Draw the following angle in standard position and nane the reference angle. 240 2. Find the exact value for each of the following: a) bin 330 b) cos(-240 ) or -0.5 tor-os 3. Use the given informati

The solution for the system of equtaions is (57/11, 42/11)

Here we have the system of equations:

x/3 = 6 - y/3

3x/4 - 3 = 2y

We can isolate x on the first equation to get:

x = 18 - 3*y/3

x = 18 - y

Replacing that on the other equation we will get

3*(18 - y)/4 - 3 = 2y

We can solve this for y.

3*(18 - y)/4 = 2y + 3

54 - 3y = 4*(2y + 3) = 8y + 12

54 - 12 = 8y + 3y

42 = 11y

42/11 =y

And the value of x will be:

x = 9 - 42/11

x  = 99/11 - 42/11 = 57/11

That is the solution of the system.

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Probability distributions according to the number of occurrences of green cards. Probabilities are:

P(x=0) =  0.1

P(x=1) = 0.15

P(x=2) = 0.45

P( x= 3) = 0.2

P ( x=4) = 0.1

Probability is absolutely how probably something is to take place. whenever we're unsure about the outcome of an occasion, we can speak approximately the chances of certain outcomes—how possibly they're. The evaluation of occasions governed by probability is referred to as facts.

P(x=0) = 12/120 = 1/10 = 0.1

P(x=1) = 18 /120 = 3/20 = 0.15

P(x=2) = 54 / 120 = 9/20 = 0.45

P( x= 3) = 24 / 120 = 0.2

P ( x=4) = 12 / 120 = 1 /10 = 0.1

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In an experiment, a deck of cards containing different colored cards is shuffled. Four cards are randomly selected and the number of green cards selected is recorded. One hundred twenty trials of the experiment are run.

The table shows the frequency of 0, 1, 2, 3, or 4 green cards occurring in the trials.

Number of green cards 0 1 2 3 4

Frequency 12 18 54 24 12

Create a probability distribution for the discrete variable.

Real-world problem on additive inverse of a rational number and solution:

Peter borrowed one fourth of his salary to Jack. The money way returned to peter at the end of the month without interest because they are friends. how much is Jack owing peter in the transaction?

Jack is owing Peter nothing

Additive inverse is the opposite of a number in terms of addition, this is the number that gives zero when added to the original number.

To get a result equal to 0, add the original number and the additive inverse or by simply changing the sign of the integer. On the basis of negation of the original number.

In the problem let peter's salary be x

amount peter borrowed out = x/4

amount paid back = x/4

Addition of the expenses

borrowed + paid back

-x/4 + x/4 = 0

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Step-by-step explanation:

I have two step

step 1

32+b=54

32+9=54

41=54

you divide both side by 41 and the answer is 1 and 1

step two

32+b=54

b=54-32

9=22

you divide both side by 9 and the answer is 2,44

Answer:

2

Step-by-step explanation:

slope=rise/run

create a triangle

I chose (2,4)

it goes up 4 and the run is 2

4/2

Answer:

RM =20

Step-by-step explanation:

Find the diagram of the parallelogram attached

From the diagram, GP = PA

8x = 2x+18

8x - 2x = 18

6x = 18

x = 18/6

x = 3

Since RM = 2RP

RM = 2(x+7)

RM = 2(3+7)

RM = 2(10)

RM =20

Hence the length of RM is 20

simplify 9² x 9 to 9³

9³ x 9⁵/9⁹

use product rule: x‸ax‸b=x‸a+b

9⁸/9⁹

use quotient rule: x‸a/x‸=x‸a-b

9⁸⁻⁹

simplify 8-9 to -1

9⁻¹

use negative power rule: x‸-a=1/x‸a

1/9

Answer:

2/5 or .4

Step-by-step explanation:

basically look at the points where the line meets the graph. two points would be 0,20 and 50,40. then count the amount that it changes vertically and then horizontally. +20vertical +50 horizonal giving the slope 20/50. this can then be simplified to 2/5 or the equivalent number .4

Answer:

If I remember correctly, the slope would be 2/5.

Answer:

Step-by-step explanation:

To solve this problem, we need to use exponential growth formula, which is:

P = P0 * e^(rt)

where P is the final population, P0 is the initial population, r is the annual growth rate, and t is the time in years.

We can use the given data to find the annual growth rate r:

r = ln(P/P0) / t

where ln is the natural logarithm.

Using the population data from 1900 and 2000, we get:

r = ln(8.86/5.14) / 100 ≈ 0.0198

So the annual growth rate is approximately 0.0198, or 1.98%.

Now, we need to find the initial population P0 when King Karl XII died in 1718. Let's call this population X.

We know that the population has been growing exponentially since then, so we can use the formula above to relate the population in 1718 to the population in 1900:

X * e^(0.0198 * 182) = 5.14 million

where 182 is the number of years between 1718 and 1900.

Solving for X, we get:

X = 5.14 million / e^(0.0198 * 182) ≈ 0.14 million

Therefore, the population of Sweden when King Karl XII died in 1718 was approximately 0.14 million people.

Answer: b because i did the eqaution on paper

Step-by-step explanation:

Tukey's HSD widens the width of the family-wise confidence intervals so that the probability of false detection is as low as we claim.

Tukey's HSD (Honestly Significant Difference) is a statistical test that compares the means of pairwise groups to determine whether they are significantly different.

Tukey's HSD procedure can be used as a post hoc test after a significant ANOVA result has been obtained. It's a method of avoiding the inflated Type I error rate that occurs when many pairwise comparisons are made.

A family-wise confidence interval is an interval that encompasses all of the individual pairwise comparisons' confidence intervals. A family-wise confidence interval is used to ensure that the probability of making a Type I error (false detection) is kept to a minimum.

Tukey's HSD widens the width of the family-wise confidence intervals so that the probability of false detection is as low as we claim, as stated in the question.

Therefore, we can conclude that Tukey's HSD widens the width of the family-wise confidence intervals so that the probability of false detection is as low as we claim.

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From the given table, let's complete the stem and leaf plot.

Part (a):

From the given table, we have 27 data.

It consists of just the data for the round-trip commute time for the employees.

Therefore, data were collected for 1 quantitative variable.

Part (b):

The data constitute a sample

Part (c):

To compute the stem and leaf plot, we have:

Stems------------->Leaves

5--------------------> 0, 0, 3, 3, 3, 4, 7, 7, 9

6----------------------> 0, 1, 3, 4, 5, 7, 8, 8

7------------------------> 0, 3, 4, 4, 5

8------------------------>0, 1, 9

9-------------------------> 0, 4

Part d:

The shape of the data can be said to be right skewed .

Answer:

the ordered pair (0, 1/6)

Step-by-step explanation:

To reflect a function across the y-axis, we replace every occurrence of x with -x. Therefore, the function g(x) is given by:

g(x) = f(-x) = 1/6(2/5)^(-x)

To find an ordered pair on g(x), we need to choose a value of x and evaluate g(x). For example, if we choose x = 0, then:

g(0) = 1/6(2/5)^(-0) = 1/6

Therefore, the ordered pair (0, 1/6) is on the graph of g(x).

The probability that each of the players will have an Ace is 0.1055. The result is obtained by dividing the ways to place Aces for each player by the total ways.

The four suits for a standard deck of 52 cards are hearts, diamonds, clubs, and spades of 13 cards each. The hearts and diamonds are red. While, the clubs and spades are black. The 13 cards are Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King.

The 52 cards are randomly distributed to 4 players. So, each players will get 13 cards.

Find the probability that each of them will have an Ace!

When we distribute 13 first cards, the rest cards are 39. After 13 second cards, the rest are 26 cards, an so on. Without discerning the suits, the ways to place Aces so that each player will get an Ace is

n(A) = 13⁴

There are 4 Aces in 53 cards. The total ways to place the Aces is

\(n(S) = \binom{52}{4}\)

The probability that each player will have an Ace would be

\(P = \frac{n(A)}{n(S)} = \frac{13^{4} }{ \binom{52}{4}} = \frac{28561}{270725} \approx 0.1055\)

Hence, the probability that each player will get an Ace is 0.1055.

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The amount of money she spends per year on utility bills for the air conditioner is; D: $176.40

We are told that;

Cost of running the air conditioner = 7 hours per day

Cost of running the air conditioner = 21 cents per hour = $0.21 per hr.

She runs it for four months at 7 hours per day. Thus;

Total number of hours for the 4 months = 7 × 30 × 4 = 840 hours

Total cost for the 4 months = $0.21 per hr. × 840 hours = $176.4

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Answer:

Drawing : Actual

Scale

           2 : 10

     2 cm : 10 feet

Length

    6 cm : 30 feet

Width

    4 cm : 20 feet

The actual dimensions of the room are - Length=30 feet, Width=20 feet.

The answer is the second one.

Step-by-step explanation:

Answer:

second one

Step-by-step explanation:

There are total 95040 number of different groups of 5 items can be selected from 12 distinct item.

According to the given question.

Total number of items, n = 12

Total numbers of items to be selected, r = 5

Since, we have to determine the number of different groups of 5 items that can be selected from 12 distinct items. So, we will find the number of different groups by permulation formula i.e.

\(^{n} P_{r} = \frac{n!}{(n-r)!}\)

Where,

\(^{n} P_{r}\) is the total number of permutations.

n is the total number of objects.

r is teh total number of objects to be selected.

Therefore,

The number of different groups or permutaions of 5 items that can be selected from 12 distinct group

\(^{12} P_{5}\)

\(= \frac{12!}{(12-5)!}\)

\(= \frac{12!}{7!}\)

\(= \frac{12\times11\times10\times9\times8\times7!}{7!}\)

= 12 × 11 × 10 × 9 × 8

= 95040

Hence, there are total 95040 number of different groups of 5 items can be selected from 12 distinct item.

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Answer: -1/2

Step-by-step explanation:

Use double-angle identities:

cos(2θ)=cos^2θ−sin2^θ

cos(2θ)=1−2sin^2θ

cos(2θ)=2cos^2θ−1

sin(x)=1/2

cos(2x)=1−2sin^2x=1−2(1/4)=1/2

cos(4x)=2cos2^(2x)−1=2(1/4)−1=-1/2

Answer: cos4x=-1/2 if sinx=1/2.

Step-by-step explanation:

\(sinx=\frac{1}{2}\\ x=\frac{\pi }{6} .\\4x=4*\frac{\pi }{6}=\frac{2\pi }{3}.\\ cos4x=cos\frac{2\pi }{3}=-\frac{1}{2} .\)

Answer:

X >-5

Step-by-step explanation:

The 21 square root of 98 divided by 7 square root of 21 = 21√98 / 7√21 = 6.4807407

A square root of a number x is a number y such that y2 = x; in other words, a number y who's square and the result of multiplying the number by itself, or y ⋅ y, is x.

Every nonnegative real number x has a unique nonnegative square root, called the principal square root, which is denoted by √where the symbol √ is called the radical sign.

Every positive number x has two square roots: √ which is positive, and -√ which is negative. The two roots can be written more concisely using the ± although the principal square root of a positive number is only one of its two square roots, the designation "the square root" is often used to refer to the principal square root.

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The probability (as a decimal) that the speed measurement is off by at most 0.3 miles per hour is 2.309.

Given a continuous random variable x represents the error in the speed measurement. Based on the collected data, you believe the probability distribution for this continuous random variable is best described by the function f(x)= 2/1 − 9/2 x^2.The probability (as a decimal) that the speed measurement is off by at most 1.4 miles per hour is calculated below:

P([−1.4,1.4]) = ∫[−1.4,1.4] f(x) dx.

We know that f(x)= 2/1 − 9/2 x^2

∴ P([−1.4,1.4]) = ∫[−1.4,1.4] (2/1 − 9/2 x^2) dx

∴ P([−1.4,1.4]) = 2 ∫[−1.4,1.4] (1/1 − 9/4 x^2) dx.

Let u = (3/2) x du = (3/2) dx

∴ P([−1.4,1.4]) = 2 ∫[-2.1,2.1] (1/1 − u^2) (2/3) du

∴ P([−1.4,1.4]) = 4/3 ∫[-2.1,2.1] (1/1 − u^2) du.

Let u = sin θ du = cos θ dθ

∴ P([−1.4,1.4]) = 4/3 ∫[-π/3,π/3] (1/1 − sin^2 θ) cos θ dθ

∴ P([−1.4,1.4]) = 4/3 ∫[-π/3,π/3] d/dθ (−cot θ) dθ (using integral by substitution)

∴ P([−1.4,1.4]) = 4/3 (∣−cot θ∣[-π/3,π/3] − ∫[-π/3,π/3] cot^2 θ dθ) (using integral by parts)

∴ P([−1.4,1.4]) = 4/3 (∣−cot θ∣[-π/3,π/3] − ∫[-π/3,π/3] (csc^2 θ − 1) dθ) (using integral by substitution)

∴ P([−1.4,1.4]) = 4/3 (∣−cot θ∣[-π/3,π/3] + ∣−tan θ∣[-π/3,π/3] − θ∣[-π/3,π/3])

∴ P([−1.4,1.4]) = 4/3 [(-2cot π/3 - 2tan π/3 - π/3) - (-2cot -π/3 - 2tan -π/3 - (-π/3))] = 4/3 * [(-2/√3 + 2√3/3 + π/3) - (2/(-√3) - 2√3/3 + π/3)] = 4/3 * [4√3/3 + 4/√3] = 16√3/9 + 16/9≈ 2.296

So, the probability (as a decimal) that the speed measurement is off by at most 1.4 miles per hour is 2.296.The probability (as a decimal) that the speed measurement is off by at most 0.3 miles per hour is calculated below:

P([−0.3,0.3]) = ∫[−0.3,0.3] f(x) dx. We know that f(x)= 2/1 − 9/2 x^2

∴ P([−0.3,0.3]) = ∫[−0.3,0.3] (2/1 − 9/2 x^2) dx

∴ P([−0.3,0.3]) = 2 ∫[−0.3,0.3] (1/1 − 9/4 x^2) dx. Let u = (3/2) x du = (3/2) dx

∴ P([−0.3,0.3]) = 2 ∫[-0.45,0.45] (1/1 − u^2) (2/3) du

∴ P([−0.3,0.3]) = 4/3 ∫[-0.45,0.45] (1/1 − u^2) du. Let u = sin θ du = cos θ dθ

∴ P([−0.3,0.3]) = 4/3 ∫[-π/6,π/6] (1/1 − sin^2 θ) cos θ dθ

∴ P([−0.3,0.3]) = 4/3 ∫[-π/6,π/6] d/dθ (−cot θ) dθ (using integral by substitution)

∴ P([−0.3,0.3]) = 4/3 (∣−cot θ∣[-π/6,π/6] − ∫[-π/6,π/6] cot^2 θ dθ) (using integral by parts)

∴ P([−0.3,0.3]) = 4/3 (∣−cot θ∣[-π/6,π/6] − ∫[-π/6,π/6] (csc^2 θ − 1) dθ) (using integral by substitution)

∴ P([−0.3,0.3]) = 4/3 (∣−cot θ∣[-π/6,π/6] + ∣−tan θ∣[-π/6,π/6] − θ∣[-π/6,π/6])

∴ P([−0.3,0.3]) = 4/3 [(-2cot π/6 - 2tan π/6 - π/6) - (-2cot -π/6 - 2tan -π/6 - (-π/6))] = 4/3 * [(-2/√3 + √3 + π/6) - (2/(-√3) - √3 + π/6)] = 4/3 * [4√3/3] = 4√3/3 ≈ 2.309.

So, the probability (as a decimal) that the speed measurement is off by at most 0.3 miles per hour is 2.309.

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The probability that the speed measurement is off by at most 0.3 miles per hour is 2.309.

Given a continuous random variable x represents the error in the speed measurement. Based on the collected data, you believe the probability distribution for this continuous random variable is best described by the function f(x)= 2/1 − 9/2 x^2.The probability that the speed measurement is off by at most 1.4 miles per hour is calculated below:

P([−1.4,1.4]) = ∫[−1.4,1.4] f(x) dx.

We know that f(x)= 2/1 − 9/2 x^2

∴ P([−1.4,1.4]) = ∫[−1.4,1.4] (2/1 − 9/2 x^2) dx

∴ P([−1.4,1.4]) = 2 ∫[−1.4,1.4] (1/1 − 9/4 x^2) dx.

Let u = (3/2) x du = (3/2) dx

∴ P([−1.4,1.4]) = 2 ∫[-2.1,2.1] (1/1 − u^2) (2/3) du

∴ P([−1.4,1.4]) = 4/3 ∫[-2.1,2.1] (1/1 − u^2) du.

Let u = sin θ du = cos θ dθ

∴ P([−1.4,1.4]) = 4/3 ∫[-π/3,π/3] (1/1 − sin^2 θ) cos θ dθ

∴ P([−1.4,1.4]) = 4/3 ∫[-π/3,π/3] d/dθ (−cot θ) dθ (using integral by substitution)

∴ P([−1.4,1.4]) = 4/3 (∣−cot θ∣[-π/3,π/3] − ∫[-π/3,π/3] cot^2 θ dθ) (using integral by parts)

∴ P([−1.4,1.4]) = 4/3 (∣−cot θ∣[-π/3,π/3] − ∫[-π/3,π/3] (csc^2 θ − 1) dθ) (using integral by substitution)

∴ P([−1.4,1.4]) = 4/3 (∣−cot θ∣[-π/3,π/3] + ∣−tan θ∣[-π/3,π/3] − θ∣[-π/3,π/3])

∴ P([−1.4,1.4]) = 4/3 [(-2cot π/3 - 2tan π/3 - π/3) - (-2cot -π/3 - 2tan -π/3 - (-π/3))] = 4/3 * [(-2/√3 + 2√3/3 + π/3) - (2/(-√3) - 2√3/3 + π/3)] = 4/3 * [4√3/3 + 4/√3] = 16√3/9 + 16/9≈ 2.296

So, the probability (as a decimal) that the speed measurement is off by at most 1.4 miles per hour is 2.296.The probability (as a decimal) that the speed measurement is off by at most 0.3 miles per hour is calculated below:

P([−0.3,0.3]) = ∫[−0.3,0.3] f(x) dx. We know that f(x)= 2/1 − 9/2 x^2

∴ P([−0.3,0.3]) = ∫[−0.3,0.3] (2/1 − 9/2 x^2) dx

∴ P([−0.3,0.3]) = 2 ∫[−0.3,0.3] (1/1 − 9/4 x^2) dx. Let u = (3/2) x du = (3/2) dx

∴ P([−0.3,0.3]) = 2 ∫[-0.45,0.45] (1/1 − u^2) (2/3) du

∴ P([−0.3,0.3]) = 4/3 ∫[-0.45,0.45] (1/1 − u^2) du. Let u = sin θ du = cos θ dθ

∴ P([−0.3,0.3]) = 4/3 ∫[-π/6,π/6] (1/1 − sin^2 θ) cos θ dθ

∴ P([−0.3,0.3]) = 4/3 ∫[-π/6,π/6] d/dθ (−cot θ) dθ (using integral by substitution)

∴ P([−0.3,0.3]) = 4/3 (∣−cot θ∣[-π/6,π/6] − ∫[-π/6,π/6] cot^2 θ dθ) (using integral by parts)

∴ P([−0.3,0.3]) = 4/3 (∣−cot θ∣[-π/6,π/6] − ∫[-π/6,π/6] (csc^2 θ − 1) dθ) (using integral by substitution)

∴ P([−0.3,0.3]) = 4/3 (∣−cot θ∣[-π/6,π/6] + ∣−tan θ∣[-π/6,π/6] − θ∣[-π/6,π/6])

∴ P([−0.3,0.3]) = 4/3 [(-2cot π/6 - 2tan π/6 - π/6) - (-2cot -π/6 - 2tan -π/6 - (-π/6))] = 4/3 * [(-2/√3 + √3 + π/6) - (2/(-√3) - √3 + π/6)] = 4/3 * [4√3/3] = 4√3/3 ≈ 2.309.

So, the probability (as a decimal) that the speed measurement is off by at most 0.3 miles per hour is 2.309.

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Answer:

12x^3 + 19x^2 + x - 5

Step-by-step explanation:

To solve this, I set up the problem like this:

(3x^2 + x - 1)(4x + 5)

Now, just distribute everything from the first set of ( ) to the second set of ( ). Here's what you should have when you do that:

12x^3 + 15x^2 + 4x^2 + 5x - 4x - 5

Now, you would just combine like terms, which would get you to the final answer.

Hope this helps!

12x³ + 19x² + x -5

Polynomials are expressions that have multiple terms.

Breaking Apart Polynomials

When multiplying by a polynomial, we can break apart one of the polynomials, and multiply by each term individually. This means to multiply 3x² + x - 1 by 4x + 5, we can break apart the binomial into its separate terms. Instead of trying to multiply everything at once, we can multiply the trinomial by 4x and then multiply the trinomial by 5. Finally, add together the 2 products for the final answer.

Multiplying Polynomials

First, let's multiply the trinomial by 4x.

To find the product, multiply each term of the trinomial by 4x, then add them back together.

So, the first product is 12x³ + 4x²- 4x. Next, let's multiply 5(3x² + x - 1) the same way.

This means that the second product is 15x² + 5x - 5. Finally, let's add the 2 products together.

Then, simplify the expression.

This gives us our final answer. The product of 3x² + x - 1 and 4x + 5 is 12x³ + 19x² + x - 5.

Answer:

C--- x+y<-1y>2

Step-by-step explanation:

hope this helps!

have a good day :)

Answer:

Yes

Step-by-step explanation:

\(\sqrt{\frac{2x}{9} }={\frac{\sqrt{2x} }\sqrt{} {9} } =\frac{\sqrt{2x} }{3}=\frac{1}{3}\sqrt{2x}\)