it is known that amounts of money spent on clothing in a year by college students follow a normal distribution with a mean of $340 and a standard deviation of $50. what is the probability that a randomly chosen student will spend between $300 and $400 on clothing in a year?

The high school bell and junior school bell will ring at the same time 4 times during the school day.

First  we need to find the least common multiple (LCM) of 45 minutes and 30 minutes, which is the smallest multiple that both 45 and 30 share.

The prime factorization of 45 is 3 × 3 × 5, and the prime factorization of 30 is 2 × 3 × 5. To find the LCM, we need to take the highest power of each prime factor that appears in either factorization. So, the LCM of 45 and 30 is:

LCM(45, 30) = 3 × 3 × 2 × 5 = 90

Therefore, the high school bell and junior school bell will ring at the same time every 90 minutes. To find out how many times this will happen during the school day,

We need to know how many 90-minute intervals there are in the length of the school day. If the school day is 6 hours long (360 minutes), then there are:

360 ÷ 90 = 4

So the high school bell and junior school bell will ring at the same time 4 times during the school day.

Learn more about prime factorization here : brainly.com/question/18187355

#SPJ1

The probability that a randomly chosen subject comples more than the expected number of puzzles in the five minute is equals to the 0.40. So, option (b) is right one.

We have a Random variables X denotes the number of puzzles complete by random choosen subject. The above table contains probability distribution of random variable X. The expected number of puzzles in the 5-minutes period while listening to smoothing music is calculated by following formula, \(E(x) = \sum x_i p(x_i)\)

= 1(0.2) + 2(0.4) + 3(0.3) + 4(0.1)

= 0.2+ 0.8+ 0.9+ 0.4

= 2.3

Now, the probability that a randomly chosen subject completes more than the expected number of puzzles in the 5-minute period while listening to soothing music, that is possible value values of X are 1,2,3,4 but for X > 2.3 only 3 and 4. So, P(X>2.3)= P(X=3) + P(X=4)

=0.30+ 0.10=0.40

Hence, required value is 0.40.

For more information about probability, refer:

https://brainly.com/question/25870256

#SPJ4

Complete question:

The above table complete the question

what is the probability that a randomly chosen subject comples more than the expected number of puzzles in the five minute period while losing music

a. 0.1

b. 0.4

c. 0.8

d. 1

e. Cannot be determined

The equation of the circle graphed in this problem is:

(x - 5)² + y² = 16.

The equation of a circle of center \((x_0, y_0)\) and radius r is given by:

\((x - x_0)^2 + (y - y_0)^2 = r^2\)

For the circle graphed, we have that:

Hence the equation of the circle graphed is:

(x - 5)² + y² = 16.

More can be learned about the equation of a circle at https://brainly.com/question/24307696

#SPJ1

The average signal power of the given signal is 1.0156 or approximately 0.5 (rounded to one decimal place). This indicates that the signal is moderately strong and contains a reasonable amount of energy.

Therefore, the average signal power of the given signal is 1.0156 or approximately 0.5 (rounded to one decimal place). This indicates that the signal is moderately strong and contains a reasonable amount of energy.

For more such question on power

https://brainly.com/question/28782029

#SPJ11

The statements which must be true from the given statements are :

Base angles of Quadrilateral Z are congruent.

Opposite angles of quadrilateral C are congruent.

Opposite angles of quadrilateral L are congruent.

Consecutive angles of quadrilateral Z are congruent.

Consecutive angles of quadrilateral L are congruent.

Opposite angles of quadrilateral C are supplementary.

Opposite angles of quadrilateral T are supplementary.

Given are,

Quadrilateral C has 4 congruent sides.

So this must be a square and thus all angles are equal which is equal to 90°.

Opposite angles are thus congruent.

Opposite angles of a quadrilateral is always supplementary.

Quadrilateral L has two pairs of parallel sides and congruent diagonals.

So it must be a rectangle or a square.

So, opposite angles are congruent, each equal to 90 degrees.

Also, consecutive angles are equal, since each angle equal to 90°.

Quadrilateral T has at least one pair of parallel sides that are also congruent.

If at least one pair of parallel sides are congruent, then the other pair of sides are also parallel and congruent.

S it can be rectangle, square, parallelogram or rhombus.

If it is parallelogram or rhombus, base angles will not be equal.

Opposite angles are supplementary.

Quadrilateral Z has exactly one pair of parallel sides that are not congruent. The other pair of sides are congruent.

This must be an isosceles trapezium.

Base angles of an isosceles trapezium are equal and thus congruent.

So consecutive angles are congruent.

Learn more about Congruence here :

https://brainly.com/question/29039487

#SPJ1

The total length of two line segments is 80 cm

A line segment is just part of a line. It has two endpoints,

given that

the first line segment is 30cm

the second line segment is 500mm

now we need to convert it into cm from mm

To convert mm to cm, we need to multiply the length in mm by 0.1 cm since 1 mm is equal to 0.1 cm.

500 mm × 0.1 cm = 50cm

now we need to add two line segments

30 cm + 50 cm = 80 cm

The total length of two line segments is 80 cm

To learn more about line segments:

https://brainly.com/question/25727583

#SPJ4

to get the equation of any straight line all we need is two points, well, let's just grab them from the table.

hmmm let's use (-49 , -39) and hmmm say (67 , 77)

\((\stackrel{x_1}{-49}~,~\stackrel{y_1}{-39})\qquad (\stackrel{x_2}{67}~,~\stackrel{y_2}{77}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{77}-\stackrel{y1}{(-39)}}}{\underset{run} {\underset{x_2}{67}-\underset{x_1}{(-49)}}}\implies \cfrac{77+39}{67+49}\implies \cfrac{116}{116}\implies 1\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-39)}=\stackrel{m}{1}(x-\stackrel{x_1}{(-49)}) \\\\\\ y+39=1(x+49)\implies y+39=x+49\implies y=x+10\)

Answer:what

Step-by-step explanation:what does this mean

Answer:

There's nothing to answer to that question, can you be specific.

Step-by-step explanation:

Answer:

Will's Age : 35

Maria's Age : 15

Step-by-step explanation:

Will is five years more than twice Maria's age.

15 doubled is 30 plus 5 is 35.

In five years, when Will will be 40 and Maria will be 20 years, their ages will add up to 60.

Answer:

-2x -3

Step-by-step explanation:

Answer: 5:1, 1:6, 15,000.

Step-by-step explanation:

a. logic

b.5+1

c. 18000 divided by 6 is 3000 so you subtract 3000 from the total which is 18000.

This condition alone does not guarantee that n is an absolute pseudoprime; it still needs to pass a prime number test while being composite.

An integer n of the form (6k+1)(12k+1)(18k+1) is said to be an absolute pseudoprime if all three factors are prime. This type of integer is interesting because it behaves like a prime number in some ways, even though it may not be prime.

To understand why this is the case, we need to look at the properties of absolute pseudoprimes. One important property is that if n is an absolute pseudoprime, then it passes the Miller-Rabin test for all bases up to log2(n). This means that it is very difficult to tell whether or not n is actually prime, since it behaves like a prime in terms of the Miller-Rabin test.

Another interesting property of absolute pseudoprimes is that they are related to the Fermat pseudoprimes. In particular, if n is an absolute pseudoprime, then it is also a Fermat pseudoprime to base 2.

Overall, absolute pseudoprimes are an intriguing mathematical concept that have many interesting properties. While they may not be prime, they behave like prime numbers in some important ways, making them a valuable tool for number theorists and mathematicians.
An integer n is an absolute pseudoprime if it is a composite number (non-prime) that passes the prime number test, such as the Fermat primality test. In the given expression, n = (6k + 1)(12k + 1)(18k + 1), n would be considered an absolute pseudoprime if all three factors (6k + 1, 12k + 1, and 18k + 1) are prime numbers.

To learn more about integer visit;

brainly.com/question/15276410

#SPJ11

Answer:

25,300

Step-by-step explanation:

Its already rounded.

Considering the definition of the zeros of a quadratic function, it taks for the rocket 3.5 seconds to hit the ground.

The points where a polynomial function crosses the axis of the independent term (x) represent the so-called zeros of the function, and  are those values ​​of x for which the expression is equal to 0.

That is, the zeros represent the roots of the polynomial equation that is obtained by making f(x)=0.

In a quadratic function that has the form:

f(x)= ax² + bx + c

the zeros or roots are calculated by:

\(x1,x2=\frac{-b+-\sqrt{b^{2} -4xaxc} }{2xa}\)

The height, h, of a rocket (in feet) is given by h= -16t² + 36t + 70

Being:

when the rocket hits the ground, the height is 0. So, the zeros of the function are calculated as:

\(t1=\frac{-36+\sqrt{36^{2} -4x(-16)x70} }{2x(-16)}\)

\(t1=\frac{-36+\sqrt{1296 +4480} }{-32}\)

\(t1=\frac{-36+\sqrt{5776} }{-32}\)

\(t1=\frac{-36+76}{-32}\)

\(t1=\frac{40}{-32}\)

t₁= -1.25 s

and

\(t2=\frac{-36-\sqrt{36^{2} -4x(-16)x70} }{2x(-16)}\)

\(t2=\frac{-36-\sqrt{1296 +4480} }{-32}\)

\(t2=\frac{-36-\sqrt{5776} }{-32}\)

\(t2=\frac{-36-76 }{-32}\)

\(t2=\frac{-112 }{-32}\)

t₂= 3.5 s

Finally, since time cannot have negative values, it taks for the rocket 3.5 seconds to hit the ground.

Learn more about the zeros of a quadratic function:

brainly.com/question/842305

#SPJ1

The biconditional statement is a polygon has four sides if and only if it is a quadrilateral. Option C

A biconditional statement is defined as a statement that combines both an converse and conditional statement.

It is written in the "if and only if" from.

It is a statement that states a condition depends on another being and vice versa.

From the statement given;

"if a polygon has four sides, then it is a quadrilateral

The biconditional statement is ;

Polygon has four sides if and only if it is a quadrilateral.

Thus, the biconditional statement is a polygon has four sides if and only if it is a quadrilateral. Option C

Learn more about a biconditional statement here:

https://brainly.com/question/24528571

#SPJ1

a) The solution for b in the equation 2b × 3 = 6 is b = 1.

b) The solution for b in the equation 32 - 3b = 2 is b = 10.

c) The solution for b in the equation 6 + 7b = 41 is b = 5.

d) The solution for b in the equation 100/5b = 2 is b = 10.

a) To solve for b in the equation 2b × 3 = 6, we can start by dividing both sides of the equation by 2 to isolate b.

2b × 3 = 6

(2b × 3) / 2 = 6 / 2

3b = 3

b = 3/3

b = 1

Therefore, the solution for b in the equation 2b × 3 = 6 is b = 1.

c) To solve for b in the equation 6 + 7b = 41, we can start by subtracting 6 from both sides of the equation to isolate the term with b.

6 + 7b - 6 = 41 - 6

7b = 35

b = 35/7

b = 5

Therefore, the solution for b in the equation 6 + 7b = 41 is b = 5.

b) To solve for b in the equation 32 - 3b = 2, we can start by subtracting 32 from both sides of the equation to isolate the term with b.

32 - 3b - 32 = 2 - 32

-3b = -30

b = (-30)/(-3)

b = 10

Therefore, the solution for b in the equation 32 - 3b = 2 is b = 10.

d) To solve for b in the equation 100/5b = 2, we can start by multiplying both sides of the equation by 5b to isolate the variable.

(100/5b) × 5b = 2 × 5b

100 = 10b

b = 100/10

b = 10.

Therefore, the solution for b in the equation 100/5b = 2 is b = 10.

In summary, the solutions for b in the given equations are:

a) b = 1

c) b = 5

b) b = 10

d) b = 10

For similar question on equation.

https://brainly.com/question/30451972  

#SPJ8

Answer:

20 Aussies

Step-by-step explanation:

20% times 5 = 100%

4 times 5 = 20 Aussies

So, there are 20 Aussies in a group.

Answer:

20

Step-by-step explanation:

4/20%

4/\(\frac{2}{10}\)

4 x \(\frac{10}{2}\) = \(\frac{40}{2}\) = 20

This pooled estimate provides a common probability of success for both populations under the null hypothesis H0: p1 = p2, and is used in the calculation of the test statistic for the hypothesis test.

To calculate the best pooled estimate p for the population probability of success using H0: p1 = p2, we first need to calculate the individual sample proportions for each population.

The sample proportion for the first population is r1/n1, and the sample proportion for the second population is r2/n2.

Then, we can calculate the pooled estimate p as:

p = (r1 + r2) / (n1 + n2)

This is the weighted average of the sample proportions, where the weight is proportional to the sample size.

Using this pooled estimate p, we can then calculate the test statistic for the hypothesis test of difference of proportions.

More on population probability: https://brainly.com/question/14125181

#SPJ11

Work Shown:

y = 15.6 - 3.8x

y = 15.6 - 3.8*3

y = 4.2

If f'(x)= (x-1)^2(x+4), then the function y=f(x) has: (C) one local minimum and one local maximum.

To determine the local minimums and maximums of y=f(x), we need to find the critical points where f'(x)=0 or where f'(x) does not exist.

In this case, f'(x)= (x-1)^2(x+4), which equals zero at x=1 and has a vertical tangent at x=-4.

To determine the behavior of the function around these critical points, we can use the first derivative test.

- At x=1, f'(x) changes from negative to positive, indicating that the function has a local minimum at x=1.
- At x=-4, f'(x) is negative on both sides, indicating that the function has a local maximum at x=-4.

Therefore, the answer is (C) one local minimum and one local maximum.

To learn more about tangent, refer below:

https://brainly.com/question/19064965

#SPJ11

Step-by-step explanation:

The answer is as follows

p+20=14

p=-6

Nash spent 15.20 dollars altogether on candies. we need to calculate the total cost of the candies he bought from both Nash and Richard.

To find out how much Nash spent altogether,

First, let's calculate the cost of the candies Nash bought.

He bought 37 candies for 20 cents each.

So, the total cost of candies bought from Nash is

\(37 x 20 = 740 cents.\)

Next, let's calculate the cost of the candies Richard sold to Nash.

He sold 52 candies for 15 cents each.

So, the total cost of candies bought from Richard is

\(37 x 20 = 740 cents.\)
To find the total cost altogether,

we add the cost of candies bought from Nash and Richard.

\(740 cents + 780 cents = 1520 cents.\)
Since we need to express the answer in dollars,

we divide 1520 cents by 100 to convert it to dollars.

\(1520 cents / 100 = 15.20 dollars.\)

To know more about Richard visit:

https://brainly.com/question/4943777

#SPJ11

Answer:

$7.08

Step-by-step explanation:

I'm pretty sure it correct but if not sorry

Answer:

12 cans  = $49.56

bc

12 cans x 4.13 = $49.56

Step-by-step explanation:

Answer:

x = -2, y = -1, z = 4

Step-by-step explanation:

4x + 6y - z=-18

z  = 18  + 4 x  +  6 y

3x +2y - 4z = -24

z  = 6  + (3x)/ 4  +  y /2

- 5x + 3y + 2z = 15

z = 15/2 + (5x)/2 - (3y)/2

18  + 4 x  +  6 y = 6  + (3x)/ 4  +  y /2  = 15/2 + (5x)/2 - (3y)/2

x = -22y/13 - 48/13

4(-22y/13 - 48/13) + 6y - (15/2 + (5(-22y/13 - 48/13))/2 - (3y)/2) = -18

Compute the output value of the variables x and y with respect to the input values of x, y, and z coefficients.

Answer:

Coating the seed typically improves seed quality and germination rates, so the same seeding rate can be maintained even with coated seed.

To convert mass-based seeding rates to population-based establishment rates, we need to consider the area conversion factors provided:

a. Given a seeding rate of 60 lbs/acre for cereal rye, we can convert it to seeds per square foot by using the conversion factor of 1 acre = 43,560 square feet.

b. Given a seeding rate of 15 kg/ha for crimson clover, we can convert it to seeds per square meter using the conversion factor of 1 hectare = 10,000 square meters.

To convert population-based seeding rates to mass-based seeding rates, we can use the given area conversion factors:

a. Given a seeding rate of 30 plants/square foot for oats, we can convert it to pounds of seed per acre.

b. Given a seeding rate of 20 plants/square meter for hairy vetch, we can convert it to kilograms of seed per hectare.

Learn more about square here:

https://brainly.com/question/14198272

#SPJ11

Answer:

x = -26

Step-by-step explanation:

ab - cd = ?

2(-3) - 4(5) = x

-6 - 20 = x

-26 = x