We have been given that the 5th term in a geometric sequence is 160. The 7th term is 40. We are asked to find the possible values of 6th term of the sequence.
We know that an geometric sequence is in form [tex]a_n=a\cdot r^{n-1}[/tex], where,
[tex]a_n[/tex] = nth term of sequence,
a = First term,
r = Common ratio,
n = Number of terms.
We will get two equations using our given information as:
[tex]160=a\cdot r ^{5-1}...(1)[/tex]
[tex]160=a\cdot r ^{4}...(1)[/tex]
[tex]40=a\cdot r ^{7-1}...(2)[/tex]
[tex]40=a\cdot r ^{6}...(2)[/tex]
Upon dividing equation (2) by equation (1), we will get:
[tex]\frac{40}{160}=\frac{a\cdot r^6}{a\cdot r^4}[/tex]
[tex]\frac{1}{4}=r^{6-4}[/tex]
[tex]\frac{1}{4}=r^{2}[/tex]
[tex]r^{2}=\frac{1}{4}[/tex]
[tex]\sqrt{r^{2}}=\pm\sqrt{\frac{1}{4}}[/tex]
[tex]r=\pm\frac{1}{2}[/tex]
Let us solve for a.
[tex]160=a\cdot (\frac{-1}{2})^{4}[/tex]
[tex]160=a\cdot \frac{1}{16}[/tex]
[tex]160\cdot 16=a\cdot \frac{1}{16}\cdot 16[/tex]
[tex]2560=a[/tex]
So our formula would be [tex]a_n=2560\cdot (\pm\frac{1}{2})^{n-1}[/tex].
We cannot determine whether the common ratio would be positive or negative, so we will take both values.
[tex]a_6=2560\cdot (\pm\frac{1}{2})^{6-1}[/tex]
[tex]a_6=2560\cdot (\pm \frac{1}{2})^{5}[/tex]
[tex]a_6=2560\cdot \pm \frac{1}{32}[/tex]
[tex]a_6=\pm 80[/tex]
Therefore, the 6th term of the sequence would be [tex]\pm 80[/tex] and option C is the correct choice.
Answer:
C.+- 80
Step-by-step explanation:
How many 2/3 cup servings are in an 8-cup container of juice?
Help please
You can get 12 servings of 2/3 cup each from an 8-cup container of juice. You find this by dividing the total volume (8 cups) by the volume of each serving (2/3 cup).
Explanation:To find out how many 2/3 cup servings you can get from an 8-cup container of juice, you simply divide the total volume by the volume of each serving.
In this case, you divide 8 (the total volume) by 2/3 (the volume of each serving). Here are the step-by-step calculations:
Write 8 as a fraction, which becomes 8/1.Divide by 2/3, which in practice means multiplying 8/1 by the reciprocal of 2/3, which is 3/2.When you multiply 8/1 by 3/2, you get 24/2, which simplifies to 12.So, you can get 12 servings of 2/3 cup each from an 8-cup container of juice.
Learn more about Dividing Fractions here:https://brainly.com/question/18511795
#SPJ11
what is the slope of y= 2/3x + 4
Answer:
2/3
Step-by-step explanation:
m is the variable for slope
the equation of a line
is y=mx+b
the slope is next to the x
Answer:
[tex]slope = \frac{2}{3} [/tex]
Step-by-step explanation:
[tex]Think \: of \: y = mx + b \\ \\ m\: is \: the \: slope \\ b \: is \: the \: y \: intercept \\ \\ So, \: since \: \frac{2}{3} \: is \: on \: the \: m \: the \: slope \: is \\ \frac{2}{3}[/tex]
Which is equivalent to (3/125)*?
Answer:
The answer is A as when simplified the number is 125^x/3
and the only one taht represents this is a
Factor completely.
5
x
2
−
20
x
+
20
=
5x
2
−20x+20=5, x, squared, minus, 20, x, plus, 20, equals
Show Calculator
Answer:
[tex]5(x-2)^2[/tex]
Step-by-step explanation:
[tex]5x^2-20x+20=\\5(x^2-4x+4)=\\5(x-2)^2[/tex]
Below is the graph of f '(x), the derivative of f(x), and has x-intercepts at x = -3, x = 1 and x = 2. There are horizontal tangents at x = -1.5 and x = 1.5. Which of the following statements is true?
f has a relative minimum at x = 1.5.
f has a relative maximum at x = -1.5.
f is decreasing on the interval from x = 1 to x = 2.
None of these is true.
Thank you in advance!
Answer:
f is decreasing on the interval from x = 1 to x = 2.
Step-by-step explanation:
f has a relative minimum when f' changes signs from - to +.
f has a relative maximum when f' changes signs from + to -.
f is decreasing when f' is negative.
f' is not changing signs at x=-1.5 or x=1.5, so neither of these are minimums or maximums of f. However, f does have relative minimums at x=-3 and x=2, and a relative maximum at x=1
f' is negative between x=1 and x=2. So f is decreasing in this interval.
Solve the equation 2x-1=13.
Answer:
7
Step-by-step explanation:
2 time 7 = 14-1 = 13
Answer:
x=7
Step-by-step explanation:
Collect like terms
2x=13+1.
2x=14
Divide both side by 2
[tex] \frac{2x}{2} = \frac{14}{2} [/tex]
x=7
The equations x minus 3 y = negative 3, 2 x + y = 2, x + 3 y = 3, and 2 x minus y = negative 2 are shown on the graph below. On a coordinate plane, there are 4 lines. Green line goes through (0, 2) and (negative 1, 0). Blue line goes through (0, 2) and (1, 0). Pink line goes through (negative 1.5, 1.5), and (1.5, 0.5). Orange line goes through (negative 1.5, 0.5) and (1.5, 1.5). Which system of equations has a solution of approximately (–0.4, 1.1)? x + 3 y = 3 and 2 x minus y = negative 2 x minus 3 y = negative 3 and 2 x + y = 2 x minus 3 y = negative 3 and 2 x minus y = negative 2 x + 3 y = 3 and 2 x + y =2
Answer:
(A)x+3y=3 and 2x-y=-2
Step-by-step explanation:
In the attached graph
Green line is the graph of 2x-y=-2Red line is the graph of x-3y=-3Orange line is the graph of x+3y=3Blue Line is the graph of 2x+y=2The point of the intersection of the orange and green line has an approximate solution of (-0.4,1.1).
Therefore, the system of equation which has the approximate solution is: x+3y=3 and 2x-y=-2
The correct option is A
Answer:
A
Step-by-step explanation:
Simplify (−2x3+9)(8x2+6x+1)
Answer:
-16x^4 - 12x^3 + 70x² + 54x + 9
Step-by-step explanation:
(-2x² + 9)(8x² + 6x + 1)
-16x^4 - 12x^3 -2x² + 72x² + 54x + 9
-16x^4 - 12x^3 + 70x² + 54x + 9
I am pretty sure that this is the answer.
Tell me if I am wrong.
Can I get brainliest
Sorry, It wont let me put my answer.
please help me!!!
find the arc length of partial circle.
Either enter an exact answer in terms of n pi or use 3.14 for n pi and enter as a decimal.
* This is from Khan academy and the lesson is (Circumstance of part of circles)*
Answer: 1.57
Step-by-step explanation:
When solving for the arc you have to find the circumference.
For circumference you'll need the diameter which is 2x the radius.
So, your equation would be
1/4{(pi)(2)} = x
or
1/4{(3.14)(2)} = x
To Solve:
3.14 times 2 equals 6.28
Divide by 4 or multiply by 1/4 to get 1.57
Not sure if this is correct, I haven't learned the topic myself, but this week's to be there most reasonable way to look at it. For me anyway.
The arc length of a partial circle can be calculated using the formula Arc length = (θ/360) * 2πr, where 'θ' is the angle of the sector in degrees and 'r' is the radius of the circle. This is applicable in high school Mathematics.
Explanation:The subject of your question is the arc length of a partial circle, a concept in Mathematics. The arc length of a partial circle can be calculated using the formula: Arc length = (θ/360) * 2πr, where 'θ' is the angle of the sector in degrees and 'r' is the radius of the circle.
For instance, if a circle has a radius of 8 units and the angle of the sector is 60 degrees, the arc length can be calculated as follows: Arc length = (60/360) * 2 * 3.14 * 8 = 8.38 units (in terms of 3.14 for n π). Using n π, the exact answer would be expressed as: Arc Length = 4π/3 units.
Learn more about Arc Length here:https://brainly.com/question/31647763
#SPJ2
the jedi have a weapon that can shoot a projectile 20 miles. find the area that the projectile can land in.
Answer:
The area he can cover with that weapon is 1,256 miles².
Step-by-step explanation:
Assuming that the Jedi won't move and that he can shoot in every direction, he'd be shooting at a circle with a radius of 20 miles. Therefore the are that he can cover with that weapon is the area of the circle, which is shown below:
area = pi*r²
area = 3.14*(20)²
area = 3.14*400
area = 1,256 miles²
The area he can cover with that weapon is 1,256 miles².
The area a projectile can land in can be determined by considering the distance the missile can travel as the circle's radius. The area of this circle, calculated by the formula A = πr², is the area the shell can land in.
Explanation:The area where the projectile can land is determined by considering the weapon as the centre of a circle and the possible distance it can travel as the radius. This forms a circular area where the projectile can land. The area A of a process is calculated using the formula A = πr², where r is the circle's radius.
Here, our radius is 20 miles, the distance the projectile can travel. Therefore, we substitute this distance into our formula to find the area:
A = π(20)²
Calculating the above will give you the area that the projectile can land in.
Learn more about the Area of Projectile Landing here:https://brainly.com/question/30530884
#SPJ12
Find m<1.
A.30
B.35
C.40
D.55
Answer:
m <1 = 30
Step-by-step explanation:
The sum of the angles of a triangle add to 180
Let x be the unknown angle
75+75+x = 180
Combine like terms
150+x =180
Subtract 150 from each side
150-150+x = 180-150
x = 30
In Johnny's bowl there are many type of stones 1/8 of the stones are red and 5/6 of the stones are white what fraction of Johnny's stones are white or red
Answer:
[tex]\frac{23}{24}[/tex]
Step-by-step explanation:
1/8 of the stones in Johnny's bowl are red and 5/6 of the stones are white.
The fraction of stones that are red or white is obtained by adding the fraction that are red with the fraction that are white. That is:
[tex]\frac{1}{8} + \frac{5}{6} = \frac{23}{24}[/tex]
The fraction of the stones that are red or white is [tex]\frac{23}{24}[/tex].
Follow below steps:
The fraction of Johnny's stones that are white or red can be calculated by adding the fractions of white and red stones.
Given that 1/8 of the stones are red and 5/6 of the stones are white:
Red stones: 1/8
White stones: 5/6
Total fraction of white or red stones: 1/8 + 5/6 = 5/24 + 20/24 = 25/24
Since the total is greater than 1, it indicates a mistake in the initial information provided.
Triangle A B C is shown. Angle A B C is a right angle. The length of hypotenuse A C is 9, the length of B C is 2, and the length of A B is 8.77. Law of cosines: a2 = b2 + c2 – 2bccos(A) What is the measure of AngleC to the nearest whole degree? 70° 77° 80° 85°
Answer:
answer is B 77
Step-by-step explanation:
got it right on edg 2020-2021
The nearest whole degree is 77
What are trigonometric functions?In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.
Given here: ABC is a right angle triangle AC=9, BC=2 and AB=8.77
The formula for law of cosines is given by a²=b²+c²-2bcosA
81=4+76.9129-2×2cos A
0.0871=-4Cos A
cos A=-0.21775
A=77.43208
Hence, The nearest whole degree is 77
Learn more about trigonometric functions here:
https://brainly.com/question/6904750
#SPJ6
This is a really easy question Just need to make sure it is right. Is it B
Which ratio is equivalent to 3:3?
The ratio 3:3 signifies equality between two quantities and an equivalent ratio can be found by scaling both parts by the same number. Dividing both parts by 3 gives us the simplest form, which is 1:1.
Explanation:A ratio compares two quantities and can be written in various forms such as fractions, with a colon, or with the word "to". The ratio 3:3 is an expression comparing two equal quantities. To find an equivalent ratio, we can simplify or scale the ratio by multiplying or dividing the numerator and denominator (the two parts of the ratio) by the same number.
In this case, dividing both parts of the ratio 3:3 by 3 gives us an equivalent ratio of 1:1, which also represents equality between two quantities. Multiplying both parts by a common number will also produce an equivalent ratio. For example, multiplying 3:3 by 2 gives us 6:6, which is still equivalent. It's essential to maintain the equality of the two parts when finding an equivalent ratio.
Ratios can be applied to various situations, including unit conversions, scale factors, proportions, and comparisons in scientific experiments, such as the ratio of amplitudes in a double-slit experiment in Physics.
Easy Question, Easy points
Topic: Volume
Answer:
about 141.37
Step-by-step explanation:
pi x 20 (h) x 1.5 (r)
radius is half of diameter :)
Answer:
141.37
Step-by-step explanation:
Would you mind giving me brainliest?
What did you include in your response? Check all that apply.
The boycott ended segregation on Montgomery buses.
The boycott led to violence against African Americans in Montgomery.
The boycott showed African Americans that they had some support in the white community.
The boycott provided a sense of personal power to African Americans.
The boycott gave national attention to the civil rights movement.
Answer:
the 1st and 3 and 2end one its the right one
Step-by-step explanation:
Answer:
its the first three answers :)
Step-by-step explanation:
A random sample of 100 people from region A and a random sample of 100 people from region B were surveyed about their grocery-shopping habits. From the region A sample, 16 percent of the people indicated that they shop for groceries online. From the region B sample, 24 percent of the people indicated that they shop for groceries online. At the significance level of α=0.05, do the data provide convincing statistical evidence that there is a difference between the two regions for the population proportions of people who shop online for groceries? Complete the appropriate inference procedure to support your answer.
Answer:
Step-by-step explanation:
This is a test of 2 population proportions. Let a and b be the subscript for people from region A and region B. The population proportions would be pa and pb
pa - pb = difference in the proportion of people from region A and region B.
The null hypothesis is
H0 : pa = pb
pa - pb = 0
The alternative hypothesis is
H1 : pa ≠ pb
pa - pb ≠ 0
it is a two-tailed test
Sample proportion = x/n
Where
x represents number of success
n represents number of samples
For region A,
xa = 16
na = 100
pa = 16/100 = 0.16
For region B,
xb = 24
nb = 100
pb = 24/100 = 0.24
The pooled proportion, pc is
pc = (xa + xb)/(na + nb)
pc = (16 + 24)/(100 + 100) = 0.2
1 - pc = 1 - 0.2 = 0.8
z = (pa - pb)/√pc(1 - pc)(1/na + 1/nb)
z = (0.16 - 0.24)/√(0.2)(0.8)(1/100 + 1/100) = - 0.08/√0.0002891223
z = - 1.41
Since it is a 2 tailed test, we would find the p value by doubling the area to the left of the z score to include the area to right.
Area to the left from the normal distribution table is
0.07927
P value = 0.07927 × 2 = 0.16
Since 0.05 < 0.16, we would accept the null hypothesis
Therefore, the data does not provide convincing statistical evidence that there is a difference between the two regions for the population proportions of people who shop online for groceries.
Final answer:
To determine if the differences in grocery shopping habits between two regions are statistically significant, a two-proportion z-test is conducted. We first state the null and alternative hypotheses, calculate the test statistic, find the p-value, and make a decision based on the significance level of 0.05.
Explanation:
To evaluate if there is a significant difference between the population proportions of people who shop online for groceries in two regions, we need to conduct a two-proportion z-test. The steps are as follows:
State the null and alternative hypotheses. The null hypothesis (H₀) is that there is no difference in the proportions of people who shop online for groceries in the two regions (p₁ = p₂). The alternative hypothesis (Ha) is that there is a difference (p₁ ≠ p₂).Calculate the test statistic using the formula for the two-proportion z-test. To compute this, we first find the pooled proportion, which combines the successes and total sample sizes from both regions.The p-value is then determined based on the calculated z-score. This p-value represents the probability of observing a test statistic as extreme as, or more extreme than, the observed result, under the assumption that the null hypothesis is true.Decide to reject or not reject the null hypothesis by comparing the p-value to the significance level (α = 0.05). If the p-value is less than α, we reject the null hypothesis, indicating sufficient evidence to say there is a significant difference in the proportions.In this scenario, with 16% of 100 people from Region A and 24% of 100 people from Region B indicating they shop for groceries online, a two-proportion z-test will reveal if the observed difference is statistically significant at the 0.05 level.
Finn started a savings account with $5,000 and earns 3% simple interest for 5 years. How much interest will be earned over the 5 years? a) 15,000 b)759 c)3000 d)5015
Answer:
the answer is b. (since you accidentally typed 759 not 750)
Step-by-step explanation:
The formula for simple interest is
A = P (1 + rt)
A = final amount
P = initial principal balance
r = annual interest rate
t = time (in years)
and the interest is going to be 750 after you plug it in, they are not asking for the amount of money total, but the amount of interest earned.
3 percent simple interest for 5 years means you are getting 0.03 percent of money from the 5,000 initial value and for 5 years. The total interest is $750.
I hope this helped! :)
Geometry Question Help please
Answer:
<EAD = 31*
Step-by-step explanation:
Because, <CAB is similar in angle measurement
An equilateral triangle has a perimeter of 15x3 + 33x5 feet. What is the length of each side?
Answer:
70
Step-by-step explanation:
So I assumed that the x was multiplication...so...15x3=45 and 33x5=165...so the perimeter is 210, so you divide that by 3 and the answer is 70!
Jane earns money walking dogs on the weekends. Jane charges $5 dollar sign, 5 for each dog she walks.
Complete the table for the given ratio.
Dogs Charge in dollars.
1 5
3 ?
5 ?
FIND THE ?
HURRY UP I HAVE 1 MINUTE TO SOLVE THIS
Answer:
3 dogs, $15
5 dogs, $25
Step-by-step explanation:
Jane charges $5 per dog.
When she walks 3 dogs ;
1 dog = $5
3 dogs = x
x × 1 dog = $5 × 3 dogs
x= $5 × 3 dogs/ 1 dog
x= $5 × 3 = $15
When Jane Walks 5 dogs she receives,
y= $5 × 5
y= #25.
For 3 dogs, Jane would charge $15. For 5 dogs, she would charge $25. You find these amounts by multiplying the number of dogs by the charge per dog, which is $5.
Explanation:Since Jane charges $5 for each dog she walks, you can find the charge for any number of dogs by multiplying the number of dogs by 5.
For 3 dogs, she would charge $15 (3 dogs x $5 per dog = $15).
For 5 dogs, she would charge $25 (5 dogs x $5 per dog = $25).
So, the completed table would look like this:
Dogs | Charge in dollars
1 |$5
3 |$15
5 |$25
https://brainly.com/question/35502092
#SPJ3
Help!!
Find the area of the figure and type your result in the box.
4cm
4cm
Use pi*= 3.14
Answer:
22.28
Step-by-step explanation:
James goes to Walmart and spends, d, dollars. He has a coupon for 25% off. What is James total after the coupon is applied?
Answer:
c
Step-by-step explanation:
Identify the conic that is formed by the intersection of the plane described and the double-napped cone.
The plane intersects one nappe and is parallel to n.
What is the conic section formed?
A. ellipse
B. hyperbola
C. parabola
Answer:
C. Parabola
Step-by-step explanation:
A line parallel will cut only one cone (upper or lower cone, not both) making it a parabola
the formula for exponential decay is y=a(1-r)^t, where a is the initial amount, r is the rate of decay and t is the number of intervals. use the formula to determine the answer to the following problem.
on wednesday your science teacher gives you a list of twenty five terms to be memorized. you memorize all of them wednesday night and do not look at the list again. if you forget 5% of the list each day, how many terms will you remember seven days later for the chapter test?
What is the probability of getting three tales
Answer:
12.5%
Step-by-step explanation:
Answer:
[tex]\frac{1}{8}[/tex].
Step-by-step explanation:
To solve this, we will first need to think about the probability of getting "tails". A coin has two sides, meaning landing on "tails" would result in a probability of [tex]\frac{1}{2}[/tex] per toss.
In the question, a total of 3 tosses is given. This means we will need to multiply the probability 3 times:
[tex]\frac{1}{2}[/tex] ×[tex]\frac{1}{2}[/tex] ×[tex]\frac{1}{2}[/tex] = [tex]\frac{1}{8}[/tex] .
Paul, who is standing 150 feet above the water on a balcony of a cruise ship,
sees two boats located due north. The angles of depression from Paul
to the boats are 33
and 22°
Find the distance between the two boats to the nearest tenth of a foot.
Answer:140.3
Step-by-step explanation:
Answer:
140.3
Step-by-step explanation:
A family of four spent $104 for tickets to a concert on Friday and they spent $140 for tickets to dinner theater on Saturday.What was the cost per person to attend these events
Answer:
$61
Step-by-step explanation:
To determine the cost per person to attend these events, you have to add the cost of the tickets for the concert plus the cost of the tickets for dinner theater. After finding the total amount that was spent, you have to divide this by 4 that is the number of people:
Total cost= $104+$140
Total cost= $244
Cost per person= $244/4
Cost per person= $61
According to this, the cost per person to attend these events is $61.
Answer:
Cost of first event: $26 per person
Cost of second event: $35 per person
Cost of both events together: $61 per person
Step-by-step explanation:
In the first event, the four people spent $104, so the cost per person of this event is:
104 / 4 = $26
Each person pays $26 for this event.
For the second event, the four people spent $140, so the cost per person of this event is:
140 / 4 = $35
The cost per person to attend both events together is:
26 + 35 = $61
Find the value of x. Round to the nearest degree.
Answer:
x = 42
Step-by-step explanation:
sin theta = opposite / hypotenuse
sin x = 6/9
Take the inverse of each side
sin ^-1 sin x = sin ^-1 (6/9)
x =41.8103149
To the nearest degree
x = 42
Answer:
did u also u 3.14 as pie too help u cause that what u are going to have to do