.
Answer: The correct option is B; Angle 7 and angle 1 are congruent
Step-by-step explanation: Please refer to the picture attached for more details. The parallel lines AB and CD have been drawn and a transversal line have also been drawn to cut both lines as shown in the picture.
Since both lines are parallel, the angles formed by the transversal would be equal.
A careful observation would show that the interior angle formed by the transversal (which is the supplement of angle 120), is equal or congruent to the interior angle formed at angle 7. These are commonly referred to as "z angles" by virtue of the shape formed. Angle 1 and angle 7 are the exterior alternate angles formed by the transversal and they are both congruent, that is, they both have the same measurement.
The angles cannot be described as supplementary, because supplementary angles add up to 180 degrees. That is, if angle A plus angle B equals 180, then angles A and B are both supplementary. This does not apply to angle 1 and angle 7.
of the 800 participants in a marathon 120 are running to raise money for a cause. How many participants out of 100 are running for a cause
Answer:
divide 120 by 800 should give you the answer 15/100
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
i-ready okurrr
Ana played 4 rounds of golf and then played her lowest round of golf with a score of 80 The scores of the first 4 round and the lowest round start
Answer:
Step-by-step explanation:
6
Answer:
c
Step-by-step explanation:
Eric put several CD's in a case. Four CDs are country, six are rap and ten are pop. If Eric picks one CD from the case without looking, what is the probability that he will pick a country CD?
Probability that Eric will pick a country CD is 0.2.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Given that,
Number of CD's which are country = 4
Number of CD's which are rap = 6
Number of CD's which are pop = 10
Total number of CD's = 4 + 6 + 10 = 20
Probability = Number of likely outcomes / Total number of outcomes3
Probability of getting country CD = 4 / 20
= 1/5
= 0.2
Hence the required probability is 0.2.
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A bag contains 666 red jelly beans, 444 green jelly beans, and 444 blue jelly beans. If we choose a jelly bean, then another jelly bean without putting the first one back in the bag, what is the probability that the first jelly bean will be green and the second will be red?
Answer:
12/91
Step-by-step explanation:
The question is not properly formatted, here is how it should be formatted.
A bag contains 6red jelly beans, 4 green jelly beans, and 4 blue jelly beans. If we choose a jelly bean, then another jelly bean without putting the first one back in the bag, what is the probability that the first jelly bean will be green and the second will be red
Step one
This is selection without replacement.
Sample space
6red jelly beans,
4 green jelly beans, and
4 blue jelly beans.
S= 6+4+4= 14
Probability that the first jelly bean will be green = 4/14= 2/7
Without replacement, Probability that the second jelly bean will be red = 6/13
Hence for the two selections the probability is= 2/7*6/13= 12/91
tan(pi/2) =
A)1
B) -1
C)0
D) Undefined
Answer:
D) Undefined
Step-by-step explanation:
[tex] \tan \: \bigg( \frac{\pi}{2} \bigg) = \infty \: or \: undefined\\ [/tex]
Find the volume of the cylinder.
Either enter an exact answer in terms of or use 3.14 for pi. with a radius of 4 and a height of 10
HELP PLEASE!!!!
Karen is on a game show. She will choose a box to see if she wins a prize. The odds in favor of Karen winning a prize are 5/7. Find the probability of Karen winning a prize
Answer:
0.71
Step-by-step explanation:
P(Karen wins a prize) = 5/7 = 0.71
Please help me now plz
I will mark you brainliest
Answer:
theta = 24.4 degrees
Step-by-step explanation:
This is a right triangle.
sin theta = opp/ hyp
sin theta = 33/80
Take the inverse of each side
sin^-1 sin(theta) = sin^-1 (33/80)
theta =24.36197794
To the nearest tenth
theta = 24.4 degrees
Which graph represents this equation?
Y=3/2x^2-6x
The parabola is passing through (0, 0) and (9, 0). Then the correct option is C.
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
The equation of the parabola is given below.
y = (3/2)x² - 6x
Then the factor of the equation will be
y = 3x (x / 2 - 3)
Then the zeroes of the function will be
y = 0
x = 0, 9
Then the correct option is C.
The graph is given below.
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The Haskins family spends $600 per month on groceries for their family. If this is 15% of their monthly budget, , then what is their monthly budget?
Hi
15/100 = 600 / X
X = 600 *100 /15 = 4000
monthly budget =4000
Answer:
Their monthly budget is $600
Suppose a parabola has vertex (–8, –7) and also passes through the point (–7, –4). Write the equation of the parabola in vertex form.
mia wants to earn 2500 in her job at a bycicle store she is paid 55 for every bycicle she tunes up the minimum number of bycicles mia needs to tune up to reach her goal of 2500
Mia needs to tune up at least 46 bicycles at $55 each to reach her goal of $2500, as she cannot tune up a fraction of a bicycle.
To calculate the minimum number of bicycles Mia needs to tune up to reach her goal of $2500, we must divide her goal amount by the amount she earns per bicycle. Thus, the calculation is as follows:
Number of bicycles = Total goal amount / Earnings per bicycle
Number of bicycles = $2500 / $55
When we divide 2500 by 55, we get approximately 45.4545. Since Mia cannot tune up a fraction of a bicycle, she will need to tune up a whole number of bicycles. Therefore, she needs to tune up at least 46 bicycles to reach or exceed her goal of $2500.
Find the area of a regular octagon (8 sides) that has an apothem of 12.1 meters and a side length of 10 meters.
Encuentra el área de un octágono regular (8 lados) que tiene una apotema de 12.1 metros y una longitud lateral
de 10 metros.
0
m2
1
2
3
0 1
0
4.
5
6
+
7
8
-
a lo
0
.
The radius of a circle is 15 inches.
Enter the area of the circle, in square inches. Round your answer to the nearest tenth and use 3.14 for pi.
______ square inches
Answer:
706.5
it's saying i need to fill in twenty characters to answer
so here is my twenty characters
Answer:
[tex]706.5 {in}^{2} [/tex]
Step-by-step explanation:
[tex]area \\ = \pi {r}^{2} \\ = 3.14 \times 15 \times 15 \\ = 706.5 {in}^{2} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
When April made tortillas for the first time, she used all the dough to make 10 tortillas. After making quesadillas, she decided that the tortillas were not large enough. The next time, using the same amount of dough, she made each tortillas the same thickness for 25% larger. How many tortillas did April make the second time? If the area of each tortilla in the second batch is 201 in2, what was the area of each tortilla in the first batch?
Answer:
Second time: 8 tortillas
Area of tortillas in the first batch: 160.8 in2
Step-by-step explanation:
Let's say that the amount of dough to make a tortilla is x.
So, in the first time, the amount of dough used is 10 * x = 10x
Then, she made the tortillas 25% larger, so the amount of dough used for each tortilla now is 1.25x
So, using the same amount of dough (10x), the amount of tortillas she can make is:
10x / 1.25x = 8 tortillas
If the area of the larger tortilla is 201 in2, and this tortilla is 25% larger than the ones in the first batch, to find the area of the inicial tortillas we just need to divide this new area by 1.25:
Area of first tortillas = 201 / 1.25 = 160.8 in2
A baker purchases flour each week from a wholesale warehouse. The chart shows the quantities and prices available this week. If the best deal last week for flour was $1.60 per pound. What is the difference between the unit price for last week's best deal and this week's best deal?
The chart showing the quantities and prices is;
Best Deal 1
Quantity of Flour Price
3 pounds $5.25
5 pounds $9.75
7 pounds $12.60
10 pounds $14.20
12 pounds $18.24
Answer:
difference between last weeks best deal = $0.3
Step-by-step explanation:
Let's calculate the unit price for each of the quantities in the chart.
For quantity of 3 pounds;
We have; unit price = 5.25/3 = $1.75
For 5 pounds;. Unit price = 9.75/5 = $1.95
For 7 pounds; unit price = 12.6/7 = $1.8
For 10 pounds; unit price = 14.2/10 = $1.42
For 12 pounds; unit price = 18.24/14 = $1.3
Thus, last weeks best deal is the lowest = $1.3
Thus; difference between last weeks best deal is given as;
= this weeks best deal - last weeks best deal
This gives;
$1.6 - $1.3 = $0.3
Answer:
0.18
Step-by-step explanation:
Triangles A and B are right angled.
a) show that the two shorter sides in triangle A have the same length as the two shorter sides in triangle B.
b) explain why the two triangles are congruent.
Answer:
13²-12²
169-144
=25
√25
=5
The 2 shortest sides are 5cm and 12cm
Let the sides of the triangles be a, b and c. According to Pythagoras theorem;
[tex]c^2=a^2+b^2[/tex] where:
a is the hypotenuse (longest side)
For triangle A:
c = 13
b = 12
Get "a"
[tex]13^2=12^2+b^2\\169=144+b^2\\b^2=169-144\\b^2=25\\b=5cm[/tex]
Similarly for triangle B:
[tex]c^2=5^2+12^2\\c^2=25+144\\c^2=169\\c^2=\sqrt{169} \\b=13cm[/tex]
We can see that the two shorter sides have the same length which is 5cm
Since all the sides of the triangle are the same, hence the two triangles are congruent.
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Please help need it I can really use it!
Answer:
B
Step-by-step explanation:
The highest MOC is 4 in group A but in group B the MOC is 3. So group A has one more dot than group B.
5: Un músico golpea un tambor una vez cada 24 segundos exactamente, mientras que otro lo hace cada 14 segundos. Suponiendo que acaban de golpear ambos a la vez, ¿cuándo volverán a coincidir?
Answer:
168 seconds
Step-by-step explanation:
To find out when they coincide again, the least common multiple between both numbers must be calculated:
24 14 | 2
12 7 | 2
6 7 | 2
3 7 | 3
1 7 | 7
1 1
Therefore the least common multiple is:
2 * 2 * 2 * 3 * 7 = 168
This means that they will coincide again at 168 seconds, when the first musician has struck 7 times (168/24) and the other 12 times (168/14)
An airline finds that 6% of the people who make reservations on a certain flight do not show up for the flight. If the airline sells 190 tickets for a flight with only 185 seats, use the normal approximation to the binomial distribution to find the probability that a seat will be available for every person holding a reservation and planning to fly. (Round your answer to four decimal places.)
Answer:
0.9826 = 98.26% probability that a seat will be available for every person holding a reservation and planning to fly.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
6% of the people who make reservations on a certain flight do not show up for the flight. So 100-6 = 94% show up, which means that [tex]p = 0.94[/tex]
190 tickets, so [tex]n = 190[/tex]
So
[tex]\mu = E(X) = np = 190*0.94 = 178.6[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{190*0.94*0.06} = 3.27[/tex]
Find the probability that a seat will be available for every person holding a reservation and planning to fly.
At most 185 people show up.
Using continuity correction, we have to find [tex]P(X \leq 185 + 0.5) = P(X \leq 185.5)[/tex], which is the pvalue of Z when X = 185.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{185.5 - 178.6}{3.27}[/tex]
[tex]Z = 2.11[/tex]
[tex]Z = 2.11[/tex] has a pvalue of 0.9826
0.9826 = 98.26% probability that a seat will be available for every person holding a reservation and planning to fly.
Randy has 4 pennies , 3 nickels , and 3 dimes in his pocket if he randomly chooses 2 coins without replacement what is the probility they are both dimes.
[tex]3 \div 10 \times 2 \div 9 = 1 \div 15[/tex]
the probability of drawing one dime is 3/10. if you don't replace the coin, there are only 9 left, 2 of which are dimes. so multiple the to probabilities and there you have it
Answer:
0.09
Step-by-step explanation:
What kind of salad do snowmen eat? Punchline 73 answer key
Answer:
Coldslaw
Step-by-step explanation:
Please I need help ASAP!!
Answer:
I think 3%
Step-by-step explanation:
Hope this helps:)
Answer:
33.3%
Step-by-step explanation:
I had answered another question first. This is the answer for this problem. Sorry!
hope this helps :)