find the value of sin2a, if tana=-12/5 in the fourth quadrant

The probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5 is, 60%

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We have to given that;

To find the probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5.

Since, From 1 to 5, there are three numbers 1, 3, 5 are odd numbers.

Hence, the probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5 is,

P = 3/5

Change into percent as;

P = 3/5 x 100%

P = 60%

Thus, the probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5 is, 60%

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Mia can donate up to 4 leashes without requiring regrouping to find the total number of items donated.

To determine how many leashes Mia needs to donate such that you would need to regroup to find the total number of items donated, we need to know the maximum capacity of the shelter's storage or the maximum number of items that can be comfortably accommodated without regrouping.

If we assume that the shelter's storage can hold a maximum of 20 items comfortably without needing to regroup, then we can calculate the number of items Max and Mia can donate without regrouping:

Max donated 16 dog collars, and the shelter can accommodate 20 items without regrouping. So, Max has donated within the capacity without needing to regroup.

Now, let's see how many leashes Mia can donate without exceeding the capacity:

20 (maximum capacity) - 16 (Max's donation) = 4

Mia can donate up to 4 leashes without requiring regrouping to find the total number of items donated. If Mia donates more than 4 leashes, you would need to regroup to calculate the total number of items donated.

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Here, we need to calculate the expected number of students who are liberal arts major.

It is given that, 60 out of 65 students are liberal arts major.

So, we will calculate the percentage of liberal arts major from the total.

Percentage of liberal arts major = [tex] \frac{Number of liberal arts major}{Total students} [/tex] X 100

Percentage of liberal arts major = [tex] \frac{60}{65} [/tex] X 100

Percentage of liberal arts major = 92.31 %

Now, we will calculate for 8,943 liberal arts majors -

In total students of 8,943, liberal arts majors = 92.31 % X 8,943

In total students of 8,943, liberal arts majors =8,256 students (approximately)

The height formed by this 25 foot ladder that leans against a wall is 24 feet.

Given the following data:

Pythagorean theorem can be defined as a fundamental mathematical expression in Euclidean geometry that can be used to determine any of the three (3) sides of a right-angled triangle.

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

[tex]h^2 = a^2 + b^2[/tex]

Where:

Substituting the given parameters into the formula, we have;

[tex]h^2 = a^2 + b^2\\\\25^2 = 7^2 +b^2\\\\625=49+b^2\\\\b^2=625-49\\\\b=\sqrt{576}[/tex]

b = 24 feet.

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Final answer:

The average of three numbers that sum to 144 is 48, found by dividing 144 by 3.

Explanation:

The average of three numbers is the sum of those numbers divided by three. In this case, if the sum of three numbers is 144, then the average can be found by dividing 144 by 3. Calculating this, we get the average, which is 48 (144 ÷ 3 = 48). Hence, the average of the three numbers is 48.

Answer:

A is rational, but B is irrational.

Step-by-step explanation:

Answer:

1)  Area of ΔABD = Area of ΔACD and

2)  Area of ΔABO = Area of ΔCDO

Step-by-step explanation:

1) In the given trapezoid ABCD,

AD || BC

Triangles ΔABD and ΔACD lie on the same base AD and lie between the parallel lines AD and BC.

Hence, they are equal in area.

Therefore, Area of ΔABD = Area of ΔACD.

2) From 1), we have

Ar (ΔABD) = Ar(ΔACD)

Subtract Ar (ΔAOD) from both sides,

Ar (ΔABD) - Ar (ΔAOD) = Ar(ΔACD) - Ar (ΔAOD)

Ar (ΔABO) = Ar (ΔCDO)

The value of x is -3 and the solution to this system of equations is (-3 , 7).

When a number of variables are involved, the system of equation is generated. The system of equation has been the set of simultaneous equations as well.

Given :

[tex]y = -3x-2[/tex]   ----  (1)

[tex]y=7[/tex]  -----  (2)

Solution :

From, equation (1) and (2) we get the value of x to be:

[tex]7=-3x-2[/tex]

[tex]9=-3x[/tex]

[tex]x=-3[/tex]

Therefore, the value of x is -3.

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Answer:

The answer is D) $897.12

Step-by-step explanation:

3 years = 36 months

173.33 * 36 = 6239.88

5 years = 60 months

118.95 * 60 = 7137.00

7137.00 - 6239.88 = 897.12

After calculating the number of games already played as a fraction of the total and adding 10 more games, it is determined that the team will have played 61 games.

The subject of this question is Mathematics, particularly it involves operations with fractions. The team has played 3/5 of the total scheduled games. So let's calculate how many games that would be by multiplying the total number of games, 85, by 3/5:

The team has already played 85 * 3/5 = 51 games.

If the team plays 10 more games, we need to add this to the number of games already played:

51 (already played games) + 10 (more games) = 61 games.

Therefore, the total number of games the team will have played after 10 more games is 61 games.

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Answer:

6 checks

Step-by-step explanation:

The expected number of checks out of 20 checks that should arise Over Run expect to go to their TreeHuggers Campaign is given by: Option D: 6 checks.

Binomial distributions consists of n independent Bernoulli trials.

Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as

[tex]X \sim B(n,p)[/tex]

The probability that out of n trials, there'd be x successes is given by

[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]

The expected value and variance of X are:

[tex]E(X) = np\\ Var(X) = np(1-p)[/tex]

For this case, we're specified that:

The spinner has 10 parts.

Thus, the probability of getting the spinner fall on treehugger is 3/10 (three favorable parts of spinner to ten total parts, all parts assumingly equally probable and spinner assumingly not falling in the mid of two parts).

20 checks, all will be accompanied with 20 spins, all independent of each other.

Let X = total number of times the spinner falls on Treehuggers

And let Success for a spin = It landing on Treehugger

Failure for a spin = It not landing on Treehugger

n = 20, so we get:

[tex]X \sim B(n=20,p=0.3)[/tex]

The expected number of checks out of 20 checks that should arise Over Run expect to go to their TreeHuggers Campaign = expected number of successes in those 20 spins =  the expected number of values of X.

Since X follows a binomial distribution, we get:

[tex]E(X) = np = 20 \times 0.3 = 6[/tex]

Thus, the expected number of checks out of 20 checks that should arise Over Run expect to go to their TreeHuggers Campaign is given by: Option D: 6 checks.

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Answer:

Mucus

Step-by-step explanation:

Final answer:

The expression that represents the sum of r and 7 is written simply as r + 7. This is a basic operation in algebra involving the addition of a variable and a constant.

Explanation:

To write an expression that represents the sum of r and 7, you simply add these two together. The mathematical expression for this is r + 7. This is a basic algebraic expression that demonstrates how to represent the addition of a variable, in this case r, with a constant number, which is 7.