A password consists of 3 digits (0 - 9) followed by two letters (a-z or A-Z; note: 26 letters in the alphabet). i) How many different passwords are possible if repetition of digits and letters is allowed and passwords are not case sensitive (so 123AB is the same as 123aB)? ii) How many different passwords are possible if repetition of digits and letters is not allowed and the passwords are case-sensitive? (s0 123AB is different from 123aB)? b) A 4-student committee is to be randomly selected from a pool of 5 Biology Majors, 10 Math Majors and 5 Music Majors. 1) What is the probability that all 4 randomly selected students were Math Majors? (State your answer as a reduced fraction OR a decimal rounded to 3 places) ii) Suppose now that the 4 student committee needs to have exactly two math majors. How many different pairs of math majors could be chosen.

Answer:

the number of boxes that would take fill

the storage completely is 60 boxes.

Step-by-step explanation:

given:

A storage unit has the dimensions 6 ft. x 7 1/2 ft. x 4 1/2 ft.

find:

What number of

1 1/2 ft. x 1 1/2 ft. x 1 1/2 ft. cardboard boxes would it take to completely

fill this storage unit?

Volume of a storage unit = 6 x 7.5 x 4.5

Volume of a storage unit = 202.5  ft³

Volume of a cardboard box = 1.5 x 1.5 x 1.5

Volume of a cardboard box = 3.38 ft³

to get the number of cardboard boxes to fill in the storage unit,

Number of boxes =     202.5 ft³    

                                     3.38 ft³

Number of boxes = 60

therefore,

the number of boxes that would take fill the storage completely is 60 boxes.

To multiply a square root by a square root and a whole number, you can use the distributive property of multiplication

Given data ,

Let the numbers be represented by the expression A

Now , the value of A is

A = √2 × 3√5

First, you can simplify each square root:

√2 = 1.4142 (rounded to 4 decimal places)

3√5 = 5.1962 (rounded to 4 decimal places)

Next, you can multiply the two simplified square roots and the whole number:

√2 × 3√5 = 1.4142 × 5.1962 × 3

= 22.3607 × 3

= 67.0821

Hence , the expression is A = √2 × 3√5 = 67.0821

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Answer:

20

Step-by-step explanation:

Triangle inequality says that the third side can only be 18-3...15, that is bigger than 15.

And 18+3... 21, that is smaller than 21.

If the third side is 21, the 18 and the 3 will just lay right on top of the 21 and not make a triangle. So it has to be 20 in order to be a whole number.

Answer:

7/2 cups of milk.

Step-by-step explanation:

1 3/4=7/4

2(7/4)=14/4=7/2

Answer:

7/2 cups of milk.

Step-by-step explanation:

If you want double the pancakes You must double the amount of milk:

First change it into an improper fraction:

1 3/4=7/4

then multiply it by two and simplify:

2(7/4)=14/4=7/2

Answer:

1/64 or 0.015625

Step-by-step explanation:

Answer:

456.29 miles

Step-by-step explanation:

Hope this helps!

Answer:

y = x + 1

Step-by-step explanation:

1) First, find the slope of the line between the two points. Whichever option has the same slope would be the right answer. To find this, use the slope formula \(\frac{y_2-y_1}{x_2-x_1}\). \(x_1\) and \(y_1\) represent the x and y values of one point, and \(x_2\) and \(y_2\) represent the x and y values of another point.

So, use the points given to answer the question. Substitute 4 for \(x_1\), 5 for \(y_1\), 8 for \(x_2\), and 9 for \(y_2\) then solve:

\(\frac{(9)-(5)}{(8)-(4)} \\= \frac{9-5}{8-4} \\= \frac{4}{4} \\= 1\)

Therefore, the slope is 1.

2) Any line that is in a "y = a number" format is a horizontal line, and all horizontal lines have a slope of 0 - so the second option can't be the answer.

The rest of the options are in slope-intercept form, or y = mx + b format. Remember that the coefficient of the term with the x is the slope. Knowing this, y = x + 1 would need to be the answer since the coefficient of the term with the x is 1, and we already calculated that the slope is 1.

Answer:

im just adding this so you can give them brainliest lol

Step-by-step explanation:

yes, they are correct

Since we know that the heptagon is convex, all of its interior angles are less than 180 degrees. Let's call the smallest angle x degrees.

According to the problem, the other six angles are each 1 degree larger than the angle just smaller than it. This means the second angle is x+1, the third angle is x+2, and so on, until we get to the seventh angle which is x+6.

We know that the sum of the interior angles of a heptagon is (7-2) * 180 = 900 degrees. So we can set up an equation:

x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) = 900

Simplifying this equation, we get:

7x + 21 = 900

Subtracting 21 from both sides:

7x = 879

Dividing both sides by 7:

x = 125.57

So the smallest angle is approximately 125.57 degrees.

To find the fourth largest angle, we need to find the value of x+3.

x+3 = 125.57 + 3 = 128.57

So the fourth largest angle is approximately 128.57 degrees.

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Answer:

D

Step-by-step explanation:

865 increase 25% =

865 × (1 + 25%) = 865 × (1 + 0.25) = 1081.25

Answer:D

(Sorry if I’m wrong)

Answer:

If top readers read at speeds of above 1000 words per minute (wpm) with near 85% comprehension, they only represent 1% of readers. Average readers are the majority and only reach around 200 wpm with a typical comprehension of 60%. ... The average reader is five times slower than the good reader.

Step-by-step explanation:

- Span{v1, v2, v3, 0} is equal to the span of {v1, v2, v3}.
- Span{v1, v1-v2, v3} is equal to the span of {v1, v2, v3}.
- Span{v1, v2} is NOT equal to the span of {v1, v2, v3}.

Let's analyze each of the sets of vectors to determine if they are equal to the span of {v1, v2, v3}:
1. Span{v1, v2, v3, 0}:
This set is equal to the span of {v1, v2, v3} because adding the zero vector (0) does not affect the linear independence or the span of the other vectors.

A span is the set of all possible linear combinations of the vectors, and since the zero vector does not change the linear combinations, the span remains the same.
2. Span{v1, v1-v2, v3}:
This set is also equal to the span of {v1, v2, v3}.

The reason is that the vector (v1-v2) can be written as a linear combination of v1 and v2: (v1-v2) = 1*v1 + (-1)*v2.

Since all vectors in this set can be expressed as linear combinations of {v1, v2, v3}, the span remains the same.
3. Span{v1, v2}:
This set is NOT equal to the span of {v1, v2, v3} because it is missing the vector v3.

Since v1, v2, and v3 are linearly independent, removing one of them (v3 in this case) means that the set cannot span the same space as {v1, v2, v3}.

It has a lower dimension, and therefore, the span is different.

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A measurement which could be the side lengths of a right triangle include the following: C. √24 in, √6 in, √30 in.

In order to determine which measurements could be the side lengths of a right triangle, we would have to apply Pythagorean's theorem.

Mathematically, Pythagorean's theorem is given by this formula:

x² + y² = z²

From the side lengths of the first triangle, we have the following:

(√6)² + (√30)² = (√33)²

6 + 30 = 33

36 = 33 (False).

From the side lengths of the first triangle, we have the following:

(√27)² + (√18)² = (√48)²

27 + 18 = 48

45 = 48 (False).

From the side lengths of the first triangle, we have the following:

(√6)² + (√24)² = (√30)²

6 + 24 = 30

30 = 30 (True).

From the side lengths of the first triangle, we have the following:

(√18)² + (√21)² = (√48)²

18 + 21 = 48

39 = 48 (False).

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A

I first divided the numbers and got 61.

On the last one for 40-39= 1

That 1 will be the numerator and the 39, which is what you divided the 2,380 from goes underneath, which is the denominator.

If that doesn't make sense, here is a better explanation:

39 divided by 2380 = 61

The 61 will go to the right and keep it where it is.

That 1 after subtracting your numbers will go on top which is the numerator

The 39 divided from 2380 goes at the bottom as the denominator.

[Note: The numerator can never be bigger than the denominator!]

I hope that helps!

To find the hypotenuse of a right triangle using trigonometry, we can utilize the Pythagorean theorem and the trigonometric ratios of sine, cosine, or tangent. Here's a step-by-step explanation:

1. Identify the right triangle: Ensure that the triangle has a right angle, which is a 90-degree angle.

2. Label the sides: Identify the two sides of the right triangle that are not the hypotenuse. These sides are typically referred to as the adjacent side and the opposite side.

3. Choose the appropriate trigonometric ratio: Depending on the information you have, select the appropriate trigonometric ratio that relates the sides you know.

- If you have the adjacent side and the hypotenuse, use cosine: cosθ = adjacent/hypotenuse.

- If you have the opposite side and the hypotenuse, use sine: sinθ = opposite/hypotenuse.

- If you have the opposite side and the adjacent side, use tangent: tanθ = opposite/adjacent.

4. Substitute the known values: Plug in the values you have into the trigonometric equation and solve for the unknown side (hypotenuse).

5. Apply the Pythagorean theorem: If you don't have the hypotenuse directly but know the lengths of both the adjacent and opposite sides, you can use the Pythagorean theorem, which states that the sum of the squares of the two legs (adjacent and opposite sides) is equal to the square of the hypotenuse. The formula is a² + b² = c², where c represents the hypotenuse.

6. Simplify and calculate: After substituting the known values into the equation, simplify and solve for the hypotenuse.

By following these steps and applying the appropriate trigonometric ratio or the Pythagorean theorem, you can find the length of the hypotenuse in a right triangle using trigonometry.

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a) The statement P(2) is that 2! < 22.

b) We have to show that 2! < 22. Since 2! = 2 × 1 = 2 and 22 = 4, we have that 2! < 22, and so the statement P(2) is true.

c) The inductive hypothesis is that P(k) is true for an arbitrary integer k ≥ 2.

d) We need to prove that P(k + 1) is true, assuming that P(k) is true for some integer k ≥ 2.

e) We assume that P(k) is true for some integer k ≥ 2 and then use this assumption to prove that P(k + 1) is true.

f) We have (k + 1)! = (k + 1)k!, and so by the inductive hypothesis, we have k! < kk. Multiplying both sides by k + 1, we get (k + 1)k! < (k + 1)kk. Because k ≥ 2, we have (k + 1) < 2k.

a) P(2) states that the factorial of 2 is less than 22.

b)  By calculating the factorial and comparing it to 22, we find that 2! is indeed less than 22, confirming the truth of P(2).

c) The inductive hypothesis assumes that the statement P(k) is true for any integer k greater than or equal to 2.

d) To prove P(k + 1), we assume the truth of P(k) for a given k and aim to establish the truth of P(k + 1).

e) By assuming the truth of P(k), we use this assumption as a basis to demonstrate the truth of P(k + 1) through a logical argument or proof.

f) Therefore, (k + 1)k! < 2kk, and so (k + 1)! < 2kk. We now have to prove that 2kk < (k + 1)(k + 1), or equivalently, that 2k < k + 1. But this last inequality is true, because we assumed that k ≥ 2.f) By the principle of mathematical induction, P(n) is true for all integers n ≥ 2.

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Based on the given table which shows measurements in yards and miles, the figures given in yards have the miles equivalent of:

Miles are longer than yards which means that when converting yards to miles, you will have to multiply them with a smaller number.

A yard in miles is 0.000568182 miles.

1,760 yards in miles is therefore:

= 1,760 x 0.000568182

= 1 mile

17,600 yards in miles is:

= 10 miles

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Answer:

relationships between side lengths and angles of triangles

Step-by-step explanation:

Answer:

Study of the angles and triangles

Step-by-step explanation:

Answer:

31

Step-by-step explanation:

16(3) - 3(-1) + 5(-4)

48 + 3 - 20

31

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{31}}}}}\)

Step-by-step explanation:

Given, a = 3 , b = -4 and c = -1

To find : Value of the given expression

\( \sf{16a - 3c + 5b}\)

plug the values of a , b and c and simplify

\( \dashrightarrow \sf {16 \times 3 - 3 \times ( - 1) + 5 \times ( - 4)}\)

\( \dashrightarrow{ \sf{48 - ( - 3) + ( - 20)}}\)

\( \dashrightarrow{ \sf{48 + 3 - 20}}\)

\( \dashrightarrow{ \sf{51 - 20}}\)

\( \dashrightarrow{ \sf{31 }}\)

Hope I helped!

Best regards! :D

Answer:

Step-by-step explanation:

Los movimientos bancarios de Santiago se representan matemáticamente teniendo en cuenta que consignar es sumar y retirar el restar. Por lo tanto podes expresar los movimientos bancarios de la siguiente manera:

Al realizar la sumatoria se obtiene:

 +300.000 - 120.000 - 95.000 + 80.000 = + 165.000

En la semana Santiago obtiene en su cuenta bancaria $165.000

Mateo can fill 40 glasses with punch and this can be calculated as :

8 liters = 8 x (5/1) = 40 liters

By solving the above equation following will be obtained.

Therefore, Mateo can fill 40 glasses with punch.

Mathematics, where the numerator and denominator are divided. Each is an integer in a simple fraction. Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other.

If numerator value is less than the denominator value, it is a proper fraction.If a numerator value is greater than  denominator value, then it is called an improper fraction.

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Answer:

The answer to your problem is, 12 1/2

Step-by-step explanation:

As shown to the problem we would need to add

4 1/2 + 2 7/12

Lets make them equivalent denominators:

1/2 & 7/12

= 24

1/2 = 12/24

7/12 = 14/24

Then make the new problem into;

4 12/24 + 7 14/24

= 12 1/2

Thus the answer to your problem is, 12 1/2

The United States will have 16 additional​ shirt(s) after the trade ​(enter a numeric response using an​ integer) and 0 additional​ boot(s). At the same​ time, Canada will be able to consume 14 additional​ shirt(s) as a result of the trade and 0 additional​ boot

With Alaska in the northwest and Hawaii extending the country's reach into the Pacific Ocean, the United States is a confederation of 50 states that encloses a sizable portion of North America. Significant Atlantic Coast cities include Washington, DC, and New York, a centre of international culture and economics. Chicago, a major city in the Midwest, is renowned for its significant architecture, whereas Hollywood, near Los Angeles on the west coast, is renowned for its film production.

If the data are graphed symmetrically, the distribution demonstrates 0% skewness regardless of how long or fat the tails are. When the median of a data set is utilized, 50% of the data points in the collection have values lower than or equal to the median, and 50% of them have values greater than or equal to the median. The middle score in the set is known as the median. The first step in calculating the median is to order the data points from smallest to greatest. The median in an odd-numbered set will be the value that falls exactly in the middle of the list. You must determine the average of the two middle numbers in a set of even numbers. The average is determined by summing up each value individually and dividing that sum by the total number of observations.

The US will consume 16 shirts with trade. (4+12=16 and 16-2=14) The US will have 14 additional shirts.

With commerce, the US will consume 18 boots. 18-18=0

0 additional boots.

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Suppose the detector will sound the alarm if more than 2 milligrams of the dye are in your system. It will take 56 minutes for the visit of the doctor

The amount of radioactive dye remaining in your system after t minutes can be modeled as:

A(t) = 11 * (1/2)^(t/20)

where A(t) is the amount of dye remaining after t minutes. We want to find the time t when A(t) = 2 milligrams.

A(t) = 11 * (1/2)^(t/20) = 2

Solving for t:

(1/2)^(t/20) = 2/11

Taking the natural logarithm of both sides:

(t/20) = ln(2/11) / ln(1/2)

Multiplying both sides by 20:

t = 20 * ln(2/11) / ln(1/2)

Using a calculator or logarithm tables, we can estimate t to be approximately 56 minutes. So, your visit to the doctor would take about 56 minutes.

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no se me alludas a saber cual es

In order to determine the rate at which the searchlight is rotating when the man is 15 ft from the point on the path closest to the searchlight, the following steps should be performed in this order

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In a right triangle, we haev some trigonometric relationships between the sides and angles. Given an angle, the ratio between the opposite side to the angle by the hypotenuse is the sine of this angle, therefore, the following statement

Describes the following triangle

To find the missing length x, we could use the Pythagorean Theorem. The sum of the squares of the legs is equal to the square of the hypotenuse. From this, we have the following equation

Solving for x, we have

The missing length of the first triangle is equal to 4.

For the other triangle, instead of a sine we have a tangent relation. Given an angle in a right triangle, its tanget is equal to the ratio between the opposite side and adjacent side.The following expression

Describes the following triangle

Using the Pythagorean Theorem again, we have

Solving for h, we have

The missing side measure is equal to 13.

Now that we have all sides of both triangles, we can construct any trigonometric relation for those angles.

The sine is the ratio between the opposite side and the hypotenuse, and the cosine is the ratio between the adjacent side and the hypotenuse, therefore, we have the following relations for our angles

To calculate the sine and cosine of the sum

We can use the following identities

Using those identities in our problem, we're going to have