8. Write the frequency distribution table for the follow
data:
Marks
Below 10
Below 20
Below 30
Below 40
Below 50
Below 60

No. of
students
0
15
20
30
35
40
[CBSE

The probability that no students in a survey of five students will be in favor of opening a pub is approximately 0.32768 or 32.768%.

To calculate the probability that no students in a survey of five students will be in favor of opening a pub, we can use the binomial probability formula.

The probability of a single student being in favor of opening a pub is 0.20, and the probability of a single student not being in favor is 1 - 0.20 = 0.80.

Using the binomial probability formula, the probability of having no students in favor can be calculated as:

P(X = 0) = (0.80)^5

P(X = 0) = 0.32768

Know more about probability here:

https://brainly.com/question/31828911

#SPJ11

∫ 8 (x+a)(x+b) dx = (8/3)x³ + 4x²(a+b) + 8x(ab) + c

The antiderivative of 8 (x+a)(x+b) with respect to x is (8/3)x³ + 4x²(a+b) + 8x(ab) + c.

To evaluate the integral, we can use the distributive property to expand the expression in the integrand:

8 (x+a)(x+b) dx = 8(x² + (a+b)x + ab) dx

We can then integrate each term separately using the power rule of integration:

∫ 8(x² + (a+b)x + ab) dx = (8/3)x³ + 4(a+b)x² + 8abx + c

We can simplify this result by factoring out the constant 8/3 from the first term and using the distributive property to factor out the common factor of 4x from the last three terms:

(8/3)x³ + 4(a+b)x² + 8abx + c = (8/3)x³ + 4x²(a+b) + 8x(ab) + c

We can check our answer by taking the derivative of the result to see if it matches the original integrand. The derivative of (8/3)x³ is 8x², the derivative of 4x²(a+b) is 8x(a+b), the derivative of 8x(ab) is 8ab, and the derivative of the constant c is 0. Adding these terms together, we get the original integrand of 8(x+a)(x+b) dx, so our answer is correct.

Learn more about integral here: brainly.com/question/18125359

#SPJ4

Complete question:

Evaluate the integral. (assume a ≠ b. remember to use absolute values where appropriate. use c for the constant of integration.) 8 (x+a)(x+b) dx

Kyle's yesterday's time was 108 seconds, or 1 minute and 48 seconds, faster than his normal time.

To find the difference in time between Kyle's normal time and yesterday's time, we need to subtract his normal time from yesterday's time:

(21 minutes 38seconds)−(23 minutes 26 seconds)

(21 minutes 38 seconds)−(23 minutes 26 seconds)

We can first convert both times to seconds to make the subtraction easier:

=(21×60+38)seconds

−(23×60+26)seconds

=(21×60+38) seconds−(23×60+26) seconds

=(1298 seconds)−(1406 seconds)

=(1298 seconds)−(1406 seconds)

=−108 seconds

=−108 seconds

The result is negative because Kyle's yesterday's time is faster than his normal time. To find the positive difference, we can multiply by -1:

∣−108∣ =108seconds

∣−108∣= 108 seconds

Therefore, Kyle's yesterday's time was 108 seconds, or 1 minute and 48 seconds, faster than his normal time.

Learn more about linear equations here:

brainly.com/question/11897796

#SPJ1

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

let's do a), c) and last b).

a)

\((\stackrel{x_1}{0}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{13}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{13}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{0}}} \implies \cfrac{ 8 }{ 7 }\)

c)

well, we know it passes through (7 , 13) and we know its slope, so let's use that

\((\stackrel{x_1}{7}~,~\stackrel{y_1}{13})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{8}{7} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{13}=\stackrel{m}{ \cfrac{8}{7}}(x-\stackrel{x_1}{7}) \\\\\\ y-13=\cfrac{8}{7}x-8\implies y=\cfrac{8}{7}x+5\)

b)

another point?  well, hmmm let's pick a random "x" value hmmm say 7/8, so

\(y=\cfrac{8}{7}x+5\qquad \qquad \boxed{x=\cfrac{7}{8}}\hspace{3em}y=\cfrac{8}{7}\stackrel{x}{\left( \cfrac{7}{8} \right)}+5\implies y=1+5\implies \boxed{y=6} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{another~point}{{\Large \begin{array}{llll} \left(\frac{7}{8}~~,~~6 \right) \end{array}}}~\hfill\)

it is seen that if the number of people in the group is n = 23, the probability that at least two people will have the same birthday is at least 1/2.

Let P(A) be the probability that in a randomly selected group of n people, at least two people have the same birthday.

If we assume that the year has 365 days, then the number of ways to select n people with different birthdays is n x (n-1) x (n-2) x ... x (n-364).

the probability of selecting n people with different birthdays is P(A') = n(n - 1)(n - 2)...(n - 364)/365nThen, the probability that at least two people in a group of n have the same birthday is given by P(A) = 1 - P(A').

We need to find the smallest value of n such that P(A) ≥ 1/2.Let's solve for this.Let us find n such that P(A) ≥ 1/2.

By using the complement rule, 1-P(A') = P(A).Then:1 - n(n - 1)(n - 2)...(n - 364)/365n ≥ 1/2n(n - 1)(n - 2)...(n - 364)/365n ≤ 1/2(2)n(n - 1)(n - 2)...(n - 364) ≤ 365n/2Now, take the natural logarithm of both sides and simplify as follows:ln[n(n - 1)(n - 2)...(n - 364)] ≤ ln[365n/2]nln(n) - ln[(n - 1)!] - ln[(n - 2)!] - ... - ln[2!] - ln[1!] ≤ ln[365n/2]

Therefore, we need at least 23 people in the group for the probability of two or more people having the same birthday to be at least 1/2.

This is because n = 23 is the smallest number for which the inequality holds, and therefore, it is the smallest number of people required to ensure that the probability of two or more people having the same birthday is at least 1/2.

To know more about number visit:

brainly.com/question/3589540

#SPJ11

Answer: 816, 81.6%, 0.816, or 81600

Step-by-step explanation:

552 + 264 = 816

81600 as a percent(81.6%)

0.816 as a decimal

102/125 as a fraction

The 98% confidence interval estimate of the population mean is

15.823 < μ < 22.177

In the given situation the wind on a random day in Bryan  is normally distributed with the following values;

Standard Deviation = ( δ ) = 5.1 mph

A random day of 16 is taken into account for the consideration of Bryan's average value of 19mph.

n = 16

By taking the confidence level of T - Factor, we get the;

At a 98% confidence level, the t is,

tα /2,df = t₀.₀₄,₂₄ = 2.492                ( df = hours in a day)

Margin of error = E = tα/2,df * (δ /√n)

                              = 2.492 * (5.1 / √16)

                              = 3.177

The 98% confidence interval estimate of the population mean is,

x - E < μ < x + E

19 - 3.177 < μ < 19 + 3.177

15.823 < μ < 22.177

The 98% confidence interval estimate of the population mean is

15.823 < μ < 22.177

To learn more about Standard Deviation click here:

brainly.com/question/13905583

#SPJ4

It will take 56 days for the lilypad to cover the entire pond. On day 28, the lilypad covers 1/2 of the pond, as we saw earlier.

The lilypad doubles in size each day, which means that if it covers a certain fraction of the pond on day n, it will cover twice that fraction on day n+1. In other words, if the lilypad covers 1/2^k of the pond on day k, then it will cover 1/2^(k-1) of the pond on day k+1.

If we let n be the number of days it takes for the lilypad to cover the entire pond, then we can say that on day n-28, the lilypad covers 1/2 of the pond (since on day n-28, the lilypad will be half the size of what it is on day n). Therefore, we want to solve for n-28 when the lilypad covers the entire pond, which is equivalent to the lilypad doubling in size 28 times:

1/2 * 2^28 = 2^(28-n+28)

Simplifying, we get:

2^(n-28) = 2^28

Taking the logarithm base 2 of both sides, we get:

n-28 = 28

Solving for n, we get:

n = 56

Therefore, it will take 56 days for the lilypad to cover the entire pond. On day 28, the lilypad covers 1/2 of the pond, as we saw earlier.

Learn more about "Fraction" : https://brainly.com/question/30154928

#SPJ11

Answer:

no sé cómo hacer pero para la próxima lo intento

Answer:

Step-by-step explanation:

Answer:

100/275=x/37

Step-by-step explanation:

37 heads for 100 guests that means the ratio is 37/100

To calculate how many is needed for 275 guests we should to multiply 275 by 37 and divide it by 100

And the expression for it is 100/275 = x/37

Answer:

Week two

Step-by-step explanation:

Using the formula they gave us:

Cost of shipping = 2.79 + 0.38(8)

Cost of shipping = 2.79 + 3.04

Cost of shipping = 5.83(currency unit)

The random variable X represents the length of each engineering conference, and is measured in days.

The normal distribution should be used for this problem, as the underlying population is normal. The normal distribution is a continuous probability distribution that is characterized by a symmetric bell-shaped curve. It is a useful model for events that follow a normal or Gaussian pattern, such as the lengths of engineering conferences.

c. i. The 95% confidence interval for the population mean length of engineering conferences is (3.38, 4.50) days.

ii. The graph of the 95% confidence interval for the population mean length of engineering conferences is shown below.

iii. The error bound for the 95% confidence interval is 0.77 days. This can be calculated using the formula: Error Bound = 1.96*(standard deviation/√sample size). In this case, the error bound is calculated as: 1.96 * (1.28/√84) = 0.77.

Learn more about normal distribution here:

https://brainly.com/question/29509087

#SPJ4

Answer:

6%

Step-by-step explanation:

0.06 is 6% as a decimal

The value of x is in the solution set of the inequality 9(2x + 1) < 9x – 18 is -4.

Inequality is defined as relationship between non-equal numbers or expressions. The solution set of an inequality is the set of values that satisfies the given inequality.

To determine the solution set of the given inequality, isolate the variable to one side and simplify.

9(2x + 1) < 9x - 18

18x + 9 < 9x - 18

18x - 9x < -18 - 9

9x < -27

x < -3

x = (-∞, -3)

Hence, the solution set of the given inequality is the set of numbers less than -3. Among the given choices, only -4 is less than -3. Therefore, the value of x is -4.

Learn more about inequality here: brainly.com/question/13912022

#SPJ4

Answer: -4

Step-by-step explanation: edge2020

Barney's new crate is 1,440 cubic inches larger than his old crate. This means the new crate provides significantly more space for Barney to move and grow comfortably.

The volume of a rectangular prism is calculated by multiplying its length, width, and height. For the old crate, the volume is 16 x 9 x 10 = 1,440 cubic inches. Similarly, the volume of the new crate is 24 x 10 x 12 = 2,880 cubic inches.

To find the difference in volume, we subtract the volume of the old crate from the volume of the new crate: 2,880 - 1,440 = 1,440 cubic inches. Therefore, Barney's new crate is 1,440 cubic inches larger than his old crate. This means the new crate provides significantly more space for Barney to move and grow comfortably.

QUESTION : Sam needs a new crate for his puppy, Barney. The old crate, which is shaped like a rectangular prism, is 16 inches long, 9 inches wide, and 10 inches tall. Barney's new crate is also shaped like a rectangular prism, but it is 24 inches long, 10 inches wide, and 12 inches tall. How many cubic inches larger is Barney's new crate than his old crate? Write your answer as a whole number or decimal. Do not round.  

To learn more about volume click here, brainly.com/question/28058531

#SPJ11

The option that is not a statistical question is D. how tall are the corn plants?

A statistical question is one that may be answered by gathering data and for which the data will vary. Questions answered with a single data point are not statistical questions since the data utilized to answer the question is not variable.

A statistical question is one that can be answered by gathering varying amounts of data. A statistical inquiry is one that yields varying responses and outcomes (data). It must be collected on more than one person and there must be room for the facts to vary.

Therefore, based on the information illustrated, the correct option is D. It was too general and not specific

Learn more about statistics on;

https://brainly.com/question/12150562

#SPJ1

Answer:

I might be able to help. :))

True. The correlation coefficient (r) must also be positive, indicating a strong positive linear relationship between the two variables.

The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where a value of -1 indicates a perfectly negative linear relationship, a value of 1 indicates a perfectly positive linear relationship, and a value of 0 indicates no linear relationship.  If the slope (b) of ŷ is positive, it means that as the independent variable increases, the dependent variable also increases.

In addition to the above explanation, it is important to note that while a positive slope (b) of ŷ indicates a positive linear relationship between two variables, it does not necessarily mean that the correlation coefficient (r) will always be positive. For example, if there is a weak positive linear relationship between two variables, the correlation coefficient (r) may still be positive but not as strong as if there was a strong positive linear relationship. Similarly, there may be situations where the correlation coefficient (r) is positive but the slope (b) of ŷ is not positive, such as in a curvilinear relationship where the relationship between the two variables is not linear.

To know more about correlation coefficient visit :-

https://brainly.com/question/29978658

#SPJ11

Answer:

The sum of two numbers = 12

x+y=12

product of two numbers = 35

xy=35

The sum of reciprocals =  x

1

​

+

y

1

​

=

xy

x+y

​

=

35

12

​

Step-by-step explanation:

Answer: 10 and 14.

Step-by-step explanation:

Let the numbers be x and y.

Make and solve a system of equations:

\(\displaystyle\\\left \{ {{\frac{x+y}{2}=12\ \ \ \ (1) } \atop {\frac{1}{4}xy=35\ \ \ \ (2) }} \right. \\\\\\\)

Multiply equation (1) by 2 and equation (2) by 4:

\(\displaystyle\\\left \{ {{x+y=24} \atop {xy=140}} \right. \\\\\\\left \{ {{x=24-y} \atop {(24-y)*y=140\right.\\\\\\\left \{ {{x=24-y} \atop {24y-y^2=140}} \right. \\\\\\\left \{ {{x=24-y} \atop {-y^2+24y-140=0\ \ \ \ (3)}} \right.\)

Multiply equation (1) by (-1):

\(y^2-24x+140=0\\\\y^2-10x-14x+140=0\\\\y(y-10)-14(y-10)=0\\\\(y-10)(y-14)=0\\\\y-10=0\\\\y=10.\ \ \ \ \Rightarrow\\\\x=24-10\\\\x=14\\\\y-14=0\\\\y=14.\ \ \ \ \Rightarrow\\\\x=24-14\\\\x=10.\)

Answer:

(6.25,2.5)

Step-by-step explanation:

Apply the multiplicative law of distribution.

Multiply the monomial.

Calculate the product or coefficient.

Rearrange Like Terms.

Collect like terms by adding their coefficients.

Calculate the first two terms.

Answer:

f(2) = 24

Step-by-step explanation:

to evaluate f(2) substitute x = 2 into f(x) , that is

f(2) = 15(2) - 6 = 30 - 6 = 24

Answer:

Step-by-step explanation:

The greatest possible number of intersection points for four circles of different sizes is 12.

The greatest possible number of intersection points of four circles of different sizes can be calculated by considering the maximum number of intersection points each pair of circles can have and then summing them up.

When two circles intersect, they can have a maximum of two intersection points. So, if we have four circles, we can find the maximum number of intersection points by considering each pair of circles separately.

For the first circle, it can intersect with the other three circles at most two times each, giving us a total of 2 * 3 = 6 intersection points.

For the second circle, it can intersect with the remaining two circles at most two times each, giving us a total of 2 * 2 = 4 intersection points.

The third circle can intersect with the last remaining circle at most two times, giving us a total of 2 * 1 = 2 intersection points.

Finally, the fourth circle doesn't have any other circle left to intersect with, so it doesn't contribute any additional intersection points.

Now, we can sum up the intersection points from each pair of circles: 6 + 4 + 2 + 0 = 12.

More on Intersection: https://brainly.com/question/16626036

#SPJ11

Answer:

15.5813 (15.6 miles per gallon)

Step-by-step explanation:

you divide 134 by 8.6 and then round it

Answer:

a) 375

b) 7062.75 mm²

Step-by-step explanation:

b) We need to find the shortest possible width and length to get the smallest possible area.

To get the boundaries for 19.4, we go on to the next significant figure (the hundredths) and ± 5 of them.

The boundaries are, therefore: 19.35 - 19.45

As for the length, we can see they've added 5 units as the measurement is correct to 2 sig' figures, which is the tens.

And so, if we do as we did before, we go to the next sig' figure (the units) and ± 5 of them, we get the boundaries to be 365 - 375.

Now, we just multiply the lower bounds of the length and width to get the minimal/lower-bound area:

365 * 19.35 = 7062.75 mm²