Answers
Answer:
m∠8 = 4x
Step-by-step explanation:
Angle 8 is the same angle measure of angle 1, which is m∠1 = 4x
Related Questions
what three-dimensional shape is a basketball
Answers
Answer:
A sphere
Step-by-step explanation:
A sphere is a round three dimensional object with no sharp corners or vertexes. Since a basketball fits this criteria, it is a sphere.
A line passes through the points (1,2) and (3,1) what is the slope of the line
Answers
Answer:
-1/2
Step-by-step explanation:
The slope of a line is given by
m = (y2-y1)/(x2-x1)
= (1-2)/(3-1)
= -1/2
The slope is -1/2
Answer:
The slope is -1/2.
Step-by-step explanation:
Slope formula:
[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\displaystyle \frac{1-2}{3-1}=\frac{2}{-1}=-\frac{1}{2}[/tex]
[tex]\Large\textnormal{Therefore, the slope is -1/2.}[/tex]
What is the value of x in the diagram below?
A. 88
B. 100
C. 95
D. 151
Answers
the figure is four sided so it a heptagon
for a heptagon, the sum of all interior angles is 900°
i.e. x+(x+50°)+(x+50°)+(x+50°)+×+×+(x+50°)=900°
or, 7x+200°=900°
or, 7x=700°
or, x= 100°
Answer:
The value of x = 100 ⇒ answer B
Step-by-step explanation:
* Lets study how to find the sum of the interior angles of any polygon
- We can find the sum of the measures of the interior angles of any
polygon using the rule (n - 2) × 180°, where n is the number of its
sides or its angles
* Now lets solve the problem
- The polygon has 7 sides and 7 angles
- The measure of three angles of them is x°
- The measure of four angles of them is (x + 50)°
∵ The sum of the interior angles = (n - 2) × 180°
∵ n = 7
∴ The sum of the interior angles = (7 - 2) × 180° = 5 × 180° = 900°
∵ Three angles each measured x°
∵ Four angles each measured (x + 50)°
∴ 3(x°) + 4(x + 50)° = 900° ⇒ simplify it
∴ 3x + 4(x) + 4(50) = 900 ⇒ add the like terms
∴ 3x + 4x + 200 = 900 ⇒ add the like terms
∴ 7x + 200 = 900 ⇒ subtract 200 from both sides
∴ 7x = 700 ⇒ divide both side by 7
∴ x = 100
* The value of x = 100
Find the sum of the first 25 terms of a geometric sequence where the first term is 177,147 and the common ratio is -1/3
Answers
Answer:
132860 to nearest whole number.
Step-by-step explanation:
Sum of n terms = a1 .(r^n - 1) / (r - 1).
S25 = 177,147 ((-1/3)^25 - 1) / (-1/3 - 1)
= 177,147 * -1 / -4/3
= 132860.
The given task involves finding the sum of the first 25 terms of a geometric sequence with a specific first term and common ratio. This is done using the sum formula for a finite geometric sequence, with the terms alternating in sign due to a negative common ratio.
Explanation:The subject question deals with the concept of a geometric sequence, specifically finding the sum of the first 25 terms. A key formula to solve this question is the sum of a finite geometric sequence: Sₙ = a₁(1 - rⁿ)/(1 - r), where a1 is the first term, r is the common ratio, and n is the number of terms.
In this case, a₁ is 177,147, r is -1/3 and n is 25. Substituting these values into the formula, the sum, S25 = 177,147 × (1 - (-1/3)25) / (1 - -1/3).
By solving this equation, we get the sum of the first 25 terms of the given geometric sequence. Note that due to the negative common ratio, the terms alternate in sign in this particular geometric sequence.
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Michael practiced batting and kept track of his hits. He missed 2 balls but hit 8 balls that were pitched to him. How many balls can Michael predict to hit if he is pitched 20 balls?
Answers
Answer: He can predict 16 balls
Step-by-step explanation:
Answer:
16 balls; c
Step-by-step explanation:
1) Write the recursive rule for the sequence.
40 , 30 , 20 , 10 , 0 , -10, ,-20
2) Write the explicit rule for the sequence. -1, 14, 29, 44, 59
3)If the probability of an event is P(A) = 2/25 and the probability of the next event is P(B) = 5/6, what is the P(A and B) ?
4)The average weight of the animals in a petting zoo is 40 pounds. The weights of 10 animals in the zoo selected randomly are 35, 46, 59, 18, 44, 23, 61, 45, 40, 38.
The population mean is 40 pounds. What is the sample mean to the nearest pound?
Question 4 options:
43
42
39
41
Question 5 (5 points)
For which intervals is the function positive?
Question 5 options:
(−∞, 4)
(−∞, −6) (−2,4 )
( ∞ , 6) (∞, 4)
(−4, 4)
Question 6 (5 points)
What is the average rate of change from year 30 to year 60?
Question 6 options:
-.44
- .04
4.4
4
Question 7 (5 points)
A rectangular quilt has a long side of 8 feet. A ribbon runs diagonally through the center of the quilt. The angle formed by the ribbon and the shorter side is 50 degrees. What is the perimeter of the quilt? Round to the nearest foot.
Question 7 options:
31 feet
29 feet
32 feet
16 feet
Question 8 (5 points)
Which scenario would most likely be normally distributed?
Question 8 options:
Number of fingers each person has in a restaurant.
Length of a movies at the theater.
Number of crayons in a box.
Age of children at a park.
Answers
Answer:
Step-by-step explanation:
i) Recursive rule is
[tex]a_{n+1} =a_n-10[/tex]
2) Explicit rule for the sequence is
this is arithmetic sequence with a = -1 and d = 15
Hence
[tex]a_n=-1+15(n-1)\\a_n=15n-16[/tex]
3) [tex]P(A and B) = \frac{2}{25} (\frac{5}{6} )\\=\frac{1}{15}[/tex]
4) Sample men = total/no of entries
=[tex]\frac{409}{10} =40.9[/tex]
=41
kent can paint a certain room in 6 hours, but Kendra needs 4 hours to paint the same room. How long does it take them to paint the room if they work together?
Answers
About 2 and a half hours
Collin surveyed 12 teachers At his school to determine how much each person budgets for lunch. He recorded his results in the table.
(Answers are listed in photo)
Answers
Answer:
mean =median, so the data is symmetrical
Step-by-step explanation:
Given
Data set= {10,5,8,10,12,6,8,10,15,6,12,18}
Mean= Sum of data points/number of data points
= (10+5+8+10+12+6+8+10+15+6+12+18)/12
=10
Median= mid value
={5,6,6,8,8,10,10,10,12,12,15,18}
Middle values are 10 and 10
Median = 10+10/2
= 20/2
= 10
Mean= median so there will be no skewness and the distribution is equal !
Lacy draws a diamond from a standard deck of 52 cards. Without replacing the first card, she then proceeds to draw a second card and gets a spade.
Are these events independent?
Input Yes or No:
Determine the probability of drawing a diamond and then a spade without replacement.
Write your answer in decimal form, rounded to four decimal places as needed.
Answer =
Linda draws a diamond from a standard deck of 52 cards. She returns the diamond to the deck, then draws a second card. Her second card is a spade.
Are these events independent?
Input Yes or No:
Determine the probability of drawing a diamond and then a spade with replacement.
Write your answer in decimal form, rounded to four decimal places as needed.
Answer =
Answers
Answer:
a) i) No
ii) Probability of drawing a diamond and then spade without replacement is 0.0637.
b) i) Yes
ii) Probability of drawing a diamond and then spade with replacement is 0.0625
Step-by-step explanation:
Part a) Without replacement:
i) Are these events independent?
No, because the both events are dependent. because a card taken out of the deck is not replaced back before taking out the other card so the chances of event occur change.
ii) Determine the probability of drawing a diamond and then a spade without replacement.
Probability of drawing a diamond and then spade = (Probability of drawing a diamond) * (Probability of drawing a spade)
Probability of drawing a diamond :
Total cards in deck = 52
Diamonds = 13
Probability of drawing a diamond = 13/52
Probability of drawing a spade:
Total cards in deck after taking diamond = 52 -1 =51
Spades = 13
Probability of drawing a spade = 13/51
Probability of drawing a diamond and then spade = 13/52 * 13/51
= 169/2652
=0.0637
So, Probability of drawing a diamond and then spade without replacement is 0.0637
Part b) With replacements
i) Are these events independent?
Input Yes or No:
Yes, these events are independent because a card taken out of the deck is replaced back before taking out the other card so the chances of event occur doesn't change.
ii) Determine the probability of drawing a diamond and then a spade with replacement.
Probability of drawing a diamond and then spade = (Probability of drawing a diamond) * (Probability of drawing a spade)
Probability of drawing a diamond :
Total cards in deck = 52
Diamonds = 13
Probability of drawing a diamond = 13/52
Probability of drawing a spade:
Total cards in deck after replacing diamond = 52
Spades = 13
Probability of drawing a spade = 13/52
Probability of drawing a diamond and then spade = 13/52 * 13/52
= 169/2704
=0.0625
So, Probability of drawing a diamond and then spade with replacement is 0.0625
The first two events are not independent, with a probability P = 0.0637
The second pair of events is independent, and the probability is P = 0.0625
How to get the probabilities?
First, all the cards on the deck have the same probability of being randomly drawn, which will be p = 1/52.
A) Now, if Lacy first draws a diamond card, now the number of cards in the deck are less (now there are 51 cards on the deck). So the probability of drawing now a spade is larger than before. Then the first two events are not independent.
The probability of drawing a diamond card at first is:
P = 13/52 (because there are 13 diamonds and a total of 52 cards).
The probability of drawing a spade after is:
Q = (13/51)
The joint probability is the product of the individual probabilities, this will give:p = P*Q = (13/52)*(13/51) = 0.0637
B) Now we replace the first card, then the events are now independent, as the probability of drawing a spade after the first draw is not changed (because the total number of cards will be 52).
The probability of drawing a diamond is:
P = 13/52
Now we replace the diamond card drawn.
The probability of drawing a spade will be:
Q = 13/52
The joint probability is:
p = P*Q = (13/52)^2 = 0.0625
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Which of the following numbers is located between points Q and R on the number line?
Answers
your answer is b) 3.88
Reasoning: It appears that the space between each number is divided into 5 spaces, and beause decimal places are divided into tenths, simply divide ten by the fove spaces, and each dash will represent an increase in two hundredths (x.x0) in the decimal. For Q, it is located on the third dash from 3.8, therefore we have to multiply the three ticks by two hundredths for each tick, and that will come out to 6 hundredths, and when added to that 3.8, we can determine that Q is located at 3.86. The same can also go for R, as it is located one tick from 3.9, and one tick times 2 added hundredths will equal adding two more hundredths to 3.9, allowing us to determine that R is located at 3.92. So, with Q at 3.86 and R at 3.92, our answer is between those two numbers, the only option being our answer of 3.88 (b).
What is the probability of on-time arrival in class given that the subject is biology? A. 90.1% B. 88.5% C. 84.7% D. 82.4% E. insufficient data
Answers
Answer:
Answer is D 82.4%
Step-by-step explanation:
Got it right on the test :)
The probability of on-time arrival in class given that the subject is biology is 82.4%
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
From the definition, the probability is the ratio of total favourable outcome to total outcome.
From the data table, the probability of on-time arrival in class given that the subject is biology:
= 82.4%
Thus, the probability of on-time arrival in class given that the subject is biology is 82.4%
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The focus point of the parabola?
Answers
The focus point of the parabola is (2,-2).
ANSWER
[tex](2,- 1)[/tex]
EXPLANATION
The given parabola is
[tex]y = \frac{1}{4} {x}^{2} - x - 1[/tex]
We need to write this parabola in the vertex form by completing the square,
[tex]y = \frac{1}{4} ( {x}^{2} - 4x) - 1[/tex]
[tex]y = \frac{1}{4} ( {x}^{2} - 4x + 4) - \frac{1}{4} \times 4 - 1[/tex]
[tex]y = \frac{1}{4} (x - 2 )^{2} - 2[/tex]
[tex] {(x - 2)}^{2} = 4(y + 2)[/tex]
The vertex is
(2,-2)
The focal length is
[tex]p = 1[/tex]
The focus is
[tex](2,-2 + 1)[/tex]
[tex](2,- 1)[/tex]
Please help. I don’t understand what to do
Answers
[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=23.9\\ h=100 \end{cases}\implies V=\cfrac{\pi (23.9)^2(100)}{3} \\\\\\ V=\cfrac{57121\pi }{3}\implies V\approx 59816.97\implies \stackrel{\textit{rounded up}}{V=59817} \\\\[-0.35em] ~\dotfill[/tex]
now, for the second one, we know the diameter is 10, thus its radius is half that or 5.
[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5\\ V=225 \end{cases}\implies 225=\cfrac{\pi (5)^2 h}{3}\implies 225=\cfrac{25\pi h}{3} \\\\\\ \cfrac{225}{25\pi }=\cfrac{h}{3}\implies \cfrac{9}{\pi }=\cfrac{h}{3}\implies \cfrac{27}{\pi }=h\implies 8.59\approx h\implies \stackrel{\textit{rounded up}}{8.6=h}[/tex]
Hey guys I need help simplifying this radical expression please. ASAP please.
Answers
Answer:
go on symbolab type the equation in and it gives u anwsers and work
Step-by-step explanation:
=\frac{4}{\left(x+2\right)\left(x+4\right)}
the table below shows all possibilities of the outcome of rolling two 6-sided number cubes what is the possibility of rolling a sum of 8
Answers
Answer:
Final answer is [tex]\frac{5}{36}[/tex].
Step-by-step explanation:
Given that two 6-sided number cubes are rolled. Now we need to find about what is the possibility of rolling a sum of 8.
From the sample space, you can see that there are total 36 possible outcomes.
out of those outcomes, there are only 5 outcomes that has sum = 8
which are {(2,6), (3,5), (4,4), (5,3), (6,2)}.
Hence probability of rolling a sum of 8 [tex]=\frac{5}{36}[/tex].
Hence final answer is [tex]\frac{5}{36}[/tex].
Based on the sample results, about what proportion of the population has a favorite social network?
HURRYYYYYY XD
Social Network | Proportion
-------------------------------------------
Site A: | P= 0.24
Site B: | P= 0.30
Site C: | P= 0.26
No Favorite: | P= 0.20
Options--
A-about 0.54
B-about 0.80
C-about 0.20
D-about 0.24
Answers
Answer:
the real answer is about 0.80
Step-by-step explanation:
so it is asking you about what proportion of the population has a favorite social network, and you see that there is a category that is a no favorite and site A B and C are the sites that are favorites. You add 0.24 + 0.30 + 0.26 and you get 0.80. And that is how you get 0.80
Product or quotient
3.92·0.6
0.78·0.13
5.004×1.2
6.3÷0.7
2.25÷1.5
8.1÷0.003
Answers
Answer:
2 44⁄125 [2,352] → Product
507⁄5000 [0,1014] → Product
6 3⁄625 [6,0048] → Product
9 → Quotient
1½ [1,5] → Quotient
2700 → Quotient
Step-by-step explanation:
Treat the decimals as whole numbers by moving the decimal marks all the way to the end of each decimal first, evaluate, then move the decimal mark back to the left the number of times as you started on for both decimals in total.
I hope this helps you out, and as always, I am joyous to assist anyone at any time.
Help me don’t respond if you aren’t 100% sure please please
Answers
it is 8/15 because if you count all the groups it is 15 and if you count all the numbers 1 it is 8 which is 8/15
Classify the triangle shown below. Check all that apply.
Answers
Answer:
It's actually right and scalene
Step-by-step explanation:
Since there is a ninety degree angle, it isn't obtuse or acute because the angle is a right angle. And since all the side lengths are different, it must be scalene in comparison to isoceles or equilateral.
The given triangle is Right angled triangle and Scalene triangle i.e. option A and E.
What is triangle ?Triangle is a two dimensional shape having three side and sum of all angles is equals to .
We have,
A triangle with,
Angles of 90°, 53°, 37° and
Sides 3, 4, 5.
So,
We know that,
When a triangle have any angle equals to 90° then it is a Right angled triangle.
Now,
When a triangle have any three sides unequal and all three angles are of different measures, then it is Scalene triangle.
So,
From the above mentioned statements we can say that triangle is Right angled and Scalene triangle.
Hence, we can say that the given triangle is Right angled triangle, Scalene triangle.
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What is the volume of the following rectangular prism?
Answers
Step-by-step explanation:
v= 1/2x1 3/7
v= 7/8 units 3
Kloh put $3000 dollars in a savings account that earns 4% annually, compounded monthly. use logarithms to find how long would it would take for her to double her money?
Answers
Answer:
[tex]17.4\ years[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=?\ years\\ P=\$3,000\\ r=0.04\\n=12\\ A=\$6,000[/tex]
substitute in the formula above
[tex]\$6,000=\$3,000(1+\frac{0.04}{12})^{12t}[/tex]
[tex]2=(\frac{12.04}{12})^{12t}[/tex]
Applying log both sides
[tex]log(2)=log[(\frac{12.04}{12})^{12t}][/tex]
[tex]log(2)=(12t)log[(\frac{12.04}{12})][/tex]
[tex]t=log(2)/[(12)log(\frac{12.04}{12})]=17.4\ years[/tex]
Which statement is true about the given information?
BD = 1/2BC
BC = 1/2 BE
OBD CE
BC - BD
Answers
- Since lines BC, CD, and DE are all congruent, then we know that every time a line reaches either a point or an orange line, we can consider that to have a value of 1, for instance. BD and CE, in this case, both have a value of 6, and therefore the correct answer is BD=CE.
The option third BD ≅ CE is correct because BD and CE are equal in length, so they are congruent.
What is the congruent geometry?Congruent geometry are those that are exactly the same size and shape. Congruent is represented by the symbol ≅
We have a line segment shown in the figure:
From the figure:
BD = 2BC
BE = 3BC
BC ≅ BD (as the BC and BD are unequal in length, so they cannot be congruent)
BD ≅ CE (as the BD and CE are equal in length, so they are congruent)
Thus, the option third BD ≅ CE is correct because BD and CE are equal in length, so they are congruent.
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solve the system of equations
-2×+9y=11
-5×+2y=-34
×=____
y=____
someone help please!
Answers
X will equal 8 and y would equal 3
The solution to the system of equations -2x + 9y = 11 and -5x + 2y = -34 is found using the elimination method. The solution is x = 8 and y = 3.
Explanation:The system of equations provided appears to be:
-2x + 9y = 11 -5x + 2y = -34
To solve this system, we can use the method of substitution or elimination. In this case, we'll use the elimination method. First, we want to manipulate the equations so that when we add them together, one of the variables gets eliminated.
Let's multiply the first equation by 5 and the second equation by 2:
(-2x + 9y) * 5 => -10x + 45y = 55 (-5x + 2y) * 2 => -10x + 4y = -68
Now, we subtract the second equation from the first:
-10x + 45y - (-10x + 4y) = 55 - (-68)
Which simplifies to:
41y = 123
Divide both sides by 41 to find the value of y:
y = 123 / 41 = 3
Now, substitute y = 3 into one of the original equations to solve for x. We'll use the first equation:
-2x + 9(3) = 11
-2x + 27 = 11
-2x = 11 - 27
-2x = -16
Divide both sides by -2:
x = -16 / -2 = 8
The solutions to the system of equations are x = 8 and y = 3.
if $10,000 is invested in an acount earning 5.5% interest compounded continuously,determine how long it will take the money to triple.
Answers
To determine how long it will take for $10,000 to triple with a continuous compounded interest rate of 5.5%, we use the continuous compound interest formula. Solve the equation for t by taking the natural logarithm of both sides and dividing by the interest rate, which yields t = ln(3) / 0.055.
Explanation:The subject at hand deals with Continuous Compound Interest. The formula used to calculate this is A = Pe^(rt), where A is the final amount, P is the initial principal, r is the yearly interest rate and t is the time in years.
In this case, the initial principal P is $10,000, the final amount (A) we want is $30,000 (because we want to triple the money), and the rate r is 5.5% or 0.055 as a decimal. We want to find t.
Plugging into the formula, we get 30000 = 10000 * e^(0.055t). Dividing both sides by 10000 yields 3 = e^(0.055t). If we take the natural log (ln) of both sides, the equation simplifies to ln(3) = 0.055t. Finally, solving for t, we get t = ln(3) / 0.055.
This will give you the number of years it'll take for the money to triple at an interest rate of 5.5% compounded continuously.
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Can some one help me this is due to night
Answers
Answer:
Step-by-step explanation:
I am very good at Pythagorean theorem I did it this year. So A=85 E=73 S=37 L=66.5 (or 65) T=82 P=53 D=10 O=89 C=17
To do this it is actually like the easiest thing to do in math. The formula is A²+B²=C². To do this it is easier with a scientific calculator. If you don't have one you can use this online calculator: desmos.com/scientific
Step 1. get the two number and square (²) them ( multiply that number by it) For Example 30 multiplied by 30. Or on the calculator I gave you just do 30²+40²
Step 2. After that you will get 2500. Then on the calculator get this symbol √ and but the number 2500 in front of it. it should look like this. √2500.
Step 3. After that you will get 50 which is your answer. And that is how you do Pythagorean theorem.
I hope that helped you. If you don't have a scientific calculator you can use the link I provided above. If you can't use it I reccomend buying one.
A line segment begins at the point (-4,-9) and ends at the point (21, 31.625).
What are the coordinates of the point that partitions this line segment into two line segments whose lengths are in the ration of 2:3?
Answers
Answer:
(6 , 7.25)
Step-by-step explanation:
Given in the question coordinates (-4,-9) and (21,31.625)
x1 = -4
y1 = -9
x2 = 21
y2 = 31.625
Ratio
a : b
2 : 3
Formula to use
x = x1 + [tex]\frac{a}{a+b}[/tex](x2-x1)
y = y1 + [tex]\frac{a}{a+b}[/tex](y2 -y1)
Plug values on the formula
x = -4 + [tex]\frac{2}{2+3}(21+4)[/tex]
x = 6
y = -9 + [tex]\frac{2}{2+3}(31.625+9)[/tex]
y = 7.25
Co-ordinates of the point which divide the line into 2:3 is
(6 , 7.25)
Final answer:
To divide a line segment with endpoints (-4, -9) and (21, 31.625) in a 2:3 ratio, we use the section formula to find the partition point, which is (21, 7.25).
Explanation:
The student is asking how to find the point that divides a line segment in a particular ratio, which is a common problem in coordinate geometry. Given the end points of the line segment at (-4,-9) and (21, 31.625) and the ratio of 2:3, we can use the section formula to find the required point.
Here's how we do it step by step:
To partition the segment in the ratio of 2:3, multiply the coordinates of the first point by 3, and the coordinates of the second point by 2.Add the results from step 1 to obtain the sum for each coordinate.Finally, divide these sums by the sum of the ratios, which is 2+3=5.Applying the formula, the coordinates of the point (x, y) are:
x = (-4×3 + 21×2)/5 = (63 + 42)/5 = 105/5 = 21
and
y = (-9×3 + 31.625×2)/5 = (-27 + 63.25)/5 = 36.25/5 = 7.25
Therefore, the coordinates of the partitioning point are (21, 7.25).
Eric is a computer programmer who earns a years salary of $35,400. What is his weekly salary?
Answers
Answer:
Eric's weekly salary is $680.77
Step-by-step explanation:
$35,400 divided by the number of weeks in a year, Which is 52. 52/35,400=680.77
Which word does NOT belong with the others? A. triangle B. circle C. oval D. sphere
Answers
Answer:
A triangle
Step-by-step explanation:
If you slice open all of these shapes you will see a circle except the triangle.
Answer:
A triangle because the other shapes are to do with circles.
Answer A.
Permutation problem that I just do not feel like solving
Your cousin, who is planning her wedding, is working on the seating chart for the reception. She is trying to decide which 6 people should be seated at the table closest to the head table. She has narrowed her decision down to a list of 10 friends.
If the order doesn't matter, in how many ways can she choose 6 friends from the list of 10 to sit at the table closest to the head table?
Answers
210. she has 210 ways to choose 6 friends from the list of 10 to sit at the table closest to the head table no matter the order.
This is a problem of combinations and can be solved using the equation [tex]nC_{k}=\frac{n!}{k!(n-k)!}[/tex], where n! and k! is the factorial of a number. The factorial is defined in principle as the product of all positive integers from 1 (ie, natural numbers) to n.
She has a list of 10 friends and we want to know in how many ways she can choose 6 friends.
Using the combinations equation, with n = 10 and k = 6:
[tex]10C_{6}=\frac{10!}{6!(10-6)!}=\frac{10!}{6!(4!)}=\frac{10.9.8.7}{4.3.2.1}=\frac{5040}{24} =210[/tex]
Find the eighth term of the
geometric sequence, given the
first term and common ratio.
a1=6 and r=-1/3
PLEASE HELP
Answers
Answer:
see explanation
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio, hence
[tex]a_{8}[/tex] = 6 × [tex](-1/3)^{7}[/tex] = 6 × - [tex]\frac{1}{3^{7} }[/tex] = 6 × - [tex]\frac{1}{2187}[/tex] = - [tex]\frac{2}{729}[/tex]