Without any more information, the first term can be any number.
Let a be the first term in the geometric progression, and let r be the common ratio between consecutive terms. Then
a + ar + ar ² + ar ³ + ar ⁴ + ar ⁵ = 9 (a + ar + ar ²)
ar ³ + ar ⁴ + ar ⁵ = 8 (a + ar + ar ²)
r ³ + r ⁴ + r ⁵ = 8 (1 + r + r ²)
r ³ (1 + r + r ²) = 8 (1 + r + r ²)
r ³ = 8
r = 2
Now with this ratio, the sum of the first six terms is
a (1 + r + r ² + r ³ + r ⁴ + r ⁵) = a (1 - r ⁶)/(1 - r) = 63a
while the sum of the first three terms is
a (1 + r + r ²) = a (1 - r ³)/(1 - r) = 7a
and of course 63a = 9 • 7a, and this is true for any a.
Leshonda had been working at her job for almost twenty years. She felt like she worked overtime more often than not (more than 50% of the time) and deserved a raise, so she randomly selected 50 paychecks (each for one week of work) and found that she had worked overtime in 32 of those weeks. Use a TI-83, TI-83 plus, or TI-84 calculator to test whether Leshonda worked overtime more often than not. Identify the p-value, rounding to three decimal places.
Answer:
Z statistic = 1.980
Pvalue = 0.024
Step-by-step explanation:
Sample size (n) = number of paychecks = 50
Number of overtime (x) = 32
Let Number of overtime = o
Claim : Overtime work is done more than 50% of the time ;
Null hypothesis:H0: o = 0.5
Alternative hypothesis : H1: o > 0.5
Using the T84 calculator :
Selecting the 1 proportion test under the Stat menu:
p0 = 50% = 0.5
x = 32 ; n = 50 ; >p0
The z test statistic value obtained is 1.980 (3 decimal places)
The P value = 0.024 (3 decimal places)
At α = 0.05 ;
P value < α ; therefore we reject the null
Hence, overtime work is done more than 50% of the time.
What is the slope of a line that passes through the following points (4, 6) and (2, 0)?
Answer:
3
Step-by-step explanation:
Step-by-step explanation:
formula to fine slope
m=tan()=y2-y1/x2-x1
Sophia had 63¢ until she spent 5 nickels. How much money does Sophia have now?
Answer:
38 cents
Step-by-step explanation:
5x5=25
63-25=38
Please help and explain how you got the answer. Im giving out brainliest. || Q3
Answer:6:8
Step-by-step explanation:
What is the answer to this?
Answer:
dfgv nm./
Step-by-step explanation:
Point R on the coordinate grid below shows the location of a car in a parking lot. A second car needs to park 6 units above R to leave room for a utility truck. What are the coordinates of the location of the second car?
Image of a coordinate grid with point R R located at negative 1, negative 3.
(3 points)
(−1, −3)
(−1, 3)
(5, −3)
(5, 3)
Answer:
Point R is located at the point (-1,-3)
The car needs to park 6 units above point R.
When you are moving something up or down on the coordinate grid, you are affecting the y- axis. So to find the coordinates we would keep the x value and add 6 to the y value.
Coordinates of the second car
(-1, -3 +6)
(-1 , 3)
The answer to this question is B
Adding a positive to a negative is the same as subtracting.
EX:
We were adding 6 and -3
Adding 6 and -3 is the same as subtracting 3 from 6.
Either way we get the same answer.
B is your answer
Hope this helps!
The Quality Control Department employs five technicians during the day shift Listed below is the number of times each technician instructed the production foreman to shut down the manufacturing process last week.
Technician Shutdown
Taylor 4
Hurley 3
Gupta 5
Rousche 6
Huang 3
Required:
a. How many samples, without replacement, of size two are possible?
b. Compute the mean of the sample means and compare it to the population mean. (Round your answers to 1 decimal place.)
Solution :
Number of different samples of two technicians possible is = 10, as 2 technicians are to be chosen from a total of 5 technicians.
a). Therefore, 10 different samples are possible of size two.
b).
Sample Shut down Mean
1. Taylor, Hurley 4, 3 3.5
2. Taylor, Gupta 4, 5 4.5
3. Taylor, Rousche 4,6 5
4. Taylor, Huang 4, 3 3.5
5. Hurley, Gupta 3,5 4
6. Hurley, Rousche 3,6 4.5
7. Hurley, Huang 3,3 3
8. Gupta, Rousche 5,6 5.5
9. Gupta, Huang 5,3 4
10. Rousche, Huang 6,3 4.5
42
Now mean of sample means [tex]$=\frac{42}{10}$[/tex] = 4.2
Mean of population is = [tex]$\frac{4+3+5+6+3}{5}$[/tex] = 4.2
Thus both the means are equal.
Ellen collected 88 empty cans to recycle,and Carl collected 72 cans. They packed an equal number of cans into each of two boxes to the recycling center
ellen had 44 per box and carl had 36 per box
but if they had only two boxes altogether then each box had 80 cans in it
What is the value of the expression below? 3x + (12 - 3) - x, when x = 2.5 A. 13 B. 14 C. 15 D. 19
Answer:
The answer to this question is: (B)
Which is "14"
Step-by-step explanation:
Substitute the value of the variable into the equation and simplify.
HOPE this helped if so PLEASE leave a "Rating" and a "LIke" and PLEASE mark me brainliest if I have the best answer! THANKS! :))))
i need also need help with this
Answer:
umm you need help with what
Step-by-step explanation:
there is no question
lb = 64 oz Helppppppppppppp me
[tex]5[/tex]
Answer:
no u
Step-by-step explanation: no no no no no no no no no
12. A company advertises on a website. A worker tracked the number of visits to the
website and the number of clicks on the advertisement. The table shows the data
for several days. A linear function can be used to model the data.
Website Advertisement
Number of Visits
to Website, X
Number of Clicks
on Advertisement, y
14
153
629
38
471
30
914
53
307
21
1,045
60
510
32
1,106
63
Based on the table, what is the best prediction of the number of clicks on the
advertisement if 1,500 people visit the website?
Answer:
The answer is 83
Step-by-step explanation:
It's a build up of a continental slope
Im in 8th grade and hope this helped
find the amount accumlatrd after investing a principal P for t years at an interest rate compound annuay. P= $12,000 r=7.5% t=7
Answer:
A = $19,908.59
Step-by-step explanation:
Compound Interest
Compound interest occurs when the interest earned in a given period is reinvested rather than paying it out. The interest in the next period is then earned on the principal sum plus previously accumulated interest.
The formula is:
[tex]{\displaystyle A=P\left(1+{\frac {r}{k}}\right)^{kt}}[/tex]
Where:
A = final amount
P = initial principal balance
r = interest rate
k = number of times interest applied per time period
t = number of time periods elapsed
We are given the following data:
P = $12,000
r = 7.5% = 7.5/100 = 0.075
t = 7
k = 1 since there is only on compounding per year.
Applying the formula:
[tex]{\displaystyle A=\$12,000\left(1+{\frac {0.075}{1}}\right)^{7}}[/tex]
[tex]{\displaystyle A=\$12,000\left(1.075\right)^{7}}[/tex]
A = $19,908.59
does anyone know the answer ?
Answer:
your answer is D.
Step-by-step explanation:
when the square of r crosses over the square will become square-root
A= πr^2
r=√π/A
when A crosses over it has to be under.
True or false
do all states have an income tax?
Answer:
All states have a state income tax. The amount of tax withheld generally depends on the level of income and the number of exemptions claimed.
11) It takes you 15 minutes to frost a 2 layer cake. You and a friend have 100 1 point
cakes to frost for the church bake sale. How many hours will it take the two
of you to frost all of the cakes if you work at the same time rate? Hint: It
takes you 15 minutes to frost one cake, you can frost 4 cakes in 1 hr. *
B. 8 hours
O c. 12.5 hours
Answer:
12.5 hours
Step-by-step explanation:
100/4=25
25/2=12.5
HELP IM IN CLASS DOING IT RIGHT NOW The absolute value of any number is always positive. True False
Answer:
True
Step-by-step explanation:
Answer:
[tex] \huge\purple{TRUE}[/tex]
Step-by-step explanation:
The absolute value of any number is always positive.
A dozen is how much in maths?
Answer:
well for me it's
Step-by-step explanation:
12
But a german dozen is 13
please give me brainlest
x + 5y = 8
3x = 24 - 157
Answer:
x = [tex]-\frac{133}{3}[/tex], y = [tex]\frac{157}{15}[/tex]
Step-by-step explanation:
x + 5y = 8
3x = 24 - 157
3x = 24 - 157
3x = -133
x = [tex]-\frac{133}{3}[/tex]
x + 5y = 8
[tex]-\frac{133}{3}[/tex] + 5y = 8
5y = [tex]\frac{157}{3}[/tex]
y = [tex]\frac{157}{15}[/tex]
What is the volume of the rectangular prism below?
A
16 cubic units
B
20 cubic units
C
23 cubic units
D
32 cubic units
Answer:
D- 32 cubic units
Step-by-step explanation:
count each side and then multiple the numbers
A regression model to predict Y, the state-by-state 2005 burglary crime rate per 100,000 people, used the following four state predictors: X1 5 median age in 2005, X2 5 number of 2005 bank- ruptcies per 1,000 people, X3 5 2004 federal expenditures per capita, and X4 5 2005 high school graduation percentage. (a) Write the fitted regression equation. (b) Interpret each coef- ficient. (c) Would the intercept seem to have meaning in this regression
Answer:
hello your question is incomplete attached below is the complete question
Answer :
a) attached below
b) Agemed ; 2005 median age of population
Fedspend ; 2004 federal spending per capita for all functions
HSGrad% ; 2005 public high school graduation rate
Bankrupt ; 2005 corporate or individual bankruptcies filed per 1,000 population
c) No
Step-by-step explanation:
A) Fitted regression equation
attached below is the excel procedure and the answer related to the question
b) Interpret each coefficient
Agemed ; 2005 median age of population
Fedspend ; 2004 federal spending per capita for all functions
HSGrad% ; 2005 public high school graduation rate
Bankrupt ; 2005 corporate or individual bankruptcies filed per 1,000 population
C) would the intercept seem to have meaning in this regression
The intercept wouldn't have a meaning in this regression
what is the value of x in the eqation 5[x-6] = 2 [x+3]
Answer:
x = 12
Step-by-step explanation:
5x - 30 = 2x + 6
3x = 36
x = 12
Answer:
x=12
Step-by-step explanation:
1) distribute values:
5x-30=2x+6
2) add 30 to both sides
5x=2x+36
3) subtract 2x from both sides
3x=36
4) divide by 3
x=12
What is the y-value of the solution of the system of equations given below?
3x + 2y = -6
y = 2x + 4
can anybody help me and explain how to calculate it?
Answer:
[tex]\frac{\pi }{4}[/tex]
Step-by-step explanation:
1. note, that
[tex]arcsin\frac{1}{2}=\frac{\pi}{6};arcsin\frac{\sqrt{2}}{2}=\frac{\pi}{4};arcsin1=\frac{\pi }{2};arcsin\frac{\sqrt{3}}{2}=\frac{\pi}{3}[/tex]
2. after the substitution:
[tex]\frac{\pi}{6}+\frac{\pi }{4}- \frac{\pi }{2} + \frac{\pi }{3}=\frac{\pi }{4}.[/tex]
A math quiz has 10 questions and is scoreout of 100. Each question is worth the same. The function S (q) represents the quiz score, S, in terms of the number of correctly answered questions, q. Determine whether each statement below is true or false. Select True or False for each stateent.
Answer:
False
True
True
False
Step-by-step explanation:
got it right on the test
I need help with this
Answer:
A
Step-by-step explanation:
process of elimination... :D
the answer below thanks
Answer:
The equation of the circle having centre (-5,-9) and radius r=3 is
x² + 10 x +y² + 14 y + 65 = 0
Step-by-step explanation:
Explanation:-
From graph The centre of the circle C( -5 , -7)
The radius of the circle r = 3cm from the centre of the given circle
The equation of the circle
From graph the centre ( h, k) = ( -5,-7) and r = 3cm
[tex](x-(-5))^2+(y-(-7))^2 = 3^2[/tex]
x² + 10 x +25 +y² + 14 y + 49 =9
x² + 10 x +25 +y² + 14 y + 49 -9=0
The equation of the circle
x² + 10 x +y² + 14 y + 65 = 0
Assume that you have a choice between a manufacturing job and a sales job. The annual earnings from the manufacturing job will have a normal distribution with a mean of $40 000 and a standard deviation of $9 000. The annual earnings from the sales job will have a normal distribution with a mean of $35 000 and a standard deviation of $9 000. What is the probability that you would earn more than $45 000 per year if you select one or the other
Answer:
0.42124
Step-by-step explanation:
Manufacturing job :
Mean (m) = 40,000
Standard deviation (s) = 9000
Sales job :
Mean (m) = 35000
Standard deviation (s) = 9000
Probability of earning more than 45000 if one or the other job is selected;
Obtaining the standardized scores and probability for each :
Z = (x - m) / s
P(x > 45000)
Z = (45000 - 40000) / 9000 = 0.5555
= 0.56
P(Z > 0.56) = 0.28774(Z probability calculator)
For sales :
P(x > 45000)
Z = (45000 - 35000) / 9000 = 1.1111111
= 1.11
P(Z > 1.11) = 0.1335 (Z probability calculator)
0.28774 + 0.1335 = 0.42124
0.25 of 40 plz plz help
What is -23/6 - 7/3
A-37/6
B-30/9
C-16/6
D37/6
Answer:
A
Step-by-step explanation:
i solved it