I need help Options for the first box: -3, 1/3, 3, -1/3 Options for the second box -303, 363, 183, -60
Answers
To find the common ratio of the sequence, divide each of the elements of the sequence by the element that precedes it:
[tex]\begin{gathered} \frac{-9}{3}=-3 \\ \frac{27}{-9}=-3 \\ \frac{-81}{27}=-3 \end{gathered}[/tex]Since the quotient is always -3, then the common ratio is equal to -3.
To find the fifth term of the sequence, multiply the fourth term, which is -81, times -3:
[tex]-81\times-3=243[/tex]Once that we know the first five terms of the sequence, add them to find their sum:
[tex]\begin{gathered} 3-9+27-81+243 \\ =-6+27-81+243 \\ =21-81+243 \\ =-60+243 \\ =183 \end{gathered}[/tex]Therefore:
The common ratio of the sequence is -3.
The sum of the first five terms of the sequence is 183.
Related Questions
The function used to compute the probability of x successes in n trials, when the trials are dependent, is the _____. a.binomial probability functionb.Poisson probability functionc.hypergeometric probability functiond.exponential probability function
Answers
Given:
The function used to compute the probability of x successes in n trials, when the trials are dependent.
Required:
To choose the correct option for the given statement.
Explanation:
The hypergeometric distribution is a discrete probability distribution. It is used when you want to determine the probability of obtaining a certain number of successes without replacement from a specific sample size.
Therefore the option c is correct.
Final Answer:
c ) hypergeometric probability function.
17. 19yd. 28in.- 16yd. 31in.18. 61wk. 4da.- 18wk. 6da.21. 8tbsp. 2tsp. * 15
Answers
We need to solve the next expressions:
17. 19yd. 28in.- 16yd. 31in
We need to solve subtract each expression.
Then:
19yd. 28in.- 16yd. 31in =
19yd - 16yd and 28in-31in
3yd -3in
Then, we have the next equivalent.
1 yard = 36 in
So:
36 in - 3 in = 33 in
Therefore
19yd. 28in.- 16yd. 31in = 2 yard 33
18 61wk. 4da.- 18wk. 6da.
We need to subtract both expression:
Then
61wk - 18wk = 43kw
4da-6da = -2da
Where 1 week = 7 days
Then
7 da - 2da = 5 da
Hence, 43kw -1 wk = 42 wk.
The result is:
42 wk 5 da
21. 8tbsp. 2tsp. * 15
We need to convert 2ts into tbsp and then multiply the result by 15.
If
1 tsp ------- 0.333tbsp
Then
2tp ------ 2(0.333tbsp)= 0.66666 tbsp
Now
(8tbsp + 0.6666 ) * 15 = 130 tbsp
Open the most convenient method to graft the following line
Answers
You have the following expression:
3x + 2y = 12
the best method to graph the previous expression is by intercepts.
In this case, you make one of the variables zero and solve for the other one. Next, repeat the procedure wi
A gumball machine contains 5 blue gumballs and 4 red gumballs. Two gumballs are purchased, one after the other, without replacement.
Find the probability that the second gumball is red.
Answers
===================================================
Work Shown:
5 blue + 4 red = 9 total
A = P(1st is red, 2nd is red)
A = P(1st is red)*P(2nd is red, given 1st is red)
A = (4/9)*(3/8)
A = 12/72
B = P(1st is blue, 2nd is red)
B = P(1st is blue)*P(2nd is red, given 1st is blue)
B = (5/9)*(4/8)
B = 20/72
C = P(2nd is red)
C = A+B
C = 12/72 + 20/72
C = 32/72
C = 4/9
How do I get my answer?
Answers
Answer:
[tex] \frac{2}{9 {d}^{14} } [/tex]
Step-by-step explanation:
[tex] \frac{ {4d}^{ - 5} }{18 {d}^{9} } = \frac{4}{18} \times \frac{ {d}^{ - 5} }{ {d}^{9} } = \frac{2}{9} {d}^{ - 14} = \frac{2}{ {9d}^{14} } [/tex]
In shop, you make a table. The sides of the table measure 36" and 18". If the diagonal of the table measures 43", is the table "square"? (In construction, the term "square" just means the table has right angles at the corners.)
Answers
We are given the following information:
Table sides = 36 inches & 18 inches
Diagonal of table = 43 inches
We are to find out if the table is "square" (that is if the table follows the Pythagoras theorem). We will check this below:
[tex]\begin{gathered} \text{The Pythagoras Theorem is given by:} \\ c^2=a^2+b^2 \\ c=43in,b=36in,a=18in \\ \text{Substituting we have:} \\ 43^2=18^2+36^2 \\ 1849=324+1296 \\ 1849=1620 \\ \Rightarrow1849\ne1620 \\ \\ \therefore\text{ The table is not ''square''} \end{gathered}[/tex]Therefore, the table is not "square" (it does not have right angles at the corners)
Dianne is 23 years older than her daughter Amy. In 5 years, the sum of their ages will be 91. How old are they now?Amy is ? years old, and Dianne is ? years old.
Answers
Currently
Let Amy's current age be x. Since Dianne is 23 years older than her daughter, then she is (x + 23) years old.
In 5 years
Amy's age will be (x + 5) years.
Dianne's age will be:
[tex]x+23+5=(x+28)\text{ years}[/tex]The sum of their ages in 5 years is 91. Therefore, we have:
[tex](x+5)+(x+28)=91[/tex]Solving, we have:
[tex]\begin{gathered} x+5+x+28=91 \\ 2x=91-5-28 \\ 2x=58 \\ x=\frac{58}{2} \\ x=29 \end{gathered}[/tex]Amy is 29 years old. Therefore, Dianne will be:
[tex]29+23=52\text{ years old}[/tex]ANSWER:
Amy is 29 years old, and Dianne is 52 years old.
200 lottery tickets are sold for $6 each. The person with the single winning ticket will get $71. What is the expected value for a ticket in this lottery?
Answers
Given:
200 lottery tickets are sold for $6 each.
The person with the single winning ticket will get $71.
So, The probability of winning = 1/200
The probability of losing =
[tex]undefined[/tex]
Answer: the expected value is. aroud 1-2
Step-by-step explanation:
How do you decide which rational number operations to use to solve problems
Answers
One can decide which rational number operations to use to solve problems based on the context of the information.
What is a rational number?Studying rational numbers is significant because they illustrate how the world is so complex that we will never be able to comprehend it.
A rational number is defined as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively. Every integer and 3/7, for example, are rational numbers.
A rational number is defined as the quotient of the fraction p/q of two integers, a numerator p and a non-zero denominator q. Every integer is a rational number since q might be equal to 1.
In this case, the operation include addition, subtraction, division, etc. This will be based on the context.
Learn more about rational numbers on:
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Eliana drove her car 81 km and used 9 liters of fuel. She wants to know how many kilometres she can drive on 22 liters of fuel. She assumes her car will continue consuming fuel at the same rate. How far can Eliana drive on 22 liters of fuel? What if Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km? How many liters of fuel does she need?
Answers
Eliana can drive 198 km with 22 liters of fuel.
If Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km then she would need 15.5 liters of fuel
In this question, we have been given Eliana drove her car 81 km and used 9 liters of fuel.
81 km=9 liters
9 km= 1 liter
She wants to know the distance she can drive on 22 liters of fuel. She assumes her car will continue consuming fuel at the same rate.
By unitary method,
22 liters = 22 × 9 km
= 198 km
Also, given that if Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km.
We need to find the amount of fuel she would need.
Let 139.4 km = x liters
By unitary method,
x = 139.4 / 9
x = 15.5 liters
Therefore, Eliana can drive 198 km with 22 liters of fuel.
If Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km then she would need 15.5 liters of fuel
Learn more about Unitary method here:
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One pump can empty a pool in 7 days, whereas a second pump can empty the pool in 14 days. How long will it take the two pumps, working together, to empty the pool? (Fractional answers are OK.)The first pump's rate is_____per day.The second pump's rate is____per day.The combined pumps rate is____per day.It will take the two pumps_____per day.
Answers
The first step is to define the daily rates of each pump
From the information given,
First pump can empty the pool in 7 days. This means that
Daily rate of first pump = 1/7
The first pump's rate is 1/7 per day
Second pump can empty the pool in 14 days. This means that
Daily rate of second pump = 1/14
The second pump's rate is 1/14 per day
Let t be the number of days it will take both pumps, working together to empty the pool. Thus,
combined daily rate of both pumps = 1/t
The rates are additive. It means that
1/7 + 1/14 = 1/t
Simplifying the left side, we have
3/14 = 1/t
The combined pumps rate is 3/14 per day
By taking reciprocal of both sides,
t = 14/3 = 4.67
It will take the two pumps 4.67 days to empty the pool together
Use Descartes Rules of signs to complete the chart with possibilities for the nature of the roots of the following equations:A) x^3 - x^2 + 4x - 6 = 0B) x^5 - x^3 + x + 1 = 0
Answers
Given:
[tex]\begin{gathered} x^3-x^2+4x-6=0 \\ x^5-x^3+x+1 \end{gathered}[/tex]Required:
To determine the possibilities for the nature of the roots of the given equation.
Explanation:
(A)
A statement of Chandler's biweekly earnings is given below. What is Chandler's gross pay?
Answers
SOLUTION:
Step 1:
In this question, we are asked to calculate Chandler's gross pay from the statement of bi-weekly earnings.
Step 2:
To get the Gross pay, we need to do the following:
[tex]\text{Gross pay - Total Deductions = Net Pay}[/tex]Now, we need to calculate Total Deductions:
[tex]\text{ \$ 105.00 + \$ 52.14 + \$ 10.62 + \$ 26. 15 = \$ 193.91}[/tex]Now, we have that the Net Pay = $ 780. 63
Then,
[tex]\begin{gathered} \text{Gross Pay - \$ 193. 91 = \$ 7}80.\text{ 63} \\ \text{Gross pay = \$ 780.63 + \$ 193.91} \\ \text{Gross Pay = \$ 974. 54} \end{gathered}[/tex]CONCLUSION:
Chandler's Gross Pay = $ 974. 54
the fraction 1-2 equals?
Answers
The given fraction is 1/2.
IF we divide, we have
[tex]\frac{1}{2}=0.5[/tex]Therefore, the answer is 0.5.What is the value of the expression below when z6?9z + 8
Answers
Hello!
Let's solve your expression:
[tex]9z+8[/tex]Let's replace where's z by 6, look:
[tex]\begin{gathered} (9\cdot z)+18 \\ (9\cdot6)+18 \\ 54+18 \\ =72 \end{gathered}[/tex]So the value of this expression when z=6 is 72.
Jim baked 48 cookies with 4 scoops of flour. How many scoops of flour does Jim need in orderto bake 96 cookies? Assume the relationship is directly proportional.
Answers
Given:
Jim baked 48 cookies with 4 scoops of flour.
So, the unit rate will be = 48/4 = 12 cookies/scoop of flour
So, for 96 cookies, the number of scoops of flour will be =
96/12 = 8
So, the answer will be 8 scoops of flour
Find the principal which amounts to #5,000 at simple interestin 5 years at 2% per annum
Answers
To answer this we have to apply the simple interest formula:
I =P x r x t
Where:
I= interest
P= Principal
R= Interest rate ( in decimal form)
t = time (years)
Replacing with the values given:
Interest= I
Principal = ?
Interest rate = 2/100 =0.02
time= 5 years
I = P x 0.02 x 5
I= 0.1P
Amount= P+I
A = P+0.1P
5,000= P+0.1P
5,000= 1.1P
5,000/1.1 =P
4,545.45 =P
Draw the angle 0=-pi/2 in standard position find the sin and cos
Answers
An angle in standard position has the vertex at the origin and the initial side is on the positive x-axis.
Thus, the initial side of the angle is:
Now, half the circumference measures pi, thus, pi/2 is a quarte of the circumference. As we want to find the angle -pi/2, then we need to rotate the terminal side clockwise:
Find the sine and the cosine.
The sine and the cosine in the unit circle are given by the coordinates as follows:
[tex](\cos\theta,\sin\theta)[/tex]As can be seen in the given unit circle, the terminal side is located at:
[tex](0,-1)[/tex]Thus, the values of cosine and sine are:
[tex]\begin{gathered} \cos\theta=0 \\ \sin\theta=-1 \end{gathered}[/tex]Can you evaluate 3 + (a + 4)(8- b ) when a= 5 and b=6
Answers
The expression to evaluate is:
[tex]3+a+4\mleft(8-b\mright)[/tex]When
a = 5 and b = 6
We simply plug in the values of 5 and 6, into a and b respectivly. And do algebra to get our answer. The process is shown below:
[tex]\begin{gathered} 3+a+4\mleft(8-b\mright) \\ 3+5+4\mleft(8-6\mright) \\ 3+5+4(2) \\ 3+5+8 \\ 16 \end{gathered}[/tex]The answer is 16.
I have tried but but there is some part that i keep getting wrong
Answers
we have that
K is the center of circle
J -----> point of tangency
segment IK is a radius
segment JL is a chord
segment GI is a secant
segment JI is a diameter
segment GJ is a tangent
arc JIL is a major arc
arc JL is a minor arc
arc JLI is a half circle (180 degrees)
Part 2
we have that
arc TU=87 degrees -------> by central anglearc ST
Remember that
arc ST+87+72=180 degrees ------> by half circle
so
arc ST=180-159
arc ST=21 degreesarc WV
we have
arc WV+arc UV=180 degrees -----> by half circle
arc UV=72 degrees
so
arc WV=180-72
arc WV=108 degreesarc VUT
arc VUT=arc VU+arc UT
substitute given values
arc VUT=72+87
arc VUT=159 degreesarc WU=180 degrees -----> by half circle deFind the interest and future value of a deposit of $12,000 at 5.5% simple interest for 10 years.
Answers
Given:
Principal - $12,000
Annual Interest Rate = 5.5% or 0.055 in decimal form
Time in years = 10 years
Find: simple interest and future value
Solution:
The formula for getting the simple interest is:
[tex]Interest=Principal\times Rate\times Time[/tex]Let's replace the variables in the formula with their corresponding numerical value.
[tex]Interest=12,000\times0.055\times10[/tex][tex]Interest=6,600[/tex]The interest after 10 years is $6, 600.
So, if the interest is 6,600, the future value of the money is:
[tex]FV=Principal+Interest[/tex][tex]FV=12,000+6,600[/tex][tex]FV=18,600[/tex]The future value of the deposited money after 10 years is $18, 600.
I'll send in pictures of the question questions 2 goes with number 1
Answers
Since the equation is y=3/8x and x is equal to 44/3, we have
[tex]\begin{gathered} y=\frac{3}{8}\cdot\frac{44}{3}=\frac{132}{24} \\ \frac{132}{24}=\frac{66}{12}=\frac{33}{6}\text{ Simplifying} \\ \frac{33}{6}=5.5\text{ Dividing} \\ \text{Answer is: }y=5.5 \end{gathered}[/tex]In 1990, the cost of tuition at a large Midwestern university was $104 per credit hour. In 1998, tuition had risen to $184 per credit hour.
Answers
We have to find the linear relationship for the cost of tuition in function of the year after 1990.
The cost in 1990 was $104, so we can represent this as the point (0, 104).
The cost in 1998 was $184, so the point is (8, 184).
We then can calculate the slope as:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{184-104}{8-0} \\ m=\frac{80}{8} \\ m=10 \end{gathered}[/tex]We can write the equation in slope-point form using the slope m = 10 and the point (0,104):
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-104=10(x-0) \\ y=10x+104 \end{gathered}[/tex]We can then write the cost c as:
[tex]c=10x+104[/tex]We then can estimate the cost for year 2002 by calculating c(x) for x = 12, because 2002 is 12 years after 1990.
We can calculate it as:
[tex]\begin{gathered} c=10(12)+104 \\ c=120+104 \\ c=224 \end{gathered}[/tex]Now we have to calculate in which year the tuition cost will be c = 254. We can find x as:
[tex]\begin{gathered} c=254 \\ 10x+104=254 \\ 10x=254-104 \\ 10x=150 \\ x=\frac{150}{10} \\ x=15 \end{gathered}[/tex]As x = 15, it correspond to year 1990+15 = 2005.
Answer:
a) c = 10x + 104
b) $224
c) year 2005.
y = 3× - 1y = -3× + 1
Answers
Given two equations,
[tex]\begin{gathered} y=3x-1 \\ y=-3x+1 \end{gathered}[/tex]Comapring both equations,
[tex]\begin{gathered} 3x-1=-3x+1 \\ 3x+3x=1+1 \\ 6x=2 \\ x=\frac{2}{6}=\frac{1}{3} \end{gathered}[/tex]Therefore, x = 1/3.
11) What is the area of the composite figure? *7 points6 ftT T2 ft5 ft3ft220O 212223
Answers
Answer: 22
Step-by-step explanation:
Consider the circle x ^ 2 + y ^ 2 = 100 and the line x + 3y = 10 and their points of intersection (10, 0) and B = (- 8, 6) . Find coordinates for a point C on the circle that makes chords AB and AC have equal length . Be sure to justify your answer.
Answers
The equation of circle is given by,
[tex]x^2+y^2=100\text{ ---(1)}[/tex]The equation of line is given by,
[tex]x+3y=10\text{ ---(2)}[/tex]The points of intersection of the circle and line is,
A=(Xa, Ya)=(10, 0)
B=(Xb, Yb)=(-8, 6)
The length of chord AB can be calculated using distance formula as,
[tex]\begin{gathered} AB=\sqrt[]{(X_b-X_a)^2+(Y_b-Y_a)^2} \\ =\sqrt[]{(-8-10)^2+(6-0)^2} \\ =\sqrt[]{(-18)^2+6^2} \\ =\sqrt[]{324+36} \\ =\sqrt[]{360} \\ =6\sqrt[]{10} \end{gathered}[/tex]Let (Xc, Yc) be the coordinates of point C on the circle. Hence, using equation (1), we can write
[tex]X^2_c+Y^2_c=100\text{ ---(3)}[/tex]Using distance formula, the expression for the length of chord AC is given by,
[tex]AC=\sqrt[]{(X_c^{}-X_a)^2+(Y_c-Y_a)^2_{}}[/tex]Since (Xa, Ya)=(10, 0),
[tex]\begin{gathered} AC=\sqrt[]{(X^{}_c-10_{})^2+(Y_c-0_{})^2_{}} \\ AC=\sqrt[]{(X^{}_c-10_{})^2+Y^2_c} \end{gathered}[/tex]It is given that chords AB and AC have equal length. Hence, we can write
[tex]\begin{gathered} AB=AC \\ 6\sqrt[]{10}=\sqrt[]{(X^{}_c-10_{})^2+Y^2_c} \end{gathered}[/tex]Squaring both sides of above equation,
[tex]\begin{gathered} 360=(X^{}_c-10_{})^2+Y^2_c\text{ } \\ (X^{}_c-10_{})^2+Y^2_c=360\text{ ----(4)} \end{gathered}[/tex]Subtract equation (4) from (3) and solve for Xc.
[tex]\begin{gathered} (X^{}_c-10_{})^2-X^2_c=360-100 \\ X^2_c-2\times X_c\times10+100-X^2_c=260 \\ -20X_c=260-100 \\ -20X_c=160 \\ X_c=\frac{160}{-20} \\ X_c=-8 \end{gathered}[/tex]Put Xc=-8 in equation (3) to find Yc.
[tex]\begin{gathered} (-8)^2+Y^2_c=100 \\ 64+Y^2_c=100 \\ Y^2_c=100-64 \\ Y^2_c=36 \\ Y^{}_c=\pm6 \\ Y^{}_c=6\text{ or }Y_c=-6 \end{gathered}[/tex]So, the coordinates of point C can be (Xc, Yc)=(-8, 6) or (Xc, Yc)=(-8, -6).
Since (-8, 6) are the coordinates of point B, the coordinates of point C can be chosen as (-8, -6).
Therefore, the coordinates of point C is (-8, -6) if chords AB and AC have equal length.
Which expression simplifies to 5. A. 27/3 - 14. B. 27/3+4. C. -27/3-4. D. -27/3+14
Answers
Approximate the intervals where each function is increasing and decreasing.
Answers
1)
[tex]\begin{gathered} \text{Increasing:} \\ I\colon(-1.2,2)\cup(1.2,\infty) \\ \text{Decreasing:} \\ D\colon(-\infty,-1.2)\cup(2,1.2) \end{gathered}[/tex]2)
[tex]\begin{gathered} \text{Increasing:} \\ I\colon(-3,0.5) \\ \text{Decreasing:} \\ D\colon(-\infty,-3)\cup(-0.5,\infty) \end{gathered}[/tex]3)
[tex]\begin{gathered} \text{Increasing:} \\ I\colon(3,\infty) \\ \text{Decreasing:} \\ D\colon(-\infty,3) \end{gathered}[/tex]4)
[tex]\begin{gathered} \text{Increasing:} \\ I\colon(-\infty,4) \\ \text{Decreasing:} \\ D\colon(4,\infty) \end{gathered}[/tex]what is the solution to the system 3x-y+5=02x+3y-4=0A. X= -1, Y= -2B. X= -1, Y= 2C. X= 2, Y= -1D. X= 2, Y= 1
Answers
To find the solution to the system of equation
we will use the elimination method
3x - y = - 5 ----------------------------(1)
2x + 3y = 4 -------------------------------(2)
We will eliminate y and solve for x
multiply equation (1) through by 3
9x - 3y = - 15 ------------------------------------(3)
add equation (2) and equation (3)
11x = -11
divide both-side of the equation by 11
x = -1
substitute x = -1 in equation (1) and solve for y
3x - y = - 5
3(-1) - y = -5
-3 - y = -5
add 3 to both-side of the equation
- y = -5 +3
-y = -2
multiply through byb -1
y = 2
Hence, the correct option is B
Use the change of base formula and a calculator to evaluate the logarithm
Answers
The change of base formula states that:
[tex]\log _bx=\frac{\ln x}{\ln b}[/tex]this means that we can caculate any logarithm using the natural logarithm if we make the quotient of the natural logarithm of the original value and the natural logarithm of the original base.
In this case we have:
[tex]\begin{gathered} x=14 \\ b=\sqrt[]{3} \end{gathered}[/tex]Then, using the change of base formula, we have:
[tex]\log _{\sqrt[]{3}}14=\frac{\ln 14}{\ln \sqrt[]{3}}[/tex]Once we have the expression we just evaluate the expression on the right to get the appoximation we need:
[tex]\log _{\sqrt[]{3}}14=\frac{\ln14}{\ln\sqrt[]{3}}\approx4.804[/tex]