the phone calls to a computer software help desk occur at a rate of 3 per minute in the afternoon. compute the probability that the number of calls between 2:00 pm and 2:10 pm is: (a) exactly 25. (b) more than 25.

The length of the straw, which fits exactly along this diagonal, is also [tex]\sqrt{11}[/tex] inches.

What is Pythagorean theorem?

The Pythagorean theorem is a fundamental concept in mathematics that describes the relationship between the sides of a right triangle. It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

The problem states that the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner. We can visualize this diagonal as a line that runs through the center of the box, from one corner to the opposite corner.

To find the length of this diagonal, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (the legs) is equal to the square of the length of the longest side (the hypotenuse).

In this case, the bottom and back sides of the box form the legs of a right triangle, and the diagonal of the box forms the hypotenuse. So we can apply the Pythagorean theorem as follows:

Diagonal  = [tex]\sqrt{bottom^2 + back ^2 + height ^2 }[/tex]

Therefore, the length of the straw, which fits exactly along this diagonal, is also [tex]\sqrt{11}[/tex] inches.

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15 is area of Side of Square .

What is a square, exactly?

All four of the sides and all four of the angles make up the regular quadrilateral known as the square. The square's angles are 90 degrees away from each other or at right angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle.

Length of diagonal of Square =15√2 cm-------------(1)

Let side of Square = a cm

So, Length of Diagonal

By Using Pythagorean Theorem

       = √a² + a²

        =  a√2        ........................(2)

  Equating (1) and (2)

    a√2   =  15√2

      a = 15

 cancelling root 2 from both sides.

     a = 15

Side of Square= 15 cm

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The complete question is -

Find the side of a square whose diagonal is of the given measure. Given = 15√2 cm.

The likelihood that the decision made based on the sample differs from the decision that would have been made if the entire population had been examined is called sampling risk.

Sampling error refers to the disparity between a sample's characteristics and those of the population from which it was drawn. It arises from using a sample rather than the whole population to estimate statistics such as mean, variance, and proportions.

Since a sample only represents a portion of the population, it cannot be expected to have the same characteristics as the whole population. The study of sampling error is an essential part of statistical analysis, as it is a source of uncertainty in making inferences about the population from a sample.

To reduce the sampling error in your survey, you can utilize a larger sample size. It is also beneficial to ensure that the sample is chosen randomly and without bias.

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The area of the circle with circumference 19cm is 6.42cm²( nearest hundredth).

Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr2. Where r is the radius.

The circumference of a circle is given as ;

C = 2πr

C = 9cm

therefore, 9 = 2× 3.14 × r

9 = 6.28r

r = 9/6.28

r = 1.43 cm

Area of circle = πr²

= 3.14 × 1.43²

= 6.42cm²( nearest hundredth)

therefore the area of the circle is 6.42cm²

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Explanation:

Most people with a mental illness in the United States receive care at some point in their lives, but most receive insufficient or inappropriate care. In any given year, fewer than one-third of people with a diagnosable mental illness obtain treatment.

However, according to a study, most people in the United States with a mental disorder in any given 12-month period receive treatment during the same time frame.

According to the National Survey on Drug Use and Health (NSDUH), about one in five adults (18.5%) had a mental illness in 2019. It is said that roughly 22.3 million people aged 18 and above received care for a mental health condition in the preceding year.

Treatment may involve medication, therapy, support groups, or a combination of these methods. The majority of people with mental illness may significantly benefit from these treatments.

As per a study, most people in the United States with a mental disorder in any given 12-month period receive treatment during the same time frame. This statement is true.

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Dividing the circumference of a pumpkin by its diameter gives a value approximately equal to pi (π)

When you divide the circumference of a pumpkin by its diameter, you get a value that is approximately equal to the mathematical constant pi (π), which is approximately 3.14159.

This is because pi represents the ratio of the circumference of a circle to its diameter, and a pumpkin is roughly spherical in shape. So, no matter how big or small the pumpkin is, if you measure its circumference and diameter and divide them, the result will be very close to pi.

Mathematically, this can be represented by the formula

pi ≈ circumference / diameter

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Since the sequence is always decreasing and cannot go below the lower bound, it becomes increasingly closer to the lower bound, and thus converges to a limit.

A sequence is said to be decreasing if each term is smaller than the previous one, and bounded below if there exists a lower bound such that no term in the sequence is smaller than this bound. In this case, the sequence is decreasing and bounded below by 0.

When a sequence is both decreasing and bounded below, it must have a limit because the terms cannot continue to decrease indefinitely, as they cannot go below the lower bound (in this case, 0). This means that as we progress through the terms of the sequence, the difference between consecutive terms will decrease and eventually approach a constant value.

The limit of a sequence is a value that the terms of the sequence approach as they get closer and closer to the end. In this situation, the limit is the smallest possible value that the sequence can approach, without going below the lower bound.

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Diego can make 56 bags with each bag containing 8 brownies and 12 cookies.

To package both items, he can divide the items into groups of 8 brownies and 12 cookies. He will then make 56 of these groups, ensuring each bag contains 8 brownies and 12 cookies.

Diego has 48 brownies and 64 cookies to package. To make the same combination of items in each bag, he needs to group the items into groups of 8 brownies and 12 cookies.

This can be done by dividing the 48 brownies into 6 groups of 8, and the 64 cookies into 5 groups of 12. He then needs to combine these two groups together, making 56 total bags.

Each of these bags will contain 8 brownies and 12 cookies. This is one way of packaging both items so that each bag has the same combination.

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Required value of the given expression is (1+√2)

Given expression is [tex]tan \frac{11\pi}{8} [/tex]

We want to solve it.

Now,

[tex] \tan( \frac{11\pi}{8} ) = \tan( \frac{3\pi}{8} + \frac{8\pi}{8} ) \\ = \tan( \frac{3\pi}{8} + \pi ) \\ = \tan( \frac{3\pi}{8} ) [/tex]

Finding [tex] \tan( \frac{3\pi}{4} ) [/tex]

Let,

[tex] \tan(2t) = \tan( \frac{3\pi}{4} ) = - 1[/tex]

Use half angle identity,

[tex] \tan(2t) = \frac{ 2\tan(t) }{1 - {tan}^{2} t} \\ - 1 = \frac{ 2\tan(t) }{1 - {tan}^{2} t} \\ {tan}^{2} t - 2tant - 1 = 0[/tex]

Let,[tex]x = tant[/tex]

So,[tex] {x}^{2} - 2x - 1 = 0[/tex]

Now, [tex]x = 1 \pm \sqrt{2} [/tex]

So,

[tex]tant = tan \frac{3\pi}{8} = 1 \pm \sqrt{2} [/tex]

[tex]tan \frac{3\pi}{8} [/tex] is positive,then required value is 1+√2.

So, option D is the correct answer.

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Jabu's Monthly salary is of R27500.00, with an increase of R1 746.25 per month. Jabu's monthly increase is R1 746.25. The correct answer is option 3.

To find Jabu's previous monthly salary, we can use the formula:

Previous monthly salary = (Annual salary / 12)

Since Jabu's new annual salary is R330 000, his previous annual salary would be:

Previous annual salary = (New annual salary / 1.0635) = (R330 000 / 1.0635) = R310 020.10

Therefore, Jabu's previous monthly salary would be:

Previous monthly salary = (Previous annual salary / 12) = (R310 020.10 / 12) = R25 835.01

To find the monthly increase, we can subtract Jabu's previous monthly salary from his new monthly salary:

Monthly increase = (New monthly salary - Previous monthly salary) = (R27 618.38 - R25 835.01) = R1 783.37

Therefore, Jabu's monthly increase is R1 746.25 (rounded to the nearest cent).

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A large bag contains marbles of different colors. there are 10 red marbles, 5 blue marbles and 7 yellow marbles. when selecting 3 marbles without replacement, the probability of selecting 3 red marbles is 1/54.

The probability of selecting 3 red marbles is 1/54.What is a probability?

Probability refers to the likelihood or chance of an occurrence. The probability of an event occurring is the ratio of the number of favourable outcomes to the total number of possible outcomes.

A fraction or a decimal is used to express it.The total number of marbles in the bag is 10 + 5 + 7 = 22 marbles.

There are ten red marbles in the large bag, so the number of ways to select 3 red marbles from ten red marbles is:

[tex]10C_3 = (10 \times 9 \times 8) / (3 \times 2 \times 1) = 120[/tex]

There are 22 marbles in the bag, therefore, the total number of ways to pick 3 marbles from 22 is:

[tex]22C_3 = (22 \times 21 \times 20) / (3 \times 2 \times 1) = 1540[/tex]

Hence, the probability of choosing 3 red marbles out of the 22 marbles in the bag without replacement is:120/1540 = 1/54

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The expression 3x³y² - 9xz⁴ + 8y²z have no GCF greatest common factor but the terms 3x³y² and 8y²z have GCF equal to y².

The GCF defines the highest common factor present in between given two or more numbers or algebraic expressions.

we shall determine the GCF greatest common factor for the algebraic expression 3x³y² and 8y²z as follows:

3x³y² = y² × 3x³

8y²z = y² × 8z

both terms 3x³y² and 8y²z have y² common to them, so we can write;

3x³y² + 8y²z = y² × 3x³ + y² × 8z

3x³y² + 8y²z = y²(3x³ + 8z)

In conclusion, the expression 3x³y² - 9xz⁴ + 8y²z have no GCF greatest common factor but the terms 3x³y² and 8y²z have GCF equal to y².

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Answer:

45.6%

Step-by-step explanation:

166.50 minus 45.6% equals 90 dollars

The percent that reported mushroom as their favorite from the pizza shop survey would be 10 %.

The percent that instead reported cheese or pepperoni as their favorite is 62.5 %.

Out of 400 people, the number that would say their favorite was sausage is 50 people .

The percent that prefer mushroom would be:

= Number of those who chose mushroom / Number surveyed

= 8 ( 35 + 8 + 15 + 12 + 10 )

= 8 / 80

= 10 %

The percentage that instead chose cheese or pepperoni:

= ( 15 + 35 ) / ( 35 + 8 + 15 + 12 + 10 )

= 50 / 80

= 62.5 %

The number out of 400 that would be expected to choose sausage :

= 10 / ( 35 + 8 + 15 + 12 + 10 ) x 400

= 50 people

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The fourth equation which is tan x = [tex]\frac{7000}{5000}[/tex] is the correct way to calculate x. This has been obtained by using trigonometry.

What is trigonometry?

Trigonometry is the study of right-angled triangles, which includes the sides, angles, and connections of each triangle.

We are given that the airplane is 5,000 ft above ground and has to land on a runway that is 7,000 ft away with an angle x.

Since, we are not given the hypotenuse so, we will use tan θ.

We know that in trigonometry, tan θ is calculated as the ratio of the opposite side to the adjacent side.

So,

tan x = [tex]\frac{7000}{5000}[/tex]

Hence, the fourth equation is the correct answer.

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The complete question has been attached below

Answer: two right-angled triangle, equilateral triangle

Step-by-step explanation:

It is a combination of two right-angled triangle or it is an equilateral triangle.

Explanation:

You want to prove a point P on the perpendicular bisector of segment YZ is equidistant from Y and Z.

1. PX is the perpendicular bisector of YZ . . . . given

2. angles at X are right angles . . . . definition of perpendicular

3. YX = XZ . . . . definition of bisector

4. PX = PX . . . . reflexive property of congruence

5. ∆PXY ≅ ∆PXZ . . . . LL congruence theorem

6. YP ≅ ZP . . . . CPCTC

Answer:

48 square centimeters

Step-by-step explanation:

[tex] \frac{1}{2} (4)(8)(3) = 48[/tex]

The two numbers that multiply to give 24 and add to give -11 are -3 and -8.

To find these numbers, you can use a system of equations. Let x and y be the two numbers. Then we have:

We can use the second equation to solve for one of the variables in terms of the other. For example, we can solve for x:

x + y = -11

x = -11 - y

We can then substitute this expression for x into the first equation:

xy = 24

(-11 - y)y = 24

Expanding and rearranging, we get:

y^2 + 11y + 24 = 0

This is a quadratic equation that we can solve using factoring or the quadratic formula. Factoring, we get:

(y + 3)(y + 8) = 0

So either y + 3 = 0 or y + 8 = 0. This means that y can be -3 or -8. Substituting each of these values into x = -11 - y, we get:

If y is -3, then x is -11 - (-3) = -8

If y is -8, then x is -11 - (-8) = -3.

Translated question "Numbers that multiply to give me 24 and add to give me -11"

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The number of  pounds that he will have left over from 11 3/7 pounds is  4 2/7

To find out how many bags of granola Alex can fill, we need to divide the total amount of granola he made by the amount of granola in each bag.

We can convert 11 3/7 pounds to an improper fraction:

11 3/7 pounds  = 80/7 pounds

Also, we have

2 2/3 pounds  = 8/3 pounds

Now we can divide the total amount of granola by the amount in each bag:

(80/7) ÷ (8/3)

To divide fractions, we invert the second fraction (change it to its reciprocal) and multiply:

(80/7) × (3/8)

Simplifying, we get:

(80 x 3) / (7 x 8) = 30/7

Divide

(80 x 3) / (7 x 8) = 4 2/7

Hence, the bags is 4 2/7

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The perimeter of the figure, given the rectangles and the total area, can be found to be 48 inches

The total area is 75 in² which means that the areas of all 5 rectangles add up to 75 in². We can use this to solve for x to be:

5 × ( x × ( x - 2 )) = 75 in²

5 × ( x² - 2x ) = 75 in²

x² - 2x = 15 in²

(x - 5)(x + 3) = 0

x - 5 = 0 or x + 3 = 0

x = 5 or x = -3

Dimensions of a rectangle cannot be negative so x is equal to 5.

The perimeter is then:

= ( x - 2 ) + x + ( x - 2 ) + x + (x - 2 ) + x + ( x - 2 ) + x + (x - 2 ) + x + ( x -2 ) + x

= ( 5 - 2 ) + 5 + ( 5 - 2 ) + 5 + (5 - 2 ) + 5 + ( 5 - 2 ) + 5 + (5 - 2 ) + 5 + ( 5  -2 ) + 5

= 48 inches

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Player A's weight was 0.208 standard deviations below the mean weight of the football team.

To calculate the standard deviation, we first need to calculate the mean weight of the football team

Mean weight = (sum of all weights) / (number of team members)

(174+176+178+184+185+185+185+185+188+190+200+202+205+206+210+211+211+212+212+215+215+220+223+228+230+232+241+241+242+245+247+250+250+259+260+260+265+265+270+272+273+275+276+278+280+280+285+285+286+290+290+295+302) / 52

= 225.5 pounds

Now we can calculate the standard deviation using the following formula:

Standard deviation = sqrt((sum of (x - mean)^2) / N)

Where x is the weight of a team member, N is the total number of team members.

We can simplify this formula by calculating the variance first:

Variance = (sum of (x - mean)^2) / N

So we have

Variance = ((174-225.5)^2 + (176-225.5)^2 + ... + (302-225.5)^2) / 52

= 10764.35

Now we can calculate the standard deviation

Standard deviation = sqrt(Variance)

= sqrt(10764.35)

= 103.76

To find out how many standard deviations above or below the mean Player A's weight was, we can use the following formula

Z-score = (x - mean) / standard deviation

Where x is Player A's weight, mean is the mean weight of the team, and standard deviation is the standard deviation we just calculated.

So we have

Z-score = (204 - 225.5) / 103.76

= -0.208

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The given question is incomplete, the complete question is:

Following are the published weights (in pounds) of all of the team members of Football Team A from a previous year.

174, 176, 178, 184, 185, 185, 185, 185, 188, 190, 200, 202, 205, 206, 210, 211, 211, 212, 212, 215, 215, 220, 223, 228, 230, 232, 241, 241, 242, 245, 247, 250, 250, 259, 260, 260, 265, 265, 270, 272, 273, 275, 276, 278, 280, 280, 285, 285, 286, 290, 290, 295, 302

median = 241

the first quartile = 205.5

the third quartile = 272.5

Assume the population was Football Team A. When Player A played football, he weighed 204pounds. How many standard deviations above or below the mean was he?

Tyee can afford to rent the car for at most 2 days while staying within his budget.

Let x be the number of days Tyee can rent the car within his budget.

The total cost of renting the car will be the sum of the daily rental fee and the cost of miles driven:

Total cost = rental fee + (cost per mile x miles driven)

Using the given information, we can write the inequality:

74.90x + 0.13(175)x ≤ 210

Simplifying the expression, we get:

74.90x + 22.75x ≤ 210

97.65x ≤ 210

x ≤ 2.15

Therefore, Tyee can afford to rent the car for at most 2 days while staying within his budget.

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Answer: I'm pretty bad at math, but I made it more simple for you :)

Step-by-step explanation:

The answer is y = 4 + 5x/4

I hope it helped a bit sorryy

The probability of drawing at least one spade when drawing two cards with replacement from a standard deck of cards is approximately 0.26%.

When drawing two cards at random with replacement from a standard 52-card deck, there are 4 possible outcomes for the first card being a spade and 4 possible outcomes for the second card being a spade.

However, there is also 1 possible outcome where both cards are spades, which would be counted twice if we add the outcomes for the first and second cards separately. Therefore, the total number of outcomes where at least one card is a spade is 4 + 4 - 1 = 7.

The total number of possible outcomes when drawing two cards with replacement is 52 x 52 = 2,704.

Therefore, the probability that at least one card is a spade when drawing two cards with replacement is:

P(at least one spade) = 7 / 2,704 ≈ 0.0026

So, the probability that at least one card is a spade is approximately 0.0026 or 0.26%.

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Answer:0.6

Step-by-step explanation: because i got it correct

Answer: yes, yes, no

Explanation: In order for a figure to be a triangle, the two smallest sides must add up to be larger than the biggest side. The reason why the last one isn't a triangle is because 6+8 EQUALS 14 and is not greater than 14.

Answer:

53°

Step-by-step explanation:

it’s vertical, verticals are always identical, I think  

The lower quartile of the given set of numbers 4, 6, 7, 8, 10, 12, 20 is 6. So, correct option is B.

To find the lower quartile of a set of numbers, we first need to arrange them in ascending order. The given numbers are: 4, 6, 7, 8, 10, 12, 20.

Next, we divide the data set into four equal parts. The lower quartile is the median of the lower half of the data set. In this case, the lower half is 4, 6, and 7.

To determine the median of the lower half, we need to find the middle value. Since we have an odd number of data points in the lower half, the middle value is the single value between the two extremes. In this case, the median is 6.

This corresponds to option (b) in the given choices: 6.

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Mr. Fransico had average overtime in a day is 2.1 hours.

In mathematics, the central value of a set of data is expressed as the average of a list of data. It is defined mathematically as the ratio of the total number of data points to the number of units in the list. In terms of statistics, the term "mean" also refers to the average of a certain set of numerical data. The average of 2, 3, and 4 is, for instance, (2+3+4)/3 = 9/3 = 3. The center value of 2, 3, and 4 in this instance is 3, thus. Finding the mean value of a bunch of numbers is the definition of average.

For 5 days Mr fransico had a total of 10. 5 hours of overtime in the office

Then the average daily overtime is-

10.5÷5 = 2.1 hours

Hence Mr. Fransico had total overtime in a day is 2.1 hours.

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