There are three clubs at Redwood High School: Debate, Student council, and Key club. There are 1000 students in the school. And everyone is in at least one club.
• The total number of students in the debate club is 310
• The total number of students in the Student council is 650
• The total number who are in debate and student council is 170
• The total number of students who are in both debate and the key club are 150
• The total number of students who are in both student council and the key club is 180
• There are 50 students who are in all three clubs How many students are in the key club?

Find the derivate of the expression using the general procedure to find the derivative of a polynomial function. To do it, multiply the term times the exponent of the variable and raise the variable to the original exponent minus 1:

Now that we have the expression for the derivative of the function, evaluate it at the value of x that is in the question statement, which is 1:

The derivative of the function is -2 at x=1.

Answer:

the number would be 3 because you start at 20 and then 4 times something will make 32 so 3 times 4 equals 12 and 20 plus 12 equals 32.

Solution:

Given:

The angles of a triangle are as shown in the sketch below;

Consecutive even integers are the set of integers such that each integer in the set differs from the previous integer by a difference of 2 and each integer is divisible by 2.

For the three angles to be consecutive even integers, then

Since the three angles are in the triangle, then;

Substituting the value of x into equations (1) and (2) to get the values of y and z,

Therefore, the measure of each angle if the angles are consecutive even integers are;

Answer:

58° , 60° , 62°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

let the 3 consecutive even integers be n, n + 2, n + 4 , then

n + n + 2 + n + 4 = 180

3n + 6 = 180 ( subtract 6 from both sides )

3n = 174 ( divide both sides by 3 )

n = 58

n + 2 = 58 + 2 = 60

n + 4 = 58 + 4 = 62

the 3 angles are 58° , 60° , 62°

The half-life of Radon-222 is approximately 3.77 days. It will take approximately 8.73 days for a sample of Radon-222 to decay to 20% of its original amount.

To find the half-life of Radon-222, we can use the following formula:

N = N0 * (1/2)^(t/T)

where: N is the final amount of the substance

N0 is the initial amount of the substance

t is the time elapsed

T is the half-life of the substance

We know that after 3 days, the sample of Radon-222 has decayed to 58% of its original amount. So we have:

N/N0 = 0.58

t = 3 days

Substituting these values into the formula, we get:

0.58 = (1/2)^(3/T)

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

log2(0.58) = log2(1/2)^(3/T)

-0.796 = -3/T

T = 3.77 days

Therefore, the half-life is approximately 3.77 days.

To find how long it will take for the sample to decay to 20% of its original amount, we can use the same formula as before:

N = N0 * (1/2)^(t/T)

We want to find the time t when N/N0 = 0.20. So we have:

0.20 = (1/2)^(t/T)

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

log2(0.20) = log2(1/2)^(t/T)

-2.32 = -(t/T)

t = 2.32T

Substituting the half-life T that we found in part (a), we get:

t = 2.32 * 3.77 days

t ≈ 8.73 days

Therefore, Decay will take approximately 8.73 days to reduce to 20% of original amount.

To know more about half-life of Radon:

https://brainly.com/question/28480626

#SPJ4

Answer:

12 students

Step-by-step explanation:

First, find the percentage of how many students have siblings:

3/10 = 0.3 = 30%

40 * 0.3 = 12

This means that 30% of this class are 12 students. These 12 students have siblings.

Hope this helps!

Answer:

ax + ab

Step-by-step explanation:

Step 1: Write expression

a(x + b)

Step 2: Distribute a to each term

ax + ab

\(\huge\boxed{Hello!}\)

The Distributive Property states that

a(b+c)=ab+ac

Now, let's use this property to simplify the given expression:

a(x+b)

ax+ab

This is our final answer.

\(\huge\boxed{\bf{Hope\;it\;helps!}}\)

\(\huge\bold{Good\;luck!}\)

\(\huge\mathfrak{LoveLastsAllEternity}\)

The correct answer is A. line. A line is a straight path that extends infinitely in both directions. It has no endpoints and continues indefinitely.

A line is a basic geometric object that is defined by two points or can be represented by a single equation. It is characterized by its straightness and infinite length, extending in both directions without any boundaries or endpoints. A line can be represented by a straight line segment with two distinct points or by an equation such as y = mx + b in a coordinate system.

On the other hand, a plane refers to a two-dimensional flat surface that extends infinitely in all directions. It is not a straight path but rather a flat, continuous surface. A ray, is a part of a line that has one endpoint and extends infinitely in one direction. It is not a straight path that continues indefinitely in both directions like a line.

A triangle is a closed geometric shape with three sides and three angles. It is not a straight path but rather a closed figure formed by connecting three non-collinear points.Therefore ,the correct answer is A.

learn more about straight line :

https://brainly.com/question/31693341

#SPJ4

Answer:

∠FGI=40°

Step-by-step explanation:

CE║FH ⇒ ∠CDG=∠FGI=40°

The largest possible assigned cycle time for the production line is 2.7 minutes, while the smallest possible assigned cycle time is 0.9 minutes.

In line balancing, the goal is to allocate the tasks evenly across the production line to achieve maximum efficiency. The largest possible assigned cycle time is determined by the task with the longest duration. In this case, the task with a duration of 2.7 minutes sets the upper limit for the cycle time. If all tasks were assigned the same cycle time, it would take at least 2.7 minutes to complete one cycle of the production line.

On the other hand, the smallest possible assigned cycle time is determined by the sum of the task durations. In this case, the sum of all task times is 6.4 minutes. By dividing this total time by the number of workstations or operators in the production line, we can determine the smallest possible assigned cycle time.

Since there are no constraints mentioned about the number of operators, we assume a single operator. Therefore, the smallest possible assigned cycle time would be 6.4 minutes divided by 1, which equals 6.4 minutes. However, it is worth noting that this cycle time is not realistic or practical for an operator to achieve.

Learn more about largest here:
https://brainly.com/question/31431168

#SPJ11

Answer:

45 times

Step-by-step explanation:

There are nine pink sections and 11 sections total. The probability of landing on a pink section is 9/11.

Multiply the probability by 55

\(\frac{9}{11}\) × \(\frac{55}{1}\)

Cancel the 11 and 55. The 11 becomes a 1 and 55 becomes a 5

\(\frac{9}{ 1}\) × \(\frac{5}{1}\)

45

We know that

Based on the given information, we define the following

The cost to rent a moving van is $51 plus an additional $7 per hour.

Based on the given information,

a=1

Hope this helps

have a great day!

Step-by-step explanation:

Answer:

3x-3+4=3x+1

2x-2+x-1+4=

Two length of the same frequency and amplitude moving in opposite directions combine to form a standing wave, which appears to be stationary. Given that the pool in this instance is 24 m long and has six loops, the wavelength is 4 m.

Wavelength = Length of Pool / Number of Loops

24 m / 6 loops

= 4 m

Wavelength

= 4 m

Two waves of the same frequency and amplitude moving in opposite directions combine to form a standing wave, which appears to be stationary. A stationary wave pattern is produced when the two waves collide and interfere with one another. Six loops make up the 24 m-long pool in this instance. As a result, the standing wave's wavelength is equal to the pool's length divided by the number of loops, or 24 m / 6 = 4 m. This indicates that the standing wave's wavelength is 4 metres. Standing waves can be used to determine a wave's speed because they are equal to wavelength times frequency. Understanding how waves behave in various contexts, such as swimming pools, oceans, or other bodies of water, can be helped by this.

Learn more about length here

https://brainly.com/question/13194650

#SPJ4

Answer:

15.4

Step-by-step explanation:

∠RSA =

95`

95-18=

77/5=

15.4

4 x 15.4=

61.6+7=

68.6

Answer: D) Increase the sample size and decrease the confidence level.

Step-by-step explanation:

A reduced interval width means that the data is more accurate. This can only be achieved if the sample size is increased because a larger sample size is able to capture more of the characteristics of the variables being tested.

A smaller confidence interval will also lead to a reduced interval width because it means that the chances of the prediction being correct have increased.

the value of the given infinite series is -ln(2) + ∑(n=3 to ∞) 2/n.

What is value?

In mathematics, a value refers to a numerical quantity that represents a specific quantity or measurement.

To evaluate the infinite series ∑(n=1 to ∞) 1/n(n+1)(n+2), we can use the partial fraction decomposition method. As the hint suggests, we want to find constants a, b, and c such that:

1/n(n+1)(n+2) = a/n + b/(n+1) + c/(n+2)

To determine the values of a, b, and c, we can multiply both sides of the equation by n(n+1)(n+2) and simplify the resulting expression:

1 = a(n+1)(n+2) + b(n)(n+2) + c(n)(n+1)

Expanding the right side and collecting like terms:

1 = (a + b + c)\(n^2\) + (3a + 2b + c)n + 2a

Now, we can compare the coefficients of the corresponding powers of n on both sides of the equation:

Coefficients of \(n^2\): 1 = a + b + c

Coefficients of n: 0 = 3a + 2b + c

Coefficients of the constant term: 0 = 2a

From the last equation, we find that a = 0.

Substituting a = 0 into the first two equations, we have:

1 = b + c

0 = 2b + c

From the second equation, we find that c = -2b.

Substituting c = -2b into the first equation, we have:

1 = b - 2b

1 = -b

b = -1

Therefore, b = -1 and c = 2.

Now, we have the decomposition:

1/n(n+1)(n+2) = 0/n - 1/(n+1) + 2/(n+2)

Now we can rewrite the series using the decomposition:

∑(n=1 to ∞) 1/n(n+1)(n+2) = ∑(n=1 to ∞) (0/n - 1/(n+1) + 2/(n+2))

The series can be split into three separate series:

= ∑(n=1 to ∞) 0/n - ∑(n=1 to ∞) 1/(n+1) + ∑(n=1 to ∞) 2/(n+2)

The first series ∑(n=1 to ∞) 0/n is 0 because each term is 0.

The second series ∑(n=1 to ∞) 1/(n+1) is a well-known series called the harmonic series and it converges to ln(2).

The third series ∑(n=1 to ∞) 2/(n+2) can be simplified by shifting the index:

= ∑(n=3 to ∞) 2/n

Now, we have:

∑(n=1 to ∞) 1/n(n+1)(n+2) = 0 - ln(2) + ∑(n=3 to ∞) 2/n

Therefore, the value of the given infinite series is -ln(2) + ∑(n=3 to ∞) 2/n.

To learn more about value visit:

https://brainly.com/question/24078844

#SPJ4

Answer:

The right option is option e.T-shaped.

Step-by-step explanation:

The molecular geometry or shape of clf3 is T-shaped. It acquires such shape because of presence of two lone pairs which take equatorial position and there are greater repulsions. The hybridisation is sp3d and it has 2 lone pairs

#SPJ4

Learn more about electron bonding at

https://brainly.com/question/2159156

Option e) T-shaped

The shape or molecular geometry  of ClF₃ is T-shaped. It acquires such a shape due to the presence of two lone pairs in the equatorial position and has greater repulsion. The hybrid is sp³d and it has 2 lone pairs.

Learn more about electron bonding here

https://brainly.com/question/1604211

#SPJ4

Answer:

45

Step-by-step explanation:

10%x60=6 60/10

70%=42 6x7

5%=3 6/2

42+3=45

The opposite sides will be congruent , and angles such as ∠LJI, ∠JKH, ∠KIH, ∠IHE, and ∠HGF will be equal or congruent.

As per the given statement, when we reflect the points C, B, A, L, and K across line maps, it maps these points onto E, F, G, H, and I, respectively.

As a result, the opposite angles of this figure will be congruent and equal.

Similarly, when we reflect the points L, K, J, I, and H across line maps, it maps these points onto B, C, D, E, and F, respectively.

Consequently, the opposite sides will be congruent, and angles such as ∠LJI, ∠JKH, ∠KIH, ∠IHE, and ∠HGF will be equal or congruent.

To learn more about congruent visit;

https://brainly.com/question/30596171

#SPJ11

Answer:

9x^2 - 36x + 35.

Step-by-step explanation:

One would be (x - 5/3)(x - 7/3)   <------ in factor form.

Getting rid of the fractions by multiplying each term by 3:

= (3x - 5)(3x - 7)

Converting to standard form

= 3x*3x -7*3x - 5*3x + 35

= 9x^2 - 36x + 35.

Answer: x=2.

Step-by-step explanation:

\(\displaystyle \\25^{x-1}=5^{2x-1}-100\\\\(5^2)^{x-1}=\frac{5^{2x}}{5} -100\\\\5^{2*(x-1)}=\frac{5^{2x}}{5} -100\\\\5^{2x-2}=\frac{5^{2x}}{5}-100\\\\\frac{5^{2x}}{5^2} =\frac{5^{2x}}{5} -100\\\\\frac{5^{2x}}{25} =\frac{5^{2x}}{5} -100\ |*25\\\\5^{2x}=5*5^{2x}-2500\\\\5^{2x}+2500=5*5^{2x}-2500+2500\\\\5^{2x}+2500=5*5^{2x}\\\\5^{2x}+2500-5^{2x}=5*5^{2x}-5^{2x}\\\\2500=4*5^{2x}\ |:4\\\\625=5^{2x}\\\\5^4=5^{2x}\ \ \ \ \ \ \Rightarrow\\\\4=2x\ |:2\\\\2=x\\\\Hence\ \ x=2.\)

If the defendeant is guilty, the probability that the jury makes the correct decision is approximately 0.476.

To calculate the probability that the jury makes the correct decision, we need to consider two cases: the defendant is guilty and the defendant is not guilty.

Let's start with the case where the defendant is guilty. The probability that any individual juror makes the correct decision on the defendant is 0.80. Therefore, the probability that at least 10 out of 12 jurors make the correct decision is given by the binomial distribution:

P(at least 10 out of 12 jurors say "guilty") = sum of P(k jurors say "guilty") for k = 10, 11, 12

Using a binomial calculator or formula, we can find that this probability is approximately 0.952.

Now let's consider the case where the defendant is not guilty. In this case, the probability that any individual juror makes the correct decision is 0.20 (since they should say "not guilty"). Therefore, the probability that at least 10 out of 12 jurors say "guilty" when the defendant is actually not guilty is given by the same binomial distribution:

P(at least 10 out of 12 jurors say "guilty" | defendant is not guilty) = sum of P(k jurors say "guilty") for k = 10, 11, 12

Using the binomial formula, we can find that this probability is approximately 0.0003.

To find the probability that the jury makes the correct decision, we need to weigh the two cases by their respective probabilities:

P(correct decision) = P(defendant is guilty) * P(at least 10 out of 12 jurors say "guilty") + P(defendant is not guilty) * P(at least 10 out of 12 jurors say "guilty" | defendant is not guilty)

Plugging in the values, we get:

P(correct decision) = 0.5 * 0.952 + 0.5 * 0.0003 = 0.476

To learn more about probability click on,

https://brainly.com/question/31116768

#SPJ4

Answer: R

Step-by-step explanation:

Answer:

See attachment for diagram

Step-by-step explanation:

Given

\((x_1,y_1) = (-8,8)\)

\((x_2,y_2) = (-3,8)\)

\(Area = 15\)

Required

Draw the rectangle on a coordinate plane --- (missing from the question)

First, we calculate the distance between the given pairs.

\(D = \sqrt{(x_1 - x_2)^2 + (y_1-y_2)^2}\)

\(D = \sqrt{(-8-(-3))^2 + (8-8)^2}\)

\(D = \sqrt{25}\)

\(D = 5\)

So, the distance between the given pairs is 5 units... Let this be the length of the rectangle.

Using:

\(Area = Length * Width\)

\(15 = 5 * Width\)

\(Width = \frac{15}{5}\)

\(Width = 3\)

The width is 3 units.

This implies that the opposite sides of the rectangle are either 3 units down or 3 units up the given pairs.

Assume they are 3 units up.

\((x_1,y_1) = (-8,8)\)   and \((x_2,y_2) = (-3,8)\)

\((x_3,y_3) = (x_1,y_3 + 3) = (-8,8+3) = (-8,11)\)

\((x_4,y_4) = (x_2,y_2 + 3) = (-3,8+3) = (-3,11)\)

Cosx, -sinx, -cosx + C, sinx + C are the derivative answers to the question.

The derivative of sin x with respect to x is cos x.
The derivative of cos x with respect to x is -sin x.
The antiderivative of sin x with respect to x is -cos x + C, where C is the constant of integration.
The antiderivative of cos x with respect to x is sin x + C, where C is the constant of integration.

1. The derivative of sin(x) with respect to x is cos(x).
2. The derivative of cos(x) with respect to x is -sin(x).
3. The antiderivative of sin(x) with respect to x is -cos(x) + C, where C is the constant of integration.
4. The antiderivative of cos(x) with respect to x is sin(x) + C, where C is the constant of integration.

A derivative in mathematics is a measurement of how much a function alters as its input alters. It refers to how quickly a function alters in relation to its input variable. The slope of the tangent line to the function at a certain point is what it is, in other words.

The limit of the ratio of the change in the output to the change in the input, as the change in the input approaches zero, is known as the derivative of a function, indicated by the symbols f'(x) or \(dy/dx\).

The opposite of differentiation is an antiderivative, usually referred to as an indeterminate integral. It is a function that yields the original function when differentiated. In other words, f(x) follows if \(f'(x) = g(x)\).

Learn more about derivative here:

https://brainly.com/question/31490789

#SPJ11

The reasonable class interval for a data set with a maximum value of 70 and a minimum value of 1, using 7 classes, would be option b) 10.

The class interval represents the range of values that will be included in each group or class when organizing the data.

To determine a reasonable class interval, we need to consider the range of the data, the number of classes desired, and the level of detail needed. In this case, the range of the data is 70-1=69, and we want to use 7 classes.

Dividing the range by the number of classes (69/7) gives us approximately 10. Therefore, a class interval of 10 is a reasonable choice for summarizing this data set.

to learn more about class interval click here:

brainly.com/question/30801913

#SPJ11

Answer:

$171

Step-by-step explanation:

Price of lemonade = $9 per cup

Quantity sold = 19 cups of lemonade

Revenue = price of the product × quantity of the product sold

Silvia's total revenue = price × Quantity

= $9 × 19 cups

= $171

Silvia has made a total of $171 from selling 19 cups of lemonade at $9 each