Answer: [tex]n=13[/tex]
Step-by-step explanation:
Given
Sum of the first 10 terms is equal to sum of 20, 21, and 22 term
[tex]\Rightarrow \dfrac{10}{2}[2a+(10-1)d]=[a+19d]+[a+20d]+[a+21d]\\\\\Rightarrow 5[2a+9d]=3a+60d\\\Rightarrow 10a+45d=3a+60d\\\Rightarrow 7a=15d[/tex]
No of terms to give a sum of 960
[tex]\Rightarrow 960=\dfrac{n}{2}[2a+(n-1)d]\\\\\Rightarrow 1920=n[2a+(n-1)\cdot \dfrac{7}{15}a]\\\\\Rightarrow 28,800=n[30a+7a(n-1)]\\\\\Rightarrow a=\dfrac{28,800}{n[30+7n-7]}\\\\\Rightarrow a=\dfrac{28,800}{n[23+7n]}[/tex]
Value of first term is less than 20
[tex]\therefore \dfrac{28,800}{n[23+7n]}<20\\\\\Rightarrow 28,800<20n[23+7n]\\\Rightarrow 0<460n+140n^2-28,800\\\Rightarrow 140n^2+460n-28,800>0\\\\\Rightarrow n>12.79\\\\\text{For integer value }\\\Rightarrow n=13[/tex]
Answer:
15
Step-by-step explanation:
In the previous answer halfway through they used the equation: 960 = (n÷2)×(2a+(n-1)×(7a÷15))
Using this equation we can substitute an number to replace n, the higher the number is the smaller a would be.
When we substitute 15 into a, then it leaves us with the answer to be a = 15 which is a positive integer and also is smaller than 20, this then let’s us know that 15 is how many terms can be summed up to make 960.
To double check this answer you can find that d = 7 by changing the a into 15 in the formula 7a/15 (found in the previous answer.
Then in the expression: (n÷2)×(2a+(n-1)×d)
substitute:
n = 14 (must be an even number for the equation to work)
a = 15
d = 7
This will give you an answer of 847, but this is only 14 terms as we changed n into 14. To add the final term you need to complete the following equation: 847+(a+(n-1)×d)
substituting:
n = 15
a = 15
d = 7
This will give you the answer of 960, again proving that it takes 15 terms to sum together to make the number 960.
I hope this has helped you.
P.S. Everything in the previous solution was right apart from the start of the last section and the answer
what is the value of digit 6 in9.78265.
Answer: uhh I think 60?
Step-by-step explanation:
the answer is 6p because after any value place is zero hoped I helped
ASAP What is the rule for this relation? i will give brainliest
Answer:
your selected answer is right
What is the explicit formula for the geometric sequence with this recursive
formula?
a =
8
2.-1
(
O A... ----(3)
O B.
11
1
6
• (-4)(n-1)
OC. ,- 1.(-6)(n-1)
=
OD. 2, --5•()
160
Answer:
D)
[tex]an = -6 \times {( \frac{1}{4} )}^{n - 1} [/tex]
Step-by-step explanation:
(See the picture)
The explicit formula is given as [tex]T_n=-6(\frac{1}{4} )^{n-1}[/tex]
Geometric and recursive functionsThe general explicit formula for a geometric sequence is expressed as:
[tex]T_n=ar^{n-1}[/tex]Given the following recursive functions:
[tex]a_1=-6\\ a_n=a_{n-1}\cdot\frac{1}{4} [/tex]
Get the next two terms:
[tex]a_2=a_{1}\cdot\frac{1}{4} \\ a_2=-6\cdot\frac{1}{4} \\ a_2=\frac{-3}{2} [/tex]
For the third term:
[tex]a_3=a_{2}\cdot\frac{1}{4} \\ a_3=\frac{-3}{2} \cdot\frac{1}{4} \\ a_3=\frac{-3}{8} [/tex]
The common ratio for the sequence will be [tex]\frac{1}{4} [/tex]
The explicit formula is given as [tex]T_n=-6(\frac{1}{4} )^{n-1}[/tex]
Learn more on explicit functions here: https://brainly.com/question/10308651
Question 3
A 70kg patient has approximately 8 pints of blood. The patient donates 470mL of blood.
Approximately what fraction of his body's blood is this? (one pint = 568mL)
Step-by-step explanation:
Given that,
The mass of a patient = 70 kg
A 70kg patient has approximately 8 pints of blood.
The patient donates 470mL of blood.
We know that,
1 pint = 568 mL
8 pints = 4544 mL
Required fraction,
[tex]\dfrac{470}{4544}=0.1\\\\=\dfrac{1}{10}[/tex]
So, the required fraction is approximately [tex]\dfrac{1}{10}[/tex].
The graph of f(x) with the graph of w(x)=(x-6)^2
Answer:
A
Step-by-step explanation:
graph is 6 units to the right
if it had been (x+6)^2
it would have been 6 units to left
solve for s 9s+20=−16
Answer:
s = -4
Step-by-step explanation:
Your goal is to manipulate the equation so you can isolate s
9s + 20 = -16
Subtract 20 from both sides to get:
9s = -36
Divide both sides by 9 so s is alone
you end up with s = -4
Answer:
s = -4
Step-by-step explanation:
9s+20=−16
Subtract 20 from each side
9s +20 -20 = -16 -20
9s = -36
Divide by 9
9s/9 = -36/9
s = -4
If the mean, median, and mode are all equal for the set (10, 80, 70, 120, x}, find the value of x.
X
(Simplify your answer. Type an integer or a decimal.)
Question Viewer
Answer:
x=70
Step-by-step explanation:
First, we know that the mode is the number that is the most common. As each value in the set so far only has one of each number, we know that x must be one of the current numbers, making that the mode.
Next, because x is the mode and has to be the median as well, and our number line so far is
(10, 70, 80, 120), x must be either 70 or 80 to make it the median. This is because if x is 10 or 120, we would end up with (10, 10, 70, 80, 120) with 70 as the median or (10, 70, 80, 120, 120) with 80 as the median.
Finally, to calculate the mean, we have
mean = sum / count
The mean must be x, as it is equal to the mode, so we have
x = (10+70+80+120 + x)/5 (as there are 5 numbers including x)
multiply both sides by 5 to remove the denominator
5 * x = 10+70+80+120+x
5 * x = 280 + x
subtract x from both sides to isolate the x and the coefficient
4 * x = 280
divide both sides by 4 to get x
x= 70
We see that x is 70 or 80 and is one of the current numbers, checking off all boxes.
Simplify this plz thanks
Answer:
[tex]\frac{1}{g^{5nd+10v+20dv} }[/tex]
Step-by-step explanation:
13, 5, 4, 9, 7, 14, 4 The deviations are _____.
A. "5, -3, -4, 0, 1, 6, 4"
B."5, -3, -4, 1, -1, 6, -4"
C."6, -3, -4, 1, 2, 6, -4"
D."-5, 3, 4, -1, 1, 6, 4 "
Answer:
B."5, -3, -4, 1, -1, 6, -4"
Step-by-step explanation:
We are given that
13,5,4,9,7,14,4
We have to find the deviation.
Mean=[tex]\frac{sum\;of\;data}{total\;number\;of\;data}[/tex]
Using the formula
[tex]Mean,\mu=\frac{13+5+4+9+7+14+4}{7}[/tex]
[tex]Mean,\mu=\frac{56}{7}=8[/tex]
Deviation=[tex]x_i-\mu[/tex]
[tex]x_i-\mu[/tex]
13 5
5 -3
4 - 4
9 1
7 -1
14 6
4 - 4
Hence, option B is correct.
Chloe has a small dog and a large dog. Each day, the small dog eats 3/4 cup of dog food, and the large dog 2 1/2 cups of dog food. In one week, how much more dog food does the large dog eat than the small dog ?
A. 1 3/4 cups
B. 8 3/4 cups
C. 12 1/4 cups
D. 22 3/4 cups
Answer:
A
Step-by-step explanation:
small dog eats 3/4 cup each day
large dog eats 1 cup each day
~after 1 week (x7)~
small dog = 5.25 cups
large dog = 7 cups
(7-5.25=1.75)
= therefore 1 and 3/4 cups
find out the Range coefficient of the range
marks number of students
20-29 8
30-39 12
40-49 20
50-59 7
60-69 3
Answer:
0.4494
Step-by-step explanation:
Given :
marks number of students
20-29 8
30-39 12
40-49 20
50-59 7
60-69 3
The range Coefficient is obtained thus :
Range Coefficient = (Xm - Xl) / (Xm + Xl)
Where ;
Xm = Mid value of highest class = (60+69)/2 = 64.5
Xl = Mid value of lowest class = (20+29)/2 = 24.5
Range Coefficient = (64.5 - 24.5) / (64.5 + 24.5)
Range Coefficient = 40 / 89 = 0.4494
A business woman wants to open a coffee stand across the street from a competing coffee company. She notices that the competing company has an average of 170 customers each day, with a standard deviation of 45 customers. Suppose she takes a random sample of 31 days. Identify the following to help her decide whether to open her coffee stand, rounding to the nearest whole number when necessary:
μ =_____customers per day
σ =_____customers per day
n =____
μ-x =____
σ-x =_____customers per day
Answer:
μ = 170 customers per day
σ = 45 customers per day
n = 31
[tex]\mu_x = 170[/tex]
[tex]\sigma_x = 8[/tex]
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
She notices that the competing company has an average of 170 customers each day, with a standard deviation of 45 customers.
This means that [tex]\mu = 170, \sigma = 45[/tex]
Suppose she takes a random sample of 31 days.
This means that [tex]n = 31[/tex]
For the sample:
By the Central Limit Theorem, the mean is [tex]\mu_x = 170[/tex] and the standard deviation is [tex]\sigma_x = \frac{45}{\sqrt{31}} = 8[/tex]
A committee raised 7/9 of their target goal last year and another 1/9 of the goal this year. What fraction of their goal has been raised
Answer:
8/9
Step-by-step explanation:
Find what fraction of their goal they have raised by adding the amounts from last year and this year together:
7/9 + 1/9
= 8/9
So, they have raised 8/9 of their goal
What is the correct line graph for y=3x+5?
Answer:
The equation y=−3x+5 is in slope intercept form, and represents a straight line in which -3 is the slope, and 5 is the y -intercept.
TZ is a midsegment, which of the following statements CANNOT be true
Answer:
Option C: QT < TR
Step-by-step explanation:
From the triangle, we can see that UX bisects RS into two equal parts and so it is a perpendicular bisector.
TZ Is a mid segment and it means that T bisects QR into 2 equal parts as well as QS into 2 equal parts.
Thus;
QT = QR
And QZ = SZ
So Option C is not correct because QT = QR
The following data represents the serum HDL cholesterol level for a random sample of 40 male 20- to 29-year old patients. 70 56 48 48 53 52 66 48 36 49 28 35 58 62 45 60 38 72 45 51 56 51 46 39 56 32 44 60 51 44 63 50 46 69 53 70 33 54 55 52 a. Please make a stem-and-leaf display of the serum HDL cholesterol distribution. b. Please provide the 5-number summary and the IQR and make a box-and-whisker plot of the data. Using five classes: c. Please find the class width and the upper and lower class limits. Please make a frequency table showing frequencies and relative frequencies. Please draw a frequency histogram. Please upload your picture of all of your work.
What are the roots of the polynomial equation x3 - 6x= 3x2 - 8? Use a graphing calculator and a system of equations
Answer:
Hence, the roots of the polynomial equation are:
-2, 1, 4
Step-by-step explanation:
We are asked to find the roots of the polynomial equation:
We can also equate this equation to y to obtain a system of equation as:
and
Hence, the roots of the polynomial; equation are the x-values of the point of intersections of the graph of the system of equations.
Hence, the point of intersection of the two graphs are:
(-2,4), (1,-5) and (4,40)
Hence, the roots of the polynomial equation are:
-2, 1, 4
Which statement best describes why the value of the car is a function of the number of years since it was purchased?
A. Each car value, y, is associated with exactly one time, t.
B. Each time, t, is associated with exactly one car value, y.
C. The rate at which the car decreases in value is not constant.
D. There is no time, t, at which the value of the car is 0.
Answer:
B
Step-by-step explanation:
The definition of a function is that any input will only have one output. Here, the input is the number of years, and the output is the value of the car. We know this because the question is asking why the value of the car is a function of the number of years. Therefore, based on the number of years, the value of the car is given.
Going back to the definition of a function, we can apply this year to say that any number of years will only have one car value. Another way to say this is that each time is associated with exactly one car value.
Amy worked 37.5 hours last week.
She is paid £11.50 per hour.
Her total deductions last week were £116.30.
What was Amy’s net pay last week?
£
2.6.5 A plant physiologist grew birch seedlings in the green-house and measured the ATP content of their roots. (See Example 1.1.3.) The results (nmol ATP/mg tissue) were as follows for four seedlings that had been handled identically.39 1.45 1.19 1.05 1.07 Calculate the mean and the S
Answer:
[tex](a)\ \bar x = 1.19[/tex]
[tex](b)\ \sigma_x = 0.18[/tex]
Step-by-step explanation:
Given
[tex]n = 4[/tex]
[tex]x: 1.45\ 1.19\ 1.05\ 1.07[/tex]
Solving (a): The mean
This is calculated as:
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x = \frac{1.45 + 1.19 + 1.05 + 1.07}{4}[/tex]
[tex]\bar x = \frac{4.76}{4}[/tex]
[tex]\bar x = 1.19[/tex]
Solving (b): The standard deviation
This is calculated as:
[tex]\sigma_x = \sqrt{\frac{\sum(x - \bar x)^2}{n - 1}}[/tex]
So, we have:
[tex]\sigma_x = \sqrt{\frac{(1.45 -1.19)^2 + (1.19 -1.19)^2 + (1.05 -1.19)^2 + (1.07 -1.19)^2}{4 - 1}}[/tex]
[tex]\sigma_x = \sqrt{\frac{(0.1016}{3}}[/tex]
[tex]\sigma_x = \sqrt{0.033867}[/tex]
[tex]\sigma_x = 0.18[/tex]
A student-faculty government committee of 4 people is to be formed from 20 student
volunteers and 5 faculty volunteers.
a. If one person from the group of volunteers is chosen at random to draw the names
out of a hat, what is the probability that the person drawing the names is a student?
b. How many ways can the committee of four be formed if there are no restrictions on
composition.
C. How many ways can two of the students be chosen?
d. How many ways can 2 faculty be chosen?
e. What is the probability that the random selection of the four-person committee will
result in two students and two faculty?
the answer is c i just had this question your welcome
Imagine that you need to compute e^0.4 but you have no calculator or other aid to enable you to compute it exactly, only paper and pencil. You decide to use a third-degree Taylor polynomial expanded around x = 0. Use the fact that e^0.4 < e < 3 and the Error Bound for Taylor Polynomials to find an upper bound for the error in your approximation.
I error l ≤
Answer:
upper bound for the error, | Error | ≤ 0.0032
Step-by-step explanation:
Given the data in the question;
[tex]e^{0.4[/tex] < e < 3
Using Taylor's Error bound formula
| Error | ≤ ( m / ( N + 1 )! ) [tex]| x-a |^{N+1[/tex]
where m = [tex]| f^{N+1 }(x) |[/tex]
so we have
| Error | ≤ ( 3 / ( 3 + 1 )! ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴
| Error | ≤ ( 3 / 4! ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴
| Error | ≤ ( 3 / 24 ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴
| Error | ≤ ( 0.125 ) [tex]|[/tex] -0.0256 [tex]|[/tex]
| Error | ≤ ( 0.125 ) 0.0256
| Error | ≤ 0.0032
Therefore, upper bound for the error, | Error | ≤ 0.0032
Janie can stuff 30 envelops in one minute. Find an expression for the number of envelopes she can stuff in n hours?
A line passes through the point (-9, 4) and has a slope of 2/3.
Write an equation in slope-intercept for this line.
Answer:
y=(2/3)x+10
Hope it helps!
My graph isn't really clear
The slope-intercept of the line that passes through the point (-9, 4) and has a slope of 2/3 will be y = (2/3)x + 10.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
A line is given as y = mx + c
Here m is the slope,
Put m = 2/3 and (-9, 4)
4 = (2/3)(-9) + c
c = 10
Thus equation will be y = (2/3)x + 10.
Hence "Y = (2/3)x + 10 is the slope-intercept of the line passing through the point (-9, 4), which has a slope of 2/3".
For more about the linear function,
brainly.com/question/21107621
#SPJ2
The sum of two six-digit numbers is a seven-digit number
Answer
500,000 + 500,000 = 1,000,000
Step-by-step explanation:
Geometry PLS HELP due soon
Answer:
(3) [tex]x = 7.5[/tex] and [tex]y = 51[/tex]
(4) [tex]x = 6[/tex]
Step-by-step explanation:
Question 3
Required
Solve for x and y
We have:
[tex]16x - 18 + 10x +3 = 180[/tex] --- angle on a straight line
Collect like terms
[tex]16x + 10x = 180 + 18 - 3[/tex]
[tex]26x = 195[/tex]
Solve for x
[tex]x = 195/26[/tex]
[tex]x = 7.5[/tex]
Also:
[tex]16x - 18 = 2y[/tex] ---- opposite angles
So, we have:
[tex]16 * 7.5 - 18 = 2y[/tex]
[tex]120 - 18 = 2y[/tex]
[tex]102 = 2y[/tex]
Divide by 2
[tex]51 = y[/tex]
[tex]y = 51[/tex]
Question 4:
Required
Solve for x
We have:
[tex]11x - 2 + 5x - 4 = 90[/tex] ---- angle at right-angled
Collect like terms
[tex]11x + 5x = 90 +2 + 4[/tex]
[tex]16x = 96[/tex]
Divide by 16
[tex]x = 6[/tex]
Lolz please help me I would gladly appreciate it
Pentagon has sum of 540°
What is the value of x?
Answer:
Step-by-step explanation:
the ratio of 24 to 36 is the same as x to 12
[tex]\frac{24}{36}[/tex] = [tex]\frac{x}{12}[/tex]
then
12*([tex]\frac{24}{36}[/tex])=x
[tex]\frac{24}{3}[/tex] = x
8 = x
that's it :)
The owner of a golf course wants to determine if his golf course is more difficult than the one his friend owns. He has 8 golfers play a round of 18 holes on his golf course and records their scores. Later that week, he has the same 8 golfers play a round of golf on his friend's course and records their scores again. The average difference in the scores (treated as the scores on his course - the scores on his friend's course) is 9.582 and the standard deviation of the differences is 15.9274. Calculate a 90% confidence interval to estimate the average difference in scores between the two courses.1) (13.73,-0.65).2) (-10.359,-4.021).3) (-9.259,-5.121).4) (-13.745,-0.635).5) (13.745, -0.635).
Answer:
The 90% confidence interval to estimate the average difference in scores between the two courses is (-1.088, 20.252).
Step-by-step explanation:
We have the standard deviation for the differences, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 8 - 1 = 7
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 7 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.8946
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.8946\frac{15.9274}{\sqrt{8}} = 10.67[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 9.582 - 10.67 = -1.088
The upper end of the interval is the sample mean added to M. So it is 9.582 + 10.67 = 20.252
The 90% confidence interval to estimate the average difference in scores between the two courses is (-1.088, 20.252).
Find the area of the shaded region. Round to the nearest tenth. 11.1m 130°
Area = [ ? ] m²
The area of the shaded region is 294.5 m².
What is the area of the entire circle?The area of the entire circle is calculated as follows;
A = πr²
where;
r is the radius of the circleA = π ( 11.1² )
A = 387.1 m²
The area of the sector is calculated as follows;
A = ( θ/360 ) πr²
A = ( 130/360 ) x π ( 11.1² )
A = 139.8 m²
The area of the triangle is calculated as follows;
A = ¹/₂ ( sinθ )r²
A = ¹/₂ ( sin 130 ) (11.1²)
A = 47.2 m²
Area of the unshaded region is calculated as;
A' = 139.8 m² - 47.2 m²
A' = 92.6 m²
The area of the shaded region is calculated as follow;
A'' = 387.1 m² - 92.6 m²
A'' = 294.5 m²
Learn more about area of shaded region here: https://brainly.com/question/14989383
#SPJ1