Fifteen out of the first 20 students who entered the calallen middle school (cms) on friday were wearing a spirit shirt. based on the information, if 840 students attended cms on friday, how many could be expected to be wearing a spirit shirt?

The answers to all subquestions would be

Part A: \(P(X=x)= {15 \choose x} (0.15)^{x} (0.85)^{15-x}\), x= 0, 1, 2, 3, ..., 15.

Part B: P(X = 1) = 0.2312

Part C: P(X = 2) = 0.2656

Part D: P(X ≥ 2) = 0.6814

Part E: P(X = 0) = 0.0874

What is a binomial distribution?

The binomial distribution with parameters n and p in probability theory and statistics is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-no question and each with its own Boolean-valued outcome: success or failure.

Let X be the random variable.

The number of trials n = 15, P=0.15

X ~ Bin(n, p)

Part A:

      \(P(X=x)= {n \choose x} (p)^{x} (1-p)^{n-x}\)

      \(P(X=x)= {15 \choose x} (0.15)^{x} (0.85)^{15-x}\), x=0, 1, 2, 3,..., 15.

Part B:

    \(P(X=1)= {15 \choose 1} (0.15)^{1} (0.85)^{15-1}\\\\P(X=1)= {(15)} (0.15) (0.85)^{14}\\\\P(X=1)=0.2312\)

Part C:

     \(P(X=2)= {15 \choose 2} (0.15)^{2} (0.85)^{15-2}\\\\P(X=2)= {(105)} (0.15)^2 (0.85)^{13}\\\\P(X=2)=0.2856\)

Part D:

 \(P(X\geq 2)= 1-P(X < 2)\\\\P(X\geq 2)=1-P(X=0)-P(X=1)\\\\P(X\geq 2)=1-0.0873-0.3212\\\\P(X\geq2)=0.6814\)

Part E:

  The probability of none of the children getting the disease will be

             \(P(X=0)= {15 \choose 0} (0.15)^{0} (0.85)^{15-0}\\\\P(X=0)= {(1)} (1) (0.85)^{15}\\\\P(X=1)=0.8734\)

Hence,

Part A: \(P(X=x)= {15 \choose x} (0.15)^{x} (0.85)^{15-x}\), x= 0, 1, 2, 3, ..., 15.

Part B: P(X = 1) = 0.2312

Part C: P(X = 2) = 0.2656

Part D: P(X ≥ 2) = 0.6814

Part E: P(X = 0) = 0.0874

To learn more about binomial distribution, visit:

https://brainly.com/question/9325204

#SPJ4

The values of x and y that make RAPT a parallelogram are;

x = 15 and y = 25

Angle T and angle P are supplementary angles by parallel lines. Thus they sum up to 180 degrees and we have;

3x + 10 + 8x + 5 = 180

11x + 15 = 180

11x = 165

x = 15

T = 55°

P = 125°

Likewise R and T are supplementary angles by parallel lines and so we have;

55 + 5y = 180

5y = 180 -55

5y = 125

y = 25

R = 125°

A must be 55° since the angles add up to 360°.

R + A + P + T =

125 + 55 + 125 + 55 = 360°

Read more about angles of a Parallelogram at; https://brainly.com/question/24056495

#SPJ1

Answer:

261

Step-by-step explanation:

Answer:

The answer is zero

Step-by-step explanation:

The solution to the quadratic equation 2x² - 4x - 3 = 0 is x = 1 ± √2.5

An equation is an expression that shows the relationship between two or more numbers and variables.

Solving the polynomial using completing the square:

2x² - 4x - 3 = 0

First divide through by 2:

x² - 2x - 3/2 = 0

add 3/2 to both sides:

x² - 2x - 3/2 + 3/2 = 0 + 3/2

x² - 2x = 3/2

add the square of half the coefficient x to both sides:

x² - 2x + 1 = 3/2 + 1

(x - 1)² = 2.5

taking square root:

x - 1 = ±√2.5

x = 1 ± √2.5

The solution to the quadratic equation 2x² - 4x - 3 = 0 is x = 1 ± √2.5

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer: Step 3

Step-by-step explanation: this is the right answer on the edge, hope this helps!

Let's break down the expression for Tony's combined total earnings step by step.

First, we consider Tony's earnings as a tutor. He earns $11 per hour as a tutor, so the amount he earns from tutoring is given by the product of his hourly rate ($11) and the number of hours he worked as a tutor (t). This can be represented as $11t.

Next, we consider Tony's earnings as a waiter. He earns $13 per hour as a waiter, so the amount he earns from waiting tables is given by the product of his hourly rate ($13) and the number of hours he worked as a waiter. Since Tony worked a total of 106 hours this month and spent t hours as a tutor, he must have worked (106 - t) hours as a waiter. This can be represented as $13(106 - t).

To calculate Tony's combined total earnings for the month, we add the amount he earned as a tutor ($11t) to the amount he earned as a waiter ($13(106 - t)). This yields the expression:

Earnings = $11t + $13(106 - t)

This expression represents the total dollar amount Tony earned this month, considering the number of hours he worked as a tutor (t) and waiter (106 - t).

To find the rate at which the radius of the oil spill is increasing when the area is 7 mi^2, dr/dt ≈ 0.203 mi/hr the area of the spill is 7 mi^2, dr/dt ≈ 0.203 mi/hr the radius is increasing at a rate of 0.203 mi/hr.

Where A is area and r is the radius. Taking the derivative of both sides with respect to time, we can express the rate of change of the area as dA/dt = 2πr(dr/dt). Given that dA/dt is constant at 8.5 mi^2/hr, we can substitute the values to find the rate at which the radius is increasing.

We have the equation dA/dt = 2πr(dr/dt), where dA/dt represents the rate of change of the area, r is the radius, and dr/dt is the rate at which the radius is changing. We are given that dA/dt is constant at 8.5 mi^2/hr. When the area is 7 mi^2, we can substitute these values into the equation: 8.5 = 2π(7)(dr/dt)

Simplifying the equation, we can solve for dr/dt: dr/dt = 8.5 / (2π(7)) Evaluating the expression, we find: dr/dt ≈ 0.203 mi/hr

Therefore, when the area of the spill is 7 mi^2, the radius is increasing at a rate of approximately 0.203 mi/hr.

To learn more about radius click here : brainly.com/question/13449316

#SPJ11

Answer:

20400

Step-by-step explanation:

Field data aggregation is the process of summarizing, combining, and analyzing data that has been collected from various sources. The following are some of the common ways that field data is aggregated: Count of Failures: A count of how many times a failure has occurred within a given period of time,

such as a day or a week. Number of Failed Parts: The number of parts that have failed over a given period of time, such as a day or a week. Hours of Operation: The amount of time that a machine or system was operational during a given period of time, such as a day or a week. Maintenance Time: The amount of time that was spent maintaining a machine or system during a given period of time, such as a day or a week.

Mark for Follow-Up: An indication of which issues need to be addressed or followed up on to prevent future failures or improve performance. Field data aggregation is the process of summarizing, combining, and analyzing data that has been collected from various sources. The following are some of the common ways that field data is aggregated: Count of Failures: A count of how many times a failure has occurred within a given period of time,

To know more about summarizing visit:

https://brainly.com/question/20058250

#SPJ11

Answer:

1.) 12000

2.) 6750

3.) 2.41

Step-by-step explanation:

Given the Equation :

f(t)=12,000(3/4)^t. ; where, t = time ; f(t) = worth of car at time, t

When, car was purchased, t = 0

t = 0

f(0) = 12000(3/4)^0

= 12000 * 1

= 12000

2.)

f(2) ; this mean the worth of the car after 2 years :

f(2)=12,000(3/4)^t.

12000(3/4)^2

12000 * 0.5625

= 6750

When car will be worth 6000

f(t) = 6000

f(t)=12,000(3/4)^t.

6000 = 12,000(3/4)^t

6000 / 12000 = (3/4)^t

1/2 = (3/4)^t

Take the log of both sides :

Log(0.5) = log(0.75)^t

log(0.5) = tlog(0.75)

- 0.301029 = - 0.124938t

t = - 0.301029 / - 0.124938

t = 2.4094

t = 2.41 years

Using proportions, the coordinates of point R are given as follows: R(1.2, 0.4).

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Segments pr and pq are partitioned in the ratio 3:2, hence:

\(PR = \frac{3}{5}PQ\)

\(R - P = \frac{3}{5}(Q - P)\)

The points are:

For the x-coordinate, we have that:

\(R - P = \frac{3}{5}(Q - P)\)

\(x - 6 = \frac{3}{5}(-2 - 6)\)

x - 6 = -4.8

x = 1.2.

For the y-coordinate, we have that:

\(R - P = \frac{3}{5}(Q - P)\)

\(y + 5 = \frac{3}{5}(4 + 5)\)

y + 5 = 5.4.

y = 0.4.

The coordinates are: R(1.2, 0.4).

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

The formula for calculating z score is expressed as

z = (x - μ)/σ

where

x represents sample mean

μ represents population mean

σ represents population standard deviation

From the information given,

x = 55

μ = 98

σ = 5

By substituting these values into the formula,

z = (55 - 98)/5 = - 43/5

z = - 8.6

Answer:

490 students.

Step-by-step explanation:

7 out of 10 students would be a percentage of 70% which is 0.7 in decimal form. To find out how many students would be expected to be carrying a backpack out of 700 students, 700 * 0.7 = 490 students.

Answer:

I believe the answer is B. 1/15

Step-by-step explanation:

Answer:

B. 1/15

Step-by-step explanation:

The correct statements are:

The triangle and trapezoid area formulas have 1/2.

The parallelogram and rectangle formulas are both the same.

In the trapezoid formula, the bases are added.

A triangle is a polygon with three sides and three vertices. A triangle's angles add up to 180 degrees.

Area of a triangle = 1/2 x base x height

A trapezium is a quadrilateral that is convex. A trapezium is made up of at least two parallel sides. Area of a trapezium = 1/2  x (sum of the lengths of the parallel sides) x height

A rectangle is a quadrilateral in two dimensions with four right angles. Area of a rectangle = length x width

A parallelogram is a quadrilateral with two parallel sides. The opposite sides equal in length

Area of a parallelogram = base x height

Hence, the correct statements are options (A), (B), and (D).

Learn more about the area of a triangle here:

brainly.com/question/9329354

#SPJ1

The question seems to be incomplete the correct question would be:

A neighborhood was given a vacant lot in the shape of a rectangle on which to build a park. The neighborhood is

considering how to split up the area. Which statements about the formulas for finding areas are true? Check all that

apply.

A. The triangle and trapezoid area formulas have 1/2.

B. The parallelogram and rectangle formulas are both the same.

C. In the parallelogram formula, the bases are added.

D. In the trapezoid formula, the bases are added.

E. In the triangle formula, the sides are added, then multiplied by 1/2​

Answer: The last graph

Quartiles, mean and medians all match up

Answer:

the mode remains the same

Step-by-step explanation:

42 is outlier.

mod is the most repetitive number of a number string, and outlier does not change it.

the mode remains the same.

i. The Fourier transform of (t - 2) - 38(t - 3) is [(jw)^2 + 38jw]e^(-2jw). ii. The Fourier transform of e^(-2t)u(t) is 1/(jw + 2). iii. The Fourier transform of e^(-3t+12)u(t-4) can be obtained using the result of ii. as e^(-2t)u(t-4)e^(12jw). iv. The Fourier transform of e^(-2|t|)cos(t) is [(2jw)/(w^2+4)].

i. To find the Fourier transform of (t - 2) - 38(t - 3), we can use the linearity property of the Fourier transform. The Fourier transform of (t - 2) can be found using the time-shifting property, and the Fourier transform of -38(t - 3) can be found by scaling and using the frequency-shifting property. Adding the two transforms together gives [(jw)^2 + 38jw]e^(-2jw).

ii. The function e^(-2t)u(t) is the product of the exponential function e^(-2t) and the unit step function u(t). The Fourier transform of e^(-2t) can be found using the time-shifting property as 1/(jw + 2). The Fourier transform of u(t) is 1/(jw), resulting in the Fourier transform of e^(-2t)u(t) as 1/(jw + 2).

iii. The function e^(-3t+12)u(t-4) can be rewritten as e^(-2t)u(t-4)e^(12jw) using the time-shifting property. From the result of ii., we know the Fourier transform of e^(-2t)u(t-4) is 1/(jw + 2). Multiplying this by e^(12jw) gives the Fourier transform of e^(-3t+12)u(t-4) as e^(-2t)u(t-4)e^(12jw).

iv. To find the Fourier transform of e^(-2|t|)cos(t), we can use the definition of the Fourier transform and apply the properties of the Fourier transform. By splitting the function into even and odd parts, we find that the Fourier transform is [(2jw)/(w^2+4)].

Learn more about exponential here:

https://brainly.com/question/29160729

#SPJ11

Answer: Hi The Answer is 3 (the third one)

Step-by-step explanation: Am not sure if this is correct am taking the test right now

Answer:

all real numbers

Step-by-step explanation:

Florida

The critical value used to test if there is evidence of an effect due to blocks at the 5% level of significance is 10.76.

The critical value can be determined using a statistical table.

The degrees of freedom for the blocks is 4 (df_b = 5 - 1 = 4) and for the treatments is 2 (df_t = 3 - 1 = 2).

The critical value for a 5% level of significance is 10.76.

This value can be found in the statistical table given in the textbook.

The critical value used to test if there is evidence of an effect due to blocks at the 5% level of significance can be calculated by using the F-test statistic.

The F-test is used to compare the variance between the blocks (SSBL) and the variance between the groups (SSB).

The F statistic is calculated by dividing the variance between the blocks (SSBL) by the variance between the groups (SSB).

In this case,

The F statistic is 3738/1048.93 = 3.56.

The critical value for a 5% level of significance can be found using a statistical table.

According to the table,

The critical value for an F statistic of 3.56 with four degrees of freedom in the numerator and four degrees of freedom in the denominator is 10.76

For similar question on critical value:

https://brainly.com/question/30168469

#SPJ11

The correct option is A) 5 – 1 ≠ 1 – 5  shows why the commutative property doesn't work under subtraction

The commutative property works for addition and multiplication. It says that when adding or multiplying, you can switch the order of the numbers around and still get the same answer.

For instance, in simple terms, the commutative property of addition states that changing the order of the addends will not change the sum. That is, a + b = b + a.

Similarly, the commutative property of multiplication states that changing the order of the factors will not change the product. That is, a × b = b × a.

However, the commutative property does not work for subtraction and division. You cannot change the order of numbers around and still get the same answer when you're subtracting or dividing. In other words, the order of the numbers matters in these cases.

That is, a - b ≠ b - a; a / b ≠ b / a.Here, the options C and D are not valid since they both represent addition operations, whereas the question demands subtraction. Between options A and B, A represents the subtraction operation and the result for this option is not the same as the result for the reverse subtraction operation which is why A is the right option.

To know more about commutative property refer here:

https://brainly.com/question/28747013#

#SPJ11

Answer:

it is 1

Step-by-step explanation:

Answer:

-1/2

Step-by-step explanation:

If you go to any point on the line, you count down 1 point, and over to the right by 2 points to get back to the line. That is what makes the slope -1/2.

Answer:

The slope of the line is \( - \frac{1}{2} \)

Step-by-step explanation:

☆Remember: \(slope = \frac{rise}{run} \)

▪Happy To Help <3

Answer:

6.2 oz is lower

Step-by-step explanation:

Rounding to four decimal places, the probability of getting at least one 3 in nine rolls of a single die is approximately 0.6242.

To calculate the probability of getting at least one 3 in nine rolls of a single die, we can use the concept of complementary probability.

The complementary probability states that the probability of an event not happening is equal to 1 minus the probability of the event happening.

Let's calculate the probability of not getting any 3 in nine rolls of a single die:

The probability of not rolling a 3 on a single roll is 5/6 since there are 5 other numbers on the die.

The probability of not rolling a 3 in nine rolls is \((5/6)^9\) because each roll is independent.

Now, we can calculate the probability of getting at least one 3:

Probability of at least one 3 = 1 - Probability of not getting any 3

\(= 1 - (5/6)^9\)

Using a calculator, we find:

Probability of at least one 3 ≈ 0.6242

To know more about probability,

https://brainly.com/question/31525146

#SPJ11

Claire experiences apprehension and fear during the anticipatory socialization phase of socialization when her boss proposes putting her on a task force at work, due to her negative group experiences in college.

Anticipatory socialization is the phase in the socialization process where individuals anticipate and prepare for their future roles and experiences in a particular social group or setting.

It involves forming expectations, attitudes, and behaviors based on past experiences and knowledge.

In Claire's case, her negative group experiences in college, where she often ended up doing most of the work and faced poor communication within the group, have shaped her expectations and attitudes towards group work.

As a result, when her boss proposes putting her on a task force at work, Claire immediately feels apprehensive and fearful.

She anticipates that she may face similar challenges, such as an uneven distribution of workload and ineffective communication, which could negatively impact her experience in the task force.

During the anticipatory socialization phase, individuals rely on their past experiences and perceptions to anticipate what they may encounter in a new social setting.

Claire's negative group experiences in college have influenced her apprehension and fear, as she expects the same difficulties to arise in the task force at work.

These emotions and concerns may impact her willingness to fully engage in the new group and could influence her interactions and behavior within the task force.

Learn more about communication here:

https://brainly.com/question/29468743

#SPJ11

The fourth bag also has an odd number of oranges (3 is odd).

The distribution of oranges in the four bags is as follows:

First bag: 6 oranges (odd)Second bag:

6 oranges (odd)Third bag: 6 oranges (odd)

Fourth bag: 3 oranges (odd)

To put 21 oranges in 4 bags and still have an odd number of oranges in each bag, one possible way is to put 6 oranges in each of the first three bags and the remaining 3 oranges in the fourth bag.

This way, each of the first three bags has an odd number of oranges (6 is even, but 6 + 1 = 7 is odd), and the fourth bag also has an odd number of oranges (3 is odd).

To know more about,distribution visit

https://brainly.com/question/29664127

#SPJ11

The percentage of the new quantity in letter b is 40% and the Percentage of the new quantity in letter c is 76%.

A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum.

Given data:

letter b: Original Quantity: 20 new quantity: 8

letter c: original quantity: 50 new quantity: 38

Calculate the percentage as shown below,

Percentage of new quantity in letter b = new quantity / Original Quantity × 100

Percentage of new quantity in letter b = 8 / 20 × 100 = 40%

Percentage of new quantity in letter c = new quantity / Original Quantity × 100

Percentage of new quantity in letter c = 38 / 50 × 100 = 76%

Therefore, the percentage of the new quantity in letter b is 40% and the Percentage of the new quantity in letter c is 76%.

To know more about percentages:

brainly.com/question/20818421

#SPJ1

Answer:

L2 + W2 = P

L = 3W

2(3W) + 2W = 104

6W + 2W = 104

8W = 104

W = 13

Step-by-step explanation:

perimeter is 2 times length plus two times width.

add these togethter to get 104 (the given number)

then create an equation to find length based on the given number

simplify and find w.

Answer: width = 13 ft

Step-by-step explanation:

Perimeter (P) = 2 × Length (L) + 2 × width (w)

Given: P = 104, L = 3w

  P =   2L  +  2w

104 = 2(3w) + 2w

104 = 6w + 2w

104 = 8w

13 = w

Answer:

8076 candies is the total number of candies on the truck

Step-by-step explanation:

If 1 box has 12 candies.

then 673 boxes shall have ( 673 * 12 ) = 8076 candies.