if a = 2 and b = 3, what is the value of 3a² ÷ 2b ?​

The correct answer is (b) all real numbers except odd multiples of π/2. The domain of validity for cscθ (cosecant) is restricted because cosecant is undefined when the sine of an angle is zero.

In the trigonometric identity cscθ = 1/sinθ, the denominator sinθ becomes zero at odd multiples of π/2 (such as π/2, 3π/2, 5π/2, etc.), resulting in a division by zero error. Therefore, the cosecant function is not defined for these values of θ.

For all other real numbers θ, the sine function is non-zero and well-defined, allowing us to calculate the reciprocal of the sine and determine the value of the cosecant. Hence, the domain of validity for cscθ is all real numbers except odd multiples of π/2, as stated in option (b).

It's important to note that in trigonometry, the domain of validity is determined by avoiding any values that would lead to undefined expressions or division by zero errors.

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The domain of validity for csc θ = 1/sin θ is all real numbers except multiples of π, because at these points the sine function equals zero, and division by zero is undefined.

In mathematics, the cosecant function (csc), is defined as the reciprocal of the sine function, or 1/sinθ. The domain of a function are all the possible input values that will yield real numbers (output). For the csc function, its domain includes all real numbers except where the denominator is zero because division by zero is undefined.

In the unit circle context, sine equals zero at 0, π, 2π, ..., and the negative counterparts. Basically, these are the multiples of π. Thus, for the csc function, the domain is all real numbers except multiples of π, which matches option d in your choices.

The domain of validity for csc θ = 1/sin θ is all real numbers except multiples of π.

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Answer:

8 pounds

Step-by-step explanation:

3 ft board = 2lb

12 ft board is 4 times more so

2x4 = 8 lb

The 11.25 minutes required after car b leaves will they pass each other and A meets B at  01:11:15 PM.

Car A leaves Santa Barbara at noon traveling south toward Los Angeles at 70 mph.

At 1pm car B leaves Los Angeles traveling north toward Santa Barbara at 90 mph.

The distance between the cars at noon was 100 miles.

If car B does not get pulled over, how many minutes after car B leaves will they pass each other?

:

Let t = travel time of Car B

then

(t+1) = travel time of Car A

:

Write a distance equation:

Speed tells us how fast something or someone is travelling. You can find the average speed of an object if you know the distance travelled and the time it took.

The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in meters (m) and time is in seconds (s), so the units will be in meters per second (m/s).

⇒90t + 70(t+1) = 100

⇒90t + 70t + 70 = 100

⇒160t = 100 - 70

⇒160t = 30

⇒t = 30/160

⇒t =0 .1875 hrs, 0.1875(60) = 11.25 minutes

⇒A meets B, at 01:11:15 PM

Therefore, the 11.25 minutes after car b leaves will they pass each other.

and A meets B at  01:11:15 PM.

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Car A leaves Santa Barbara at noon traveling south toward Los Angeles at 70 mph. At 1pm car B leaves Los Angeles traveling north toward Santa Barbara at 90 mph. The distance between the cars at noon was 100 miles. If car B does not get pulled over, how many minutes after car B leaves will they pass each other?

Answer:

This probability is 5/7

Step-by-step explanation:

Rewriting this problem may make it appear to be more manageable.  

The probability that the number is a solution of 3x-4 < 1 simplies to "x < 5".  

This probability is 5/7, since {0, 1, 2, 3, 4} are all less than 5.

Answer:

i would say none of the above can i get brainlest

Step-by-step explanation:

Answer:

$39

Step-by-step explanation:

3 x 9 = 27

3 x 4 = 12

27 + 12 = 39

According to the null hypothesis, the test statistic of the proportion is of z = 120.1.

The claim is that the rate of nausea is greater than the 6% rate experienced by flu patients given a placebo. At the null hypothesis, we consider the claim as false, hence the null hypothesis is:

\(H_0: p \leq 0.06\)

The test statistic is given by:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

In which:

In this problem, the parameters are:

\(p = 0.06, n = 724, \overline{p} = \frac{72}{724} = 0.0994\)

Hence, the test statistic is given by:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

\(z = \frac{0.0994 - 0.06}{\sqrt{\frac{0.06(0.94)}{724}}}\)

\(z = 120.1\)

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An inequality that shows all of the ways that Nita will win if Erik chooses 17 is

This refers to the relation in mathematics that makes an unequal comparison between two numbers or expressions.

Therefore, according to the rules of the game, they would have to make random selections from 0 to 20 and if the difference between their two numbers is less than 10, then Erik wins, the inequality that would show all of the ways that Nita will win if Erik chooses 17 are listed above.

Hence, we can see that the complete question goes thus:

"Erik and Nita are playing a game with numbers. In the game, they each think of a random number from zero to 20. If the difference between their two numbers is less than 10, then Erik wins. If the difference between their two numbers is greater than 10, then Nita wins.

Use what you know about inequalities and absolute values to better understand the game."

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Answer:

15 + 5x = 25 + 5x

You will never have the same amount of money as your friend.

Step-by-step explanation:

Let x be the number of weeks that have passed since you and your friend started saving.

The amount of money in your savings account after x weeks is 15 + 5x.

The amount of money in your friend's savings account after x weeks is 25 + 5x.

Therefore, the system of linear equations that represents this situation is:

15 + 5x = y (equation for your savings account)

25 + 5x = z (equation for your friend's savings account)

where y represents the amount of money in your savings account after x weeks and z represents the amount of money in your friend's savings account after x weeks.

To determine if you will ever have the same amount of money as your friend, we can solve the system of equations by setting y equal to z:

15 + 5x = 25 + 5x

Simplifying, we see that the equation reduces to:

15 = 25

This is a contradiction, since 15 is not equal to 25. Therefore, there is no solution to this system of equations in which y is equal to z, which means that you will never have the same amount of money as your friend.

Answer: 15 + 5x = 25 + 5x. You will never have the same amount of savings as your friend.

Step-by-step explanation:

Hence, 15 + 5x = 25 + 5x. You will never have the same amount of savings as your friend.

Answer:450

Step-by-step explanation:

450/100=4.5

Answer: 0.045

Step-by-step explanation:

4.5/100 = 0.045

(Check Work)

0.045 × 100 = 4.5

Answer:

  A (correctly marked)

Step-by-step explanation:

The graph of g(x) = f(2x) will be the graph of f(x) horizontally compressed by a factor of 2. The horizontal compression moves each point on f(x) to a distance half as far from the y-axis.

__

The graph of f(x) shows a vertical asymptote at x=2 so the graph of g(x) will have a vertical asymptote at x=1. Only Graph A shows a vertical asymptote at x=1.

The mass of the copper wire is approximately 3.65 lb, and the mass of the frisbee is approximately 339.29 kg.

To find the mass of each object, we need to integrate the density function over the given length or area.

(a) A thin copper wire:
The mass (m) can be found by integrating the density function (p(x)) over the length of the wire (0 to 1.25 ft).

m = ∫(4x² + 2x) dx from 0 to 1.25

First, find the antiderivative of the density function:

∫(4x² + 2x) dx = (4/3)x³ + x² + C

Now, evaluate the definite integral:

m = [(4/3)(1.25)³ + (1.25)²] - [(4/3)(0)³ + (0)²]
m ≈ 3.65 lb (rounded to two decimal places)

(b) A frisbee:
The mass (m) can be found by integrating the density function (p(x)) over the area of the frisbee. Since the frisbee is a circle with a radius of 6 inches, the area is given by A = πr².

m = ∫(√3x) dA from 0 to 36π

First, find the antiderivative of the density function:

∫(√3x) dA = (√3/2)x² + C

Now, evaluate the definite integral:

m = [(√3/2)(36π)²] - [(√3/2)(0)²]
m ≈ 339.29 kg (rounded to two decimal places)

So, the mass of the copper wire is approximately 3.65 lb, and the mass of the frisbee is approximately 339.29 kg.

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Answer:

The mass of the copper wire is approximately 3.65 lb, and the mass of the frisbee is approximately 339.29 kg.

To find the mass of each object, we need to integrate the density function over the given length or area.

(a) A thin copper wire:

The mass (m) can be found by integrating the density function (p(x)) over the length of the wire (0 to 1.25 ft).

m = ∫(4x² + 2x) dx from 0 to 1.25

First, find the antiderivative of the density function:

∫(4x² + 2x) dx = (4/3)x³ + x² + C

Now, evaluate the definite integral:

m = [(4/3)(1.25)³ + (1.25)²] - [(4/3)(0)³ + (0)²]

m ≈ 3.65 lb (rounded to two decimal places)

(b) A frisbee:

The mass (m) can be found by integrating the density function (p(x)) over the area of the frisbee. Since the frisbee is a circle with a radius of 6 inches, the area is given by A = πr².

m = ∫(√3x) dA from 0 to 36π

First, find the antiderivative of the density function:

∫(√3x) dA = (√3/2)x² + C

Now, evaluate the definite integral:

m = [(√3/2)(36π)²] - [(√3/2)(0)²]

m ≈ 339.29 kg (rounded to two decimal places)

So, the mass of the copper wire is approximately 3.65 lb, and the mass of the frisbee is approximately 339.29 kg.

Step-by-step explanation:

³358.....,njj2jwieiww

The answers to your questions are as follows :

Probability is a branch of mathematics that deals with the degree of occurrence of an event.

1) The situation with a probability closest or equal to 0 is rolling a number: (A) greater than 5.

Because: there is only one number greater than 5 in that list (which is 6)

2) The model which shows the probability of choosing a multiple of 4 is: ( B )  \(\frac{2}{10}\) (2/10)

Because: there are only two multiples of 4 that can be picked from number 1-10

3) The only survey that would not be valid with a sample of seventh-grade classmates is :  Bank that offer the most services.

Because: they are not working and might have little or no idea about banking services.

4) The probability of choosing a red marble, then a white marble if the marbles are replaced is : 7/10.

where the probability of picking a red marble is =  \(\frac{3}{10}\)

The probability of picking a white marble is = \(\frac{4}{10}\)

since the marbles were replaced : \(\frac{3}{10}\) + \(\frac{4}{10}\) = \(\frac{7}{10}\)

5) The probability of spinning the following. P(not 7) = 7/8

The probablity of picking a 7 is = \(\frac{1}{8}\)

The probability of not is = 1 - probability of picking 7

1 - \(\frac{1}{8}\) = \(\frac{7}{8}\)

In conclusion, go the answers related to your questionare  provided above for each question.

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The numbers that cannot be probabilities are: square root of 2, -53, 5/3, and 1.31.

Probability is a measure of the likelihood of a particular event occurring in a random experiment. It is a value between 0 and 1, with 0 indicating that an event is impossible, and 1 indicating that an event is certain to occur.

In statistics, probability is used to make predictions or draw inferences about a population based on a sample of data. For example, if we were to flip a coin, the probability of getting heads is 0.5, or 50%. In general probability can be defined as the ratio of the number of favorable outcomes to the total number of possible outcomes, which is the mathematical framework behind the random experiments.

From the set of numbers, 0, 0.08, and 3/5 are all possible values of probability.

Therefore, square root of 2, -53, 5/3, and 1.31 cannot be probabilities.

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Answer:

5 hours

Step-by-step explanation:

Variable x = number of hours

Step 1: set up equations

Cwicky Cleaners: 100 + 20x

No Mo Mess: 50 + 30x

Step 2: to find the same hours equal the two equations

100 + 20x = 50 + 30x

Isolate the variable (x)

100 - 50 = 30x - 20x

50 = 10x

50 ÷ 10 = x

5 = x

Step 3: Check your work

Plug in 5 for x on both sides and equal equations together

100 + 20(5) = 50 + 30(5)

100 + 100 = 50 + 150

200 = 200

If they equal each other, then the answer is correct.

This answer is correct.

Answer:

Each small truck can hold a total of 110 boxes.

Step-by-step explanation:

It says three small delivery trucks can hold 330. That meant all three together. So you just have to do 330 divided by 3 and you get 110. So that's the number of boxes ONE small truck can hold. Also, If u do it backward, 3 x 110 =330.

A regular hexagon has six lines of symmetry to map onto itself using reflections.

The number of lines of symmetry a hexagon have that will reflect it onto itself is 6.

The given shape is hexagon.

A line of symmetry is the line that divides a shape or an object into two equal and symmetrical parts.

A hexagon has six lines of symmetry. Each line of symmetry is a line that divides the hexagon into two equal halves that are reflections of one another. When all six lines of symmetry are present, the hexagon can be reflected over itself.

Therefore, the number of lines of symmetry a hexagon have that will reflect it onto itself is 6.

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Answer:

48

Step-by-step explanation:

4x=148+44

4x=192

x=48

Answer:

Step-by-step explanation:

there are 360 degrees inside any 4-sided polygon

so add all four angle measures and set equal to 360:

3x + x + 44 + 148 = 360

4x + 192 = 360

4x = 168

x = 42

check:

3(42) + 42 + 44 + 148 should equal 360

126 + 42 + 192 = 360

168 + 192 = 360

360 = 360

There are 20 members of a basketball team. (a) The coach must select 12 players to travel to an away game. There are \(\(\binom{20}{12}\)\) ways to select the players who will travel to the away game.

To determine the number of ways to select the players who will travel, we can use the concept of combinations. We want to choose 12 players from a group of 20 players. The notation \(\(\binom{n}{r}\)\) represents the number of ways to choose r objects from a set of n objects without regard to the order of selection. In this case, we want to choose 12 players from a group of 20, so we use the combination formula:

\(\(\binom{20}{12} = \frac{20!}{12!(20-12)!}\)\)

Simplifying the expression, we get:

\(\(\binom{20}{12} = \frac{20!}{12!8!}\)\)

This gives us the total number of ways to select 12 players from a group of 20, which is the answer to the question.

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Answer:

3/11 in decimal form is 0.272727272727....

Step-by-step explanation:

Yw ! :)

Answer:

17.3 cm

Step-by-step explanation:

(refer to the attached for reference)

since the given triangle is a right triangle (i.e with one of the angles being 90 deg), we can use trigonometry to determine the missing side.

In our case, we are given ∠ABC = 68° and the length of its adjacent side AB = 7 cm.

From trigonometry, the following relationship may be formed:

tan (68°) = opposite length / adjacent length

tan (68°) = AC / AB

tan (68°) = AC / 7   (multiply both sides by 7)

7 tan (68°) = AC (rearrange)

AC = 7 tan (68°)    (solve using calculator)

AC = 17.3256

AC = 17.3 cm (1 dec pl)Answer:

17.3 cm

Step-by-step explanation:

(refer to the attached for reference)

since the given triangle is a right triangle (i.e with one of the angles being 90 deg), we can use trigonometry to determine the missing side.

In our case, we are given ∠ABC = 68° and the length of its adjacent side AB = 7 cm.

From trigonometry, the following relationship may be formed:

tan (68°) = opposite length / adjacent length

tan (68°) = AC / AB

tan (68°) = AC / 7   (multiply both sides by 7)

7 tan (68°) = AC (rearrange)

AC = 7 tan (68°)    (solve using calculator)

AC = 17.3256

AC = 17.3 cm (1 dec pl)

The probability that the dealt hand contains exactly two aces given that we know it contains at least one ace is 2/3 or approximately 0.667.

To calculate this probability, we can use Bayes' theorem. Let A be the event that the dealt hand contains exactly two aces and B be the event that the hand contains at least one ace. Then, the probability we are looking for is P(A | B), the probability of A given that B has occurred.

Using Bayes' theorem, we have:

where P(B | A) is the probability of drawing a hand with at least one ace given that the hand contains exactly two aces, P(A) is the probability of drawing a hand with exactly two aces, and P(B) is the probability of drawing a hand with at least one ace.

We can calculate these probabilities as follows:

To calculate P(B | A), we first fix two aces in the hand and then choose three non-aces from the remaining 48 cards. Thus, we have:

Plugging these values into Bayes' theorem, we get:

Therefore, the probability that the dealt hand contains exactly two aces given that we know it contains at least one ace is 2/3 or approximately 0.667.

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(a) For a line, the ratio of the change in y to the change in x is called the slope of the line.
(b) The point-slope form of the equation of a line with slope m passing through (x1, y1) is y - y1 = m(x - x1).

The slope of a line is a measure of its steepness and is calculated by finding the ratio of the change in y (the rise) to the change in x (the run) between two points on the line.

The point-slope form of the equation of a line is a way to write the equation of a line when you know its slope and one point on the line. It is written as y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is the point on the line.

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Answer:

a. 21 = u1 + 6·d

b. 29 = u1 + 10·d

c. d = 2, u1 = 9

Step-by-step explanation:

a. The given parameters are;

The amount of therapeutic drug Kiri receives on her first at the hospital = u1 milligrams

The amount of drug increase received by Kiri each day = d

The amount of drug Kiri received on the seventh day = 21 mg

The amount of drug she received on the eleventh day = 29 mg

Therefore, we have an arithmetic progression with the formula for the nth term given as follows;

aₙ = a₁ + (n - 1)·d

Where;

a₁ = u1

n = The number of terms

Therefore, for the 7th day, the amount of drugs she receives, which is 21 milligrams, is given as follows;

a₇ = u1 + (7 - 1)·d = u1 + 6·d = 21

The equation for the amount of drugs she receives in terms of u1 and d on the seventh day is given as follows;

21 = u1 + 6·d

b. For the eleventh day, the amount of drugs she receives, which is 29 milligrams, is given as follows;

a₁₁ = u1 + (11 - 1)·d = u1 + 10·d = 29

Therefore, the equation for the amount of drugs she receives in terms of u1 and d on the  eleventh day is given as follows;

29 = u1 + 10·d

c. Therefore, we have two equations which are given as follows;

21 = u1 + 6·d................(1)

29 = u1 + 10·d..............(2)

Subtracting equation (1) from equation (2) gives;

29 - 21 = (u1 + 10·d) - (u1 + 6·d)

8 = 4·d

d = 8/4 = 2

d = 2

From equation (1), we have;

21 = u1 + 6·d = u1 + 6×2 = u1 + 12

21 = u1 + 12

21 - 12 = u1

∴ u1 = 9

d = 2, u1 = 9.

Answer:

1/36

Step-by-step explanation:

if the probability for rolling a 5 is 1/6 the first time and 1/6 rolling it a second time, multiply the two probabilities together

1/6 X 1/6 = 1/36

so the answer is a 1/36 probability of rolling two fives in a row

Answer:

A) 154x89 _s2

s

Step-by-step explanation:

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Answer:

Step-by-step explanation:

The cars travel in opposite directions from the same point.

Each hour they travel:

After x hours they will be 425 miles apart:

combined speed

Time be t

Speed=Distance/Time

Answer:

7 - 2m can be translated to "7 minus two times m" or "the difference between 7 and twice m".

3(m + 2) = 15 can be translated to "three times the sum of m and 2 is equal to 15" or "the product of 3 and the sum of m and 2 is 15".

To solve the equation, we can start by distributing the 3 on the left side:

3(m + 2) = 15

3m + 6 = 15

Then, we can subtract 6 from both sides:

3m + 6 - 6 = 15 - 6

3m = 9

Finally, we can divide both sides by 3:

3m/3 = 9/3

m = 3

Therefore, the solution to the equation 3(m + 2) = 15 is m = 3.

5m - m(2 - m) can be translated to "5m minus the product of m and the difference between 2 and m" or "the difference between 5m and m times the quantity 2 minus m".

To simplify the expression, we can use the distributive property to expand the second term:

5m - m(2 - m) = 5m - 2m + m^2 = m^2 + 3m

Therefore, the simplified expression is m^2 + 3m.