I assume \(t_n\) denotes the n-th term of the sequence, and \(s_n\) denotes the sum of the first n terms of the sequence. Then observe that
\(s_{15} - s_{14} = \displaystyle \sum_{n=1}^{15} t_n - \sum_{n=1}^{14} t_n \\\\ s_{15} - s_{14} = (t_1 + t_2 + \cdots + t_{14} + t_{15}) - (t_1 + t_2 + \cdots + t_{14}) \\\\ s_{15} - s_{14} = t_{15}\)
so the 15th term in the sequence is 147 - 123 = 24.
an english reading list has 9 american novels and 7 english novels. a student must read 4 from the list, and at least 2 must be american novels. in how many different ways can the 4 books be selected?
The total ways in which the student can readd the books are 1512 ways.
What is Combination?
A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant (unlike permutations).
Solution:
Since reading 2 american novels is compulsory
The student therefore needs to read only two more novels
It can be either American Novels or English Novels
Ways to read American Novel = 7C2
Ways to read English Novel = 7C2
Total Ways = 9C2 * (7C2 + 7C2)
Total Ways = 36 * (42)
Total Ways = 1512 ways
To learn more about Combination rfom the given link
https://brainly.com/question/11732255
#SPJ4
The cost of 3 calendars is £18. Work out the cost of 5 calendars
Answer:
$30
Step-by-step explanation:
If 3 calendars cost $18, then each should cost 18/3=$6.
6x5=$30 for 5 calendars.
79/15 en decimal???????????
Answer:
5.267
Step-by-step explanation:
Let's do long division to figure this out.
Answer: 5.26666666667
Step-by-step explanation:
If your asking for the decimal answer, than it is 5.26666666667, or you can round it to 5.3. :)
79 children and 90 women buy one ticket each. men buy the rest of the ticket. which is 31 men. how do i write this in a probability? i cannot find any answer
the probability of a man's ticket being chosen is 31/200, or 0.155 as a decimal.
To calculate the probability, we need to find the probability of a man's ticket being chosen out of all the tickets purchased.
Total number of tickets purchased = 79 (children) + 90 (women) + 31 (men) = 200 tickets
Probability of a man's ticket being chosen = Number of men's tickets / Total number of tickets = 31/200
So, the probability of a man's ticket being chosen is 31/200, or 0.155 as a decimal.
In this situation, we have calculated the probability of a man's ticket being chosen from all the tickets purchased by children, women, and men. The probability is found by dividing the number of men's tickets (31) by the total number of tickets (200).
To know more about probability visit
https://brainly.com/question/13604758
#SPJ11
the standard deviation of f$ ar{x},f$ is usually called the
The standard deviation of f$ ar{x},f$ is usually called the "sample standard deviation".
This is a commonly used statistical measure that represents the amount of variation or dispersion within a set of data. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean.
The sample standard deviation is often used to compare the variability of different sets of data and to determine the significance of differences between them. Financial contracts known as derivatives are those entered into by two or more parties and whose value is derived from an underlying asset,
collection of assets, or benchmark. A derivative may be traded over-the-counter or on an exchange. Derivative prices are based on changes in the underlying asset.
To know more about derivative click here
brainly.com/question/29096174
#SPJ11
You roll a number cube once.
what is the theoretical probability that you roll a 3 or 4?
Answer:
3 = 1/6 chance 4 = 1/6 chance
Step-by-step explanation:
BECAUSE there are 6 numbers on a number cube and there is no ganruntee that it will land on 4 or 3 so its a 1/6 chance that it will land on them.
Answer:
1/6
Step-by-step explanation:
A dice (Number cube in this case) has six sides, in only which one side is three and one side is 4.
Help plz I really need this
Answer:
14 square inches
Step-by-step explanation:
Since, three one inch cubes are stacked.
Therefore,
l = 1 in
w = 1 in
h = 3 in
Surface area of the composite figure
= 2(lw + wh + lh)
= 2( 1*1 + 1*3 + 1*3)
= 2 (1 + 3 + 3)
= 2 * 7
= 14 square inches
What is this expression in simplified form?
4/14 - 11/14
Answer:
baiBsiasbisvdxhsbhssj
Answer:
-1/7
is the answer of your question
PLEASE HELP ME
THIS ONES HARD
−7(x+3)=−2(x+3)–5x
Nabhitha broke a cell sample into 9 batches, each weighing 3. 6×10^−7 grams. How much did the original sample weigh? Use scientific notation to express your answer
The original weight of the sample is determined as 3.24×10⁻⁶ grams.
What is the original weight?
If each batch weighs 3.6×10⁻⁷ grams, then the total weight of all 9 batches can be found by multiplying the weight of one batch by the number of batches.
Total weight = 9 × 3.6×10⁻⁷ grams
= 32.4×10⁻⁷ grams
To express this number in scientific notation, we can move the decimal point one place to the left and adjust the exponent accordingly:
Total weight = 3.24×10⁻⁶ grams
Learn more about weight here: https://brainly.com/question/2337612
#SPJ4
If the input, x, is 16, which equation would result in an output of 4?y = x²y = x + 12y = x - 20y = x - 12
In order to find the equation that has an output of 4 for an input of 16, let's use the value of x = 16 in each equation and calculate the value of y:
\(\begin{gathered} y=x^2 \\ y=16^2=256 \\ \\ y=x+12 \\ y=16+12=28 \\ \\ y=x-20 \\ y=16-20=-4 \\ \\ y=x-12 \\ y=16-12=4 \end{gathered}\)So the correct option is the fourth one: y = x - 12
the american college of obstetricians and gynecologists reports that 32% of all births in the united states take place by caesarian section each year. ( national vital statistics reports , mar. 2010). a. in a random sample of 1,000 births, how many, on average, will take place by caesarian section? b. what is the standard deviation of the number of caesarian section births in a sample of 1,000 births? c. use your answers to parts a and b to form an interval that is likely to contain the number of caesarian section births in a sample of 1,000 births
a. In a random sample of 1,000 births, the expected number of births that take place by Caesarian section is:
E(X) = n*p = 1,000 * 0.32 = 320 births
Therefore, on average, 320 births out of 1,000 will take place by Caesarian section.
b. The variance of the number of Caesarian section births in a sample of 1,000 births is:
Var(X) = np(1-p) = 1,000 * 0.32 * (1-0.32) = 217.60
The standard deviation is the square root of the variance:
SD(X) = sqrt(Var(X)) = sqrt(217.60) = 14.76
Therefore, the standard deviation of the number of Caesarian section births in a sample of 1,000 births is 14.76.
c. To form an interval that is likely to contain the number of Caesarian section births in a sample of 1,000 births, we can use the normal distribution and the central limit theorem. Since n*p = 320 is greater than 10, we can assume that the distribution of the number of Caesarian section births in a sample of 1,000 births is approximately normal.
The 95% confidence interval for the number of Caesarian section births is:
320 ± 1.96*(14.76) = (291.16, 348.84)
Therefore, we can be 95% confident that the number of Caesarian section births in a sample of 1,000 births will be between 291 and 349.
Learn more about Caesarian section, here:
brainly.com/question/14361293
#SPJ11
What is the null hypothesis if we want to test the hypothesis that the mean score on Campus 1 is higher than on Campus 2
When we want to test the hypothesis that the mean score on campus 1 is higher than on campus 2, the null hypothesis will be that the mean score on campus 1 is not higher than on campus 2.
Given that we want to test the hypothesis that the mean score on campus 1 is higher than on campus 2.
We are required to find the null hypothesis when we test the hypothesis that the mean score on campus 1 is higher than on campus 2.
Hypothesis is the statement which is tested for its validity. When we want to form null hypothesis then we want to think opposite to the hypothesis that is being tested.
We have to test the hypothesis that the mean score on campus 1 is higher than on campus 2 so we have to make null hypothesis be the mean score on campus 1 is not higher than on campus 2.
Hence when we want to test the hypothesis that the mean score on campus 1 is higher than on campus 2, the null hypothesis will be that the mean score on campus 1 is not higher than on campus 2.
Learn more about hypothesis at https://brainly.com/question/606806
#SPJ4
i need help does anyone know this question
Answer:
The third answer is correct.
Step-by-step explanation:
You are going to translate the smaller quadrilateral (4 sided figure) to the larger quadrilateral. Then you need the scale factor from the smaller figure to the larger.
Side EF times the scale factor will give you side AB. Let's call the scale factor s then our equation would be:
EF x s = AB To find s divide both sides by EF
\(\frac{EF(s)}{EF}\) = \(\frac{AB}{EF}\)
s = \(\frac{AB}{EF}\) This is our scale factor.
Helping in the name of Jesus.
trey plants a 6-inch tomato plant in his garden. the plant grows by about 16% per week for several months. which function defintion represents the height of the tomato plant (in inches) as a function of the number of weeks, t since the tomato plant was planted?
The function that represents the number of weeks with the height of the tomato plants is 4t - 25y = -150.
When the week has started, the height of the plant in inches is 6 inches.
So, one point can be (0,6).
Now, it is said that the plants grows at a rate of 16% per inches for several months.
So, it means that the slope of the equation is 0.16.
Now, we can use the point slope form of the line.
So, the required equation of the line is,
(y-6)/(t-0) = 0.16
y-6 = 0.16t
16t - 100y = -600
4t - 25y = -150
So, the above equation of line is the function that will relate number of weeks with the height of the plant.
To know more about Equation of line, visit,
https://brainly.com/question/18831322
#SPJ4
What is the sum of all frequencies in a frequency distribution? and why is the sum of all relative frequencies equal to 1?
Answer:
Cumulative Frequency:
The sum of all the frequencies for all classes is equal to the number of elements in the given data and that summation is termed as the cumulative frequency which defines the number of entries of that statistical data.
The sum of relative frequencies is also equal to one, since the sum of all fractional parts must equal the whole.
Step-by-step explanation:
Determine if the statements are sometimes, always, or never true. 1. A square is a rectangle. Always 2. A rectangle is a square. Never 3. A rhombus is a square. Sometimes 4. A square is a rhombus. Always 5. A parallelogram is a rectangle. Sometimes
Let's examine the given statements and determine if they are sometimes, always, or never true.
1. A square is a rectangle. (Always true)
Explanation: A square is defined as a quadrilateral with all sides equal in length and all angles equal to 90 degrees. A rectangle is defined as a quadrilateral with all angles equal to 90 degrees. Since a square satisfies the definition of a rectangle (having all angles equal to 90 degrees), it is always true that a square is a rectangle.
2. A rectangle is a square. (Never true)
Explanation: A rectangle is defined as a quadrilateral with all angles equal to 90 degrees, but it does not necessarily have all sides equal in length. A square, on the other hand, is a special type of rectangle where all sides are equal in length. Since a rectangle can have unequal side lengths, it is never true that a rectangle is a square.
3. A rhombus is a square. (Sometimes true)
Explanation: A rhombus is a quadrilateral with all sides equal in length, but its angles are not necessarily equal to 90 degrees. A square is a special type of rhombus in which all angles are 90 degrees. Therefore, if a rhombus has all angles equal to 90 degrees, it becomes a square. However, if a rhombus has at least one angle different from 90 degrees, it is not a square. Hence, it is sometimes true that a rhombus is a square.
4. A square is a rhombus. (Always true)
Explanation: A square is a quadrilateral with all sides equal in length and all angles equal to 90 degrees. A rhombus is a quadrilateral with all sides equal in length, but its angles are not necessarily equal to 90 degrees. Since a square satisfies the definition of a rhombus (having all sides equal in length), and all its angles are 90 degrees, it is always true that a square is a rhombus.
5. A parallelogram is a rectangle. (Sometimes true)
Explanation: A parallelogram is a quadrilateral with opposite sides parallel. A rectangle is a quadrilateral with all angles equal to 90 degrees. While all rectangles are parallelograms (since their opposite sides are parallel), not all parallelograms are rectangles unless they have all angles equal to \(90\) degrees. Therefore, it is sometimes true that a parallelogram is a rectangle.
Summary:
1. Always true: A square is a rectangle.
2. Never true: A rectangle is a square.
3. Sometimes true: A rhombus is a square.
4. Always true: A square is a rhombus.
5. Sometimes true: A parallelogram is a rectangle.
To know more about Angle visit-
brainly.com/question/31818999
#SPJ11
The amount of money in a bank account is given by the function y = 600(1+0.02)^t, where y is in dollars and t is measured in months since the account was opened.What is the percent rate of growth of the bank account?Enter your answer in the box.
Given the following function:
\(\text{ y = 600(1 + 0.02)}^t\)The 0.02 in the equation represents the value of the growth rate in decimal form.
Therefore, in percentage form, the growth rate is:
0.02 x 100 = 2%
The answer is 2%
Guys, I’m giving you at least 100 points for you to answer to my last 2 weeks of my Number Sense and Numeracy: The Order of The Operations word problem homework package So guys, please listen up and pay attention to me without ignoring my last 2 weeks of my Number Sense and Numeracy: The Order of The Operations word problem homework package for no reason! :D
The question #6 is by how much is the sum of –8 and 6 more than –4?
The question #7 is how much less is the sum of –8 and –4 than the product of 4 and –2?
The question #11 is by how much is (–3 + 5)^2 more than –(–3 + 5)^2?
Please answer to my math word problem questions as soon as possible with the best efforts and the best step-by-step explanations in order to get the Brainliest award of all the time! :D
Well anyways, guys, good luck on answering 3 math word problem questions of my last 2 weeks of my Number Sense and Numeracy: The Order of The Operations word problem homework package in order to get the best Brainliest award of all of the time, and I will check the answers to see if it’s appropriate for me. :)
Answer:
ok i am here to explain :)
Step-by-step explanation:
So, for #6, all we do is -8+6, since it said sum, so we add, and we get -2. this is 2 more than -4, and to check, all we would have to do is -4+2, which equals -2.
for #7, all we have to do is -8+(-6), since again it says sum so we add. the sum of these values are -14. for the second part, because it says "product" this means we multiply! and when we multiply -2 by 4, we get -8. this would lead us to believe that the sum is 4 less than. we can check it by subtracting positive 4 from the negative 8, or -8-4, which would give us -12.
for #11, all i really did was plug it into a calculator, and for the first one, i got 4, and for the second one i got -4. this would give us a difference of 8, and to check all we would have to do is add the 8 to the negative 4, or -4+8=4.
Hope this helps, please mark as brainlest.
Answer:
6: -2
7: 14
11: -4
Step-by-step explanation:
6:
-8 + 6 = -2
-2 is bigger than -4 because it is closer to 0. If it was regular numbers, like 2 and 4, 4 would be larger! :)
7:
-8 - 4 = -12
4 - 2 = 2
The correct answer is 14 because there are 14 numbers between 4 and -12 :)
11:
(–3 + 5)^2
2^2
4
–(–3 + 5)^2
-2^2
-4
The correct answer is 4 because it is a positive number and positive numbers are ALWAYS bigger than negative numbers :)
Have a great day!!
Please rate and mark brainliest!!
Sheets of Stickers
Cho is considering buying stickers by the sheet.
Four sheets cost $14.
How much would 11 1/2 sheets cost?
Guys plz help this is do tomorrow.
The cost of 11.5 sheets of stickers costs is $40.25.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, four sheets of stickers cost $14.
Now, the cost of 1 sheet of stickers is 14/4
= $3.5
The cost of \(11\frac{1}{2}\) =11.5 sheet of stickers is
11.5×3.5
= $40.25
Therefore, the cost of 11.5 sheets of stickers costs is $40.25.
To learn more about the unitary method visit:
brainly.com/question/22056199.
#SPJ1
Pick the correct answer, and justify it briefly. a) The Kolmogorov complexity of an incompressible string of length n is at least i. logn - c ii. n-c iii. 2n - c
The correct answer is iii. 2n - c, where c is a constant.Kolmogorov complexity refers to the measure of the shortest possible description of a string in terms of computational resources required to generate it.
An incompressible string is a string that does not have any patterns or regularities that can be exploited to generate a shorter description.
For an incompressible string of length n, the Kolmogorov complexity is expected to be close to the length of the string itself. In other words, the shortest possible description of an incompressible string of length n would be of similar length to the string itself.
The option iii. 2n - c represents a bound where the constant c accounts for the details of the specific computation model used for measuring Kolmogorov complexity. It is a conservative estimate of the Kolmogorov complexity of an incompressible string, as it allows for some additional constant overhead in the description length beyond the length of the string itself.
Options i. logn - c and ii. n - c are not accurate estimations for the Kolmogorov complexity of incompressible strings. The logarithmic term in option i. is not suitable for incompressible strings because it suggests that the complexity decreases as the string length increases, which is not the case. Option ii. suggests that the complexity is simply the length of the string minus a constant, which does not account for the inherent complexity of the string itself.
Learn more about statistics here:
https://brainly.com/question/31527835
#SPJ11
You and your friend go out to dinner The cost of your meal is 12.75, your friend's meal is 13.95. You tell your friend that you will pay for the meal and the tip the waiter gave excellent service so you want to leave 20% tip. How much will you leave for a tip ?
answer: 5.34
Step by step explanation 12.75 + 13.95=26.7
20% of 26.7 is 5.34
Maya pumped 6 gallons of water into her pool each minute for 42 minutes. What was the total change in the amount of water in the pool?
look at he picture it is the first one just read at the bottom and that is the answer
Step-by-step explanation:
Find all points (x,y) of the curve C defined by the parametric equations x(t)=2cost and y(t)=4sint where the tangent line TL is vertical or horizontal.
The points (x, y) on the curve C where the tangent line TL is vertical or horizontal are: (2, 0), (-2, 0), (0, 4), and (0, -4).
To find the points (x, y) on the curve C defined by the parametric equations x(t) = 2cos(t) and y(t) = 4sin(t) where the tangent line TL is vertical or horizontal, we need to find the values of t that correspond to these points.
For the tangent line to be vertical, the derivative dy/dx must be undefined. In other words, the slope of the tangent line must be infinite. So, we look for the values of t where dx/dt = 0.
We have x(t) = 2cos(t), so dx/dt = -2sin(t). Setting dx/dt = 0, we get -2sin(t) = 0. This equation is satisfied when sin(t) = 0, which occurs at t = 0, π, 2π, etc.
Substituting these values of t back into the parametric equations, we find the corresponding points (x, y): At t = 0: x(0) = 2cos(0) = 2, y(0) = 4sin(0) = 0. So, the point (2, 0) is on the curve.
At t = π: x(π) = 2cos(π) = -2, y(π) = 4sin(π) = 0. Thus, the point (-2, 0) is on the curve. Similarly, at t = 2π, we get the points (2, 0) and (-2, 0).
For the tangent line to be horizontal, the derivative dy/dx must be zero. In other words, the slope of the tangent line must be zero. So, we look for the values of t where dy/dt = 0.
We have y(t) = 4sin(t), so dy/dt = 4cos(t). Setting dy/dt = 0, we have 4cos(t) = 0. This equation is satisfied when cos(t) = 0, which occurs at t = π/2, 3π/2, etc.
Substituting these values of t back into the parametric equations, we find the corresponding points (x, y): At t = π/2: x(π/2) = 2cos(π/2) = 0, y(π/2) = 4sin(π/2) = 4. So, the point (0, 4) is on the curve.
At t = 3π/2: x(3π/2) = 2cos(3π/2) = 0, y(3π/2) = 4sin(3π/2) = -4. Thus, the point (0, -4) is on the curve. Similarly, at t = 5π/2, we get the points (0, 4) and (0, -4).
To know more about tangent line refer:
https://brainly.com/question/31617205
#SPJ11
Fill in the missing number. 30% of = 2,700
Answer:
810!
Hope this helped! Have a nice day!!
Answer:
30% of 2,700 is 810
Step-by-step explanation:
proportions
0.30×2,700
810
x = 2y + 4z = 7
3y – Ζ=1
Z=-4
(x,y,z) =
The solution of the system of equations is as below
(x, y, z) = (-18, -1, -4)
How to solve for the parametersSubstitute the value of z = -4 in the second equation:
3y - (-4) = 1
3y + 4 = 1
3y = -3
y = -1
Now that we know the value of y, we can substitute it and the given value of z in the first equation to solve for x:
x = 2y + 4z
= 2(-1) + 4(-4)
= -2 - 16
= -18
Therefore, the solution to the system of equations is:
(x, y, z) = (-18, -1, -4)
Learn more about system of equations at:
https://brainly.com/question/13729904
#SPJ1
write the following expressions as an exponential term with a single base
(4*2^5)÷(2^3 *1/16)
Answer:
2^8
Step-by-step explanation:
(4*2^5)÷(2^3 *1/16)
\(\left ( 4\times 2^5 \right )\div \left ( 2^3\times \frac{1}{16} \right )\\\\2^7 \div 2^{-1}\\\\2^7\times 2^1\\\\2^8\)
HELP i’m begging you dude pls multiple questions
At Manzana Grocery Store, apples cost $2.80 per pound. Maricela bought 2.7 pounds of apples. How much did she pay for the apples?
Answer:
7.56
Step-by-step explanation:
Yo Wassup? >:D
You answer is $6.00!
Hopefully this helps! :D
long division with 2,000 divided by 3.2
Answer:
625
Step-by-step explanation:
with long division, you just need to remember these five steps, divide, multiply, subtract, bring it down, and repeat.
hope this helps :3
if it did pls mark brainliest
The number 2000 divided by 3.2, then the quotient is 625.
To perform long division with 2,000 divided by 3.2, follow these steps:
Step 1: Write down the division problem.
2,000 ÷ 3.2
Step 2: Convert the divisor to a whole number.
Since the divisor is a decimal, multiply both the dividend and divisor by a power of 10 to eliminate the decimal. In this case, multiply both numbers by 10 to get rid of the decimal point:
2,000 × 10 = 20,000
and
3.2 × 10 = 32.
Step 3: Divide the first digit of the dividend by the divisor.
In this case, the first digit of 20,000 is 2, and when divided by 32, the quotient is 0. Therefore, write down 0 as the first digit of the quotient.
Step 4: Multiply the quotient digit by the divisor and subtract from the dividend.
Multiply 0 by 32:
0 × 32 = 0
Subtract the result from the dividend:
20,000 - 0 = 20,000
Step 5: Bring down the next digit of the dividend.
Since we have no more digits in the dividend, stop here.
Step 6: Write down the final result.
The quotient is the result of the division:
2,000 ÷ 3.2 = 625
Therefore, when dividing 2,000 by 3.2 using long division, the quotient is 625.
Learn more about Divided here:
brainly.com/question/15381501
#SPJ6