(i). A class starts at 3:10 p.m. Four students in the class arrive at random times T1, T2, T3, T4, T5 that are independent and all have the uniform distribution on the interval 3:07 to 3:12. Let X = max(T1, T2, T3, T4, T5) be the time when the last of the five students arrives. What is the probability that X is after 3:10 p.m.? (ii). The heights of two men drawn at random from a population are independent and identically normal with mean 68 inches and SD 3 inches. Find the chance that one of the men is more than 6 inches taller than the other.

Answer:

76.4%

Step-by-step explanation:

Total area of flag:

LW = (37)(28) = 1036

Total area of red:

LW = (12 + 21)(12 + 12) = (33)(24) = 792

Percent of red:

792/1036 * 100% = 76.4%

Answer:

→(37×28) unit²=1036unit²

→[{2×(12×12)}+{2×(21×12)}]

=[{2×144}+{2×252}]

=[288+504]=792unit²

→(792/1036)×100=0.7645×100=76.45%

76.45% is the right answer.

To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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Answer:

100/50=one over two which is half and half of sixty is thirty so therefore thirty stores are in California and thirty stores are in Nevada too

The least amount that Bill must pay to buy the tiles he needs is $292.50

The total cost of buying the tiles individually is : cost per tile x total tiles needed

$0.40 x 864 = $345.60

The total cost of buying the tiles in a box of 100 is : $32.50 x 9 = $292.50

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Answer:

= $20.

Step-by-step explanation:

items pay now = x

40 : 100 = x : 50

40/100 = x/50

40× 5o = 100x

2000 = 100x

2000/100 = 100x/100

$20= x

therefore you pay $20 item that used to cost $50.

True, the eventual success of any system solely depends on how users work with it.

A system's success is determined by various factors, such as its design, functionality, and compatibility with user needs.

However, user engagement, adaptability, and willingness to work with the system notably contribute to its success.

Users who understand the system's features and can efficiently adapt and utilize them in their workflow contribute to its overall effectiveness.

In contrast, a system with poor user adoption and engagement may not achieve its intended outcomes, regardless of its inherent quality.

So, even if a system is well-designed and has all the necessary features, if users are unable to effectively use it, the system will not achieve its intended purpose.

Thus, user adoption and effective usage are crucial for the success of any system.

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Answer: 0.43ft²

Step-by-step explanation:

You didn't really specify part A but In assuming that the question you posted is part A. Anyways in this case, area will be calculated by multiplying the length by the width.

Since the piece of wood has a length that is 2.45 feet and width that is 2.097 inches, then the area will be:

= 2.45 × 0.17475

= 0.4281375 ft²

= 0.43ft² to nearest hundredths

Note 1 foot = 12 inches

Therefore, 2.097 inches = 2.097/12 = 0.17475 feet

The probability\(\( P(0 \leq z \leq 0.59) \)\) is approximately 0.2236.

To calculate the probability, we need to find the area under the standard normal curve between 0 and 0.59. This can be done by using the standard normal distribution table or a calculator.

The table provides the cumulative probability up to a given z-value. For 0, the cumulative probability is 0.5000, and for 0.59, the cumulative probability is 0.7224. To find the probability between these two values, we subtract the cumulative probability at 0 from the cumulative probability at 0.59:

0.7224

−

0.5000

=

0.2224

0.7224−0.5000=0.2224. Rounded to four decimal places, the probability is approximately 0.2217.

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Given statement 'a local variable is a variable defined inside a function that can only be used inside its function' is False

A local variable is a type of variable that we declare inside a block or a function, unlike the global variable. They can be used only by the statements that are inside the function or the block of the code. Local variables are not known to functions outside their own.

The variable declared is local within that function that is the declared variable is accessible inside that block itself, it cannot be accessible outside the given function.

Consider the following multiplication function:

ex - void multi()

{

int a = 10,  b = 2, c ;

c = a * b ;

cout << c ;

}

int main()

{

cout << "value for c is :"<< c ;

return 0;

}

Here inside the multi function variable a, b, c are declared and initialized inside the function.

Thus, a local variable is defined inside the body of the function and is not accessible outside of the function.

Therefore, given statement 'a local variable is a variable defined inside a function that can only be used inside its function' is False

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Answer:

1/8 or 12.5%

Step-by-step explanation:

2/16 are nectarines. If you randomly choose a fruit out of the basket, you have a 2/16 chance of picking out a nectarine, which can be simplified down to 1/8 or 12.5%.

Answer:

there is a 12.5 percent chance

Step-by-step explanation:

first you have to turn 2/16 in to a decimal. this is 0.125

then to turn in it into a percent you move the decimal over two spots to the right

The difference of the grandson's age in years and the grandfather's age in years is 77. Therefore, the age of the grandson is 7 years.

A grandson's age in months is equal to his grandfather's age in years.

Recall,

12 months = 1 year

Hence,

let

x = age of grandson in month

It is the same age in years for the grandfather.

Therefore,

x = age of grand father in years

The difference of the grandson's age in years and the grandfather's age in years is 77. Therefore,

x - x / 12 = 77

12x - x/12 = 77

11x / 12 = 77

cross multiply

11x = 924

x = 924 / 11

x = 84

Therefore, the grandson age in in years is 84 / 12 = 7 years.

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The average time it takes to rent a video tape is 0.141 minutes.

Given data:Customers arrive at a video rental desk at the rate of 12 per minute(Poisson).
Each server can handle 8.15 customers per minute(Poisson). If there are 3 servers, we need to determine the average time it takes to rent a video tape.
Let us assume λ = 12 and μ = 3 × 8.15 = 24.45
Average time it takes to rent a video tape = 1 / (μ - λ/n)
Where, n = number of servers⇒ Average time it takes to rent a video tape = 1 / (24.45 - 12/3)⇒ Average time it takes to rent a video tape = 1 / 8.45⇒ Average time it takes to rent a video tape = 0.1185 minutes = 0.141 rounded to three decimal places.

Thus, the average time it takes to rent a video tape is 0.141 minutes.

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Answer:

59 centimeters

Step-by-step explanation:

Just plug the value for m and solve! After 16 months, m = 16. Therefore, H = 53 + 16 = 69.

hope this helps! <3

Answer:

Step-by-step explanation:

Therefore,

NOTE: n can't be equal to a negative number

hence n=20

Answer:

c. (x2)3=x6d

Step-by-step explanation:

I'm really sure that Is the answer because I dont know how can explain

By taking quotients between the prices and the numbers of boxes, we can see that the pack of 16 boxes is the better buy.

To identify which one is the better buy, we need to see which pack gives a smaller price per juice box.

To get that, we need to take the quotient between the price and the number of boxes for each case.

The pack of 14 boxes costs $11.34, then the price per box is:

P = $11.34/14  =$0.81

For the pack of 16 boxes the price is $12.64, in this case we will have:

P' = $12.64/16 = $0.79

We can see that the second option is cheaper, so that is the better buy.

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Answer:

179

Step-by-step explanation:

180- 2=189 this is because 2 of the students the 180 received a or b

The given question is incorrect. The correct question is:

Of the 180 students in a college course, 1/4 of the students earned an A for the course, 1/3 of the students earned a B for the course, and the rest of the students earned a C for the course. How many of the students earned a C for the course?

A. 75

B. 90

C. 105

D. 120

E. 135

The number of students who earned a C for the course can be represented by the fraction of 5/12 of the total number of students and is equal to 75. Hence, option A is the right choice.

A fraction in general means a part of. We represent a part of the whole using fractions. The total number of parts is taken as the denominator, while the parts used are taken as the numerator.

Fraction = Numerator/Denominator.

We are given that there are 180 students in a college course. 1/4 of them get an A for the course while 1/3 get a B. Rest of the students to get a C for the course.

We need to find the number of students who get a C.

Let the fraction of students getting a C be x.

We know that a whole fraction is always = 1.

∴ Fraction of students getting an A + Fraction of students getting a B + Fraction of students getting a C = Whole fraction.

or, 1/4 + 1/3 + x = 1

or, x = 1 - 1/4 - 1/3 = (12 - 3 - 4)/12 = 5/12

∴ 5/12 of the students get a C for the course.

Number of Students who get a C for the course = 5/12 of 180 = 5*15 = 75.

∴ The number of students who earned a C for the course can be represented by the fraction of 5/12 of the total number of students and is equal to 75. Hence, option A is the right choice.

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Answer:

the median is 91

Step-by-step explanation:

have a good day

Answer:

Median is 9

mode is 10

range4:

Answer:

The initial value in the word problem is the output value when input value is set to zero.

Step-by-step explanation:

========================================================

Explanation:

The old dimensions of the rectangle were 30 by 15.

The new dimensions are 30+x by 15+x, where x is some positive number.

The new rectangle dimensions multiply to 1000

(30+x)(15+x) = 1000

Use the FOIL rule to expand out the left side like so

(30+x)(15+x) = 1000

450+30x+15x+x^2 = 1000

450+45x+x^2 = 1000

x^2+45x+450

Then lets get everything to one side

x^2+45x+450 = 1000

x^2+45x+450-1000 = 0

x^2+45x-550 = 0

---------------------

From here we use the quadratic formula

Plug in a = 1, b = 45, and c = -550.

\(x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(45)\pm\sqrt{(45)^2-4(1)(-550)}}{2(1)}\\\\x = \frac{-45\pm\sqrt{4225}}{2}\\\\\)

\(x = \frac{-45\pm65}{2}\\\\x = \frac{-45+65}{2} \ \text{ or } \ x = \frac{-45-65}{2}\\\\x = \frac{20}{2} \ \text{ or } \ x = \frac{-110}{2}\\\\x = 10 \ \text{ or } \ x = -55\\\\\)

Earlier we defined x to be a positive number. This means we ignore x = -55. It makes no sense to add on a negative amount to each dimension.

The only practical answer is x = 10.

So each dimension is increased by 10 feet.

--------------------------

If x = 10, then the old dimensions of 30 by 15 bump up to 30+10 = 40 by 15+10 = 25

Then note how 40*25 = 1000, which helps confirm we have the correct dimensions.

--------------------------

Now go back to the question at hand: we want to find the new width. The old width was 30 feet. The new width is 30+x = 30+10 = 40 feet

Answer:

Step-by-step explanation:

Let x be a random variable representing the life of a Brand Q car battery. With the mean and standard deviation given, then the Empirical Rule says the that

1) About 68% of the x values lie between 1 standard deviation below and above the mean.

2) About 95% of the x values lie between 2 standard deviations below and above the mean.

3) About 99.7% of the x values lie between 3 standard deviations below and above the mean.

From the information given,

mean = 36 months

Standard deviation = 4 months

Therefore,

1) 68% of all batteries will have a life between 36 - 4 = 32 months and 36 + 4 = 40 months.

2) 95% of all batteries will have a life between 36 - 2(4) = 28 months and 36 + 2(4) = 44 months.

Answer: 5390

Step-by-step explanation:

       7 0

×       7 7

+     4 9 0

+   4 9 0  

=  5 3 9 0

Answer:

abcd is parallelogram and opposite sides of parallelogram are equal.

5x-9=3x+1

5x-3x=1+9

2x=10

10/2=x

5=x

bc=

5x-9=5×5-9

=16

ad=3x+1

=3×5-1

=15-1

=14

The denotation of ¬p is given by the formula ¬p = "The opposite of p."

The symbol ¬ is commonly used in logic to represent negation or the opposite of a proposition. In this case, the proposition p is being negated. The denotation of ¬p refers to the meaning or interpretation of the expression ¬p.

When we say ¬p = "The opposite of p," we mean that ¬p is true when p is false, and ¬p is false when p is true. In other words, ¬p has the opposite truth value of p. If p is true, then ¬p is false, and if p is false, then ¬p is true.

For example, let's say p represents the statement "It is raining." If p is true, then ¬p, which means "The opposite of It is raining," would be false, indicating that it is not the case that it is not raining. On the other hand, if p is false, then ¬p would be true, indicating that it is the case that it is not raining.

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