Which of the points shown on the unit circle below is on the terminal side of angle θ such that cos θ= 1/2?
a
b
c
d

The probability to pick one candy at random that is yellow or green through which relation satisfied is [tex]\frac{65}{139}[/tex]

What about probability ?

Probability is a branch of mathematics that deals with the study of random events or experiments. It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.

The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if you roll a fair six-sided die, the probability of rolling a 3 is 1/6, since there is only one favorable outcome (rolling a 3) out of six possible outcomes (rolling any number from 1 to 6).

Probability theory is used in a wide range of fields, including statistics, economics, physics, engineering, and computer science, to model and analyze phenomena that involve uncertainty or randomness. It is also used in many practical applications, such as risk assessment, decision making, and game theory.

According to the given information:

The probability it is yellow:

[tex]\frac{20}{20+42+45+32} = \frac{20}{139}[/tex]

The probability it is green:

[tex]\frac{45}{45+20+42+32} = \frac{45}{139}[/tex]

P(green, yellow):

⇒ [tex]\frac{20}{139} + \frac{45}{139}\\\\\frac{65}{139}[/tex]

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Answer:

65/139

Step-by-step explanation:

Acellus

Step-by-step explanation:

rise = height = 5 units     run = base = 2

Use Pythagorean theorem

   L^2 = 5^2 + 2^2

     L^2 = 29

     L = sqrt (29)

Answer: cylinder a is 12.45cm^3

cylinder b is 49cm^3

Step-by-step explanation: been through this my guy it was a struggle frl but bro igy frls

Answer: 8.5 feet

Step-by-step explanation:

To determine how far Max traveled, we can use the Pythagorean theorem to find the distances between the points.

Max twirls to Lindsey's position:

Since Max is 2 feet behind Kenji and 4 feet left of Lindsey, Max and Lindsey form a right triangle with legs of 2 feet and 4 feet. Using the Pythagorean theorem:

a² + b² = c²

2² + 4² = c²

4 + 16 = c²

20 = c²

Taking the square root of both sides:

c = √20 ≈ 4.47 feet (rounded to the nearest tenth)

Max leaps to Kenji's position:

Since Max was initially 2 feet behind Kenji, the distance between Lindsey and Kenji is also 2 feet.

Max walks back to his original position:

The distance between Max's original position and Kenji's position is 2 feet.

Adding up the distances:

4.47 feet (Max to Lindsey) + 2 feet (Lindsey to Kenji) + 2 feet (Kenji to Max's original position) = 8.47 feet

So, Max traveled approximately 8.5 feet (rounded to the nearest tenth) during his movements.

The distance Max traveled can be found by calculating the distance of each movement he makes and adding them up. First, we need to use the Pythagorean theorem to calculate the distance between Lindsey and Max:

sqrt(4^2 + 2^2) = sqrt(16 + 4) = sqrt(20) = 2*sqrt(5)

So, Max travels 2*sqrt(5) feet to get to Lindsey's position. Next, he travels the distance between Kenji and Lindsey, which is 4 feet:

distance = 4

Finally, he travels in a straight line back to his original position, which is 2 feet straight behind Kenji:

distance = 2

Adding these distances together, we get:

2*sqrt(5) + 4 + 2 = 2*sqrt(5) + 6

Rounding to the nearest tenth gives us a final answer of approximately 8.5 feet.

When we simplify an equatiοn and end up with a cοntradictiοn like this, it means that the equatiοn has nο sοlutiοn.

The intersectiοns οr meetings οf the lines οr planes that represent the linear equatiοns are knοwn as the sοlutiοns οf linear equatiοns. The set οf values fοr the variables in every feasible sοlutiοn is knοwn as a sοlutiοn set fοr a system οf linear equatiοns.

Nοt a Sοlutiοn

If there is nο intersectiοn οf any lines, οr if the graphs οf the linear equatiοns are parallel, then the system οf linear equatiοns cannοt be sοlved.

The equatiοn 5 + 9z = 9z can be simplified as fοllοws:

5 + 9z = 9z

5 = 0

This is a cοntradictiοn since 5 cannοt be equal tο 0. Therefοre, there is nο sοlutiοn fοr this equatiοn.

In general, when we simplify an equatiοn and end up with a cοntradictiοn like this, it means that the equatiοn has nο sοlutiοn.

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The missing expression that was covered by the drop of ink is simply 3[tex]x^{2}[/tex].

What is Algebraic expression ?

An algebraic expressiοn is a statement in mathematics that can cοntain variables, integers, οperatοrs (including additiοn, subtractiοn, multiplicatiοn, and divisiοn), as well as grοuping symbοls like brackets.

The given expression is:

-24[tex]x^{5}[/tex] - 16[tex]x^{3}[/tex] = -8[tex]x^{3}[/tex] (? + 2)

To find the missing expression, we need to isolate the unknown factor, denoted by the question mark (?). We can begin by factoring out the common term of -8x³ from the left side of the equation:

-8[tex]x^{3}[/tex](3[tex]x^{2}[/tex] + 2) = -8[tex]x^{3}[/tex](? + 2)

Now, we can divide both sides by -8[tex]x^{3}[/tex], which gives:

3[tex]x^{2}[/tex] + 2 = ? + 2

Subtracting 2 from both sides yields:

3[tex]x^{2}[/tex] = ?

Therefore, the missing expression that was covered by the drop of ink is simply 3[tex]x^{2}[/tex].

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Answer:

Step-by-step explanation:

Fractions represent a division problem where the numerator is divided by the denominator. For example, the fraction 3/4 represents the division of 3 by 4, which can be written as 3 ÷ 4. This is why it makes sense that fractions are about division.

Furthermore, fractions are used to represent parts of a whole or a group. When we divide a whole into equal parts, we are essentially dividing the whole into groups, with each group having the same size. For example, if we divide a pizza into 8 equal slices, each slice represents 1/8th of the pizza. We can also think of this as dividing the pizza into 8 equal groups, with each group having one slice.

Therefore, fractions are a natural way to represent division, as they allow us to express how many parts we have out of a whole or a group, and how big each part is relative to the whole or group.

If the test is normally distributed, then the probability of a score greater than 115 is (a) 1.62%.

In order to find probability of a score greater than 115 in a normally distributed test with a mean of 100 and standard deviation of 7,

First, We have to calculate z-score for 115, and

The z-score formula is ⇒ z = (x - μ)/σ,

where x = score of interest, μ = mean, and σ = standard-deviation.

In this case, we have x = 115, μ = 100, and σ = 7.

The z-score for 115 is ⇒ z = (115 - 100)/7 = 2.14

By using the normal table :

⇒ P(Z > 2.14) = 0.0162

Therefore, the required probability is 0.0162 or 1.62%, the correct option is (a) 1.62%.

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The given question is incomplete , the complete question is

Assume a normally distributed test has a mean of 100 and standard deviation of 7. What probability of a score greater than 115?

(a) 1.62%

(b) 48.38%

(c) 98.38%

(d) 51.62%

Answer:

2(-3±√120)

Step-by-step explanation:

quadratic formula

Answer:

a

Step-by-step explanation:

6 - 6=0 the 0-3 -3 total of 9 and 6 + 3 is equal to 9

Answer:

The ramp will rise 11.6 inches from the ground at its highest end.

11.6 in.

Step-by-step explanation:

In this example we can use the sine function to determine how high the ramp will rise from the ground.

The definition of the sine function is

[tex]\sf \sin x= \dfrac{opposite}{hypotenuse}[/tex]

[tex]\sf \sin x= \dfrac{O}{H}[/tex]

In this case we are looking to evaluate the length of the opposite side.

We can rearrange the equation to isolate [tex]\sf O[/tex].

Multiply both sides of the equation by [tex]\sf H[/tex].

[tex]\sf H \cdot \sin x= \dfrac{O}{H} \cdot H[/tex]

Cancel the common factor of [tex]\sf H[/tex] on the right side leaves us with

[tex]\sf H \cdot \sin x= \dfrac{O}{\diagup \!\!\!\! H} \cdot \diagup \!\!\!\! H[/tex]

[tex]\boxed{\sf O= H \cdot \sin x}[/tex]

Numerical Evaluation

In this example we are given

[tex]\sf x=20\\\sf H=34[/tex]

Substituting our given values into the equation yields

[tex]\sf O= 34\cdot \sin 20[/tex]

[tex]\sf O=11.628685[/tex]

Rounding to the nearest tenth

[tex]\sf O=11.6[/tex]

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Answer:

C

Step-by-step explanation:

Because 1.2+1.8 equal to 3.

Answer:

31

Step-by-step explanation:

The end behavior of the function is: as x → -∞, f(x) → -∞, and as x → ∞, f(x) → ∞.

The end behavior of the function f(x) = 3 * cube root of x can be determined by examining the function as x approaches negative and positive infinity.
1. As x → -∞, the cube root of a large negative number will also be negative, and 3 times a negative number is still negative.

Therefore, as x → -∞, f(x) → -∞.
2. As x → ∞, the cube root of a large positive number will be positive, and 3 times a positive number is still positive. Therefore, as x → ∞, f(x) → ∞.

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Answer:

The expressions 10³÷10⁷, 10¹²/10¹⁶, and 10⁻²/10² are all equivalent to 10⁻⁴.

Step-by-step explanation:

When dividing exponents with the same base you subtract the exponents.

For visuals, in the equation 10³÷10⁷ it would be 10³⁻⁷ which would be 10⁻⁴ since 3 minus 7 is negative 4.

It is the same thing for 10¹²/10¹⁶, it would be 10¹²⁻¹⁶ which is equal to 10⁻⁴.

The same method can be used for 10⁻²/10² (10⁻²⁻²).

Step-by-step explanation:

L X W X D = cubic feet volume

17 X 30 X .25 = 127. 5  ft^3

Cartridges come in different sizes and shapes, and the amount of liquid ink

They can hold varies depending on the model and manufacturer.
Of course, I am here to help.

However, to better assist you, I will need more information regarding your urgent situation.
Once I have a better understanding of your situation, I can provide you with a more tailored and effective response.

In the meantime, I recommend taking a few deep breaths and staying calm.

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Jenna should plan to have 8 teen items in the store to maintain the same ratio of adult to teen items.

When comparing quantities and figuring out how they relate to one another, ratio and proportion are two related mathematical ideas.

A ratio is a comparison between two values that is typically stated as a fraction. The ratio of red to blue marbles, for instance, would be 3/5 if there were 3 red and 5 blue marbles in a bag.

Contrarily, the proportion equation declares that two ratios are equivalent. For instance, if there are 3/5 red to 5/5 blue marbles in one bag and 6/10 red to blue marbles in the other, we have two bags of marbles.

From the given bar graph the ratio of adult to teen items is 18 : 6 or 3:1.

Thus for 24 items,

24:x = 3:1

Cross-multiplying, we get:

24 * 1 = 3 * x

x = 24/3

x = 8

Therefore, Jenna should plan to have 8 teen items in the store to maintain the same ratio of adult to teen items.

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The complete question is:

In response to the stated question, we may state that As a result, vector v has a magnitude of 6 and a direction of 160°.

A vector in mathematics is a mathematical object with both magnitude (or length) and direction. Vectors are frequently depicted as arrows, with the length of the arrow representing the magnitude and the direction of the arrow representing the vector's direction. A vector, for example, might represent an object's velocity, where the magnitude of the vector indicates the object's speed and the direction of the vector represents the direction of motion.  

Assuming that u has a magnitude of 3 and a direction of 160°.

Vector u can be represented by its components as follows:

3 cos(160°)i + 3 sin(160°)j = u

where I and j are unit vectors pointing in the x and y directions.

We now know that vector v = 2u, implying that the magnitude of vector v is:

|v| = |2u| = 2|u| = 2(3) = 6

As a result, the magnitude of vector v is 6.

We can use the fact that vector v is in the same direction as vector u but scaled by a factor of two to determine its direction. As a result, the vector v's direction is also 160°.

As a result, vector v has a magnitude of 6 and a direction of 160°.

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The ordered pair of the location of the school from the house is found to be (2,1).

It is said that the house is located at (0,0).

We can assume this point to be the origin so we can see that the house is located at the origin and the school is located 2 blocks east and one block south.

Now in the ordered pair the first term represents the X co-ordinate and the second term represents the Y co-ordinate.

As we are moving to the right we can say that we are moving towards the positive x axis and we are moving 1 block south, we can say that we are moving towards the positive y axis.

Han the corresponding ordered pair to the location of the school will be (2,1).

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Answer:

The improper/exact form=5/3 and the decimal form is 1.(6) (which is the 6 repeated)

Step-by-step explanation:

Technically, you can't simplify 1 2/3, but these are just two ways you could change it into.

Given:-

[tex] \: [/tex]

[tex] \: [/tex]

To find:-

[tex] \: [/tex]

By using formula:-

[tex] \pink\bigstar \underline{{ \boxed{ \sf{ \color{lightgreen}Distance = \sqrt{( x_2 - x_1 )² + ( y_2 - y_1 )²}}}}}[/tex]

[tex] \: [/tex]

Solution:-

[tex] \sf{D = \sqrt{( x_2 - x_1 )² + ( y_2 - y_1 )²} }[/tex]

[tex] \: [/tex]

where ,

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \sf \: D = \sqrt{( 9 - 0 )² + ( -6 - 7)²} [/tex]

[tex] \: [/tex]

[tex] \sf \: D = \sqrt{ ( 9 )² + ( - 13 )²}[/tex]

[tex] \: [/tex]

[tex] \sf \:D = \sqrt{ 81 + 169} [/tex]

[tex] \: [/tex]

[tex] \underline{ \underline{ \sf{ \color{hotpink} \: D = \sqrt{{250}\: }}}}[/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps:)

A. The two types of transformations that can be used to transform f(x) to g(x) are translation and reflection.

B. The value for k in the transformation is -6.

C. The equation for transforming is g (x) = f (x) - 6.

What is transformation?

Shapes on a coordinate plane can be translated, rotated, and reflected using transformations. You can rotate, translate, or reflect any line, point, or vector.

A. The two types of transformations that can be used to transform f(x) to g(x) are translation and reflection.

Translation means shifting the graph left, right, up or down.

Reflection means creating a mirror image over x - axis or y - axis.

B. Both the transformations will have the same k value.

The graph g (x) is the translation of f (x) towards left with 6 units.

So, the value of k is -6.

C. The equation for transformation is as follows:

⇒ g (x) = f (x) + k

⇒ g (x) = f (x) - 6

Hence, the required solutions have been obtained.

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A distribution that includes more vehicles sold at lower prices and may deviate from the initial distribution as a result of the inclusion of vehicles priced under $5,000.

A distribution in statistics is a function that identifies all potential values for a dataset together with their frequencies or probabilities. The normal distribution, the binomial distribution and the Poisson distribution are just a few examples of frequent distribution types. Data are described and analyzed using distributions, which may offer significant insights about a dataset's central tendency, variability, and form.

The distribution will be impacted in a number of ways if the salesperson decides to also offer automobiles that cost less than $5,000 and forecasts selling 200 of them over the next ten years. In particular, it will

Growth in vehicle sales: Over the next 10 years, more vehicles under $5,000 will be sold, increasing the overall vehicle sales.

Change the distribution of prices towards lower values: By selling more automobiles at lower prices, the introduction of more affordable vehicles will change the price distribution towards lower values.

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We predict that approximately 17,204 adults in Grand City have television as their main source of news.

To predict the number of adults in Grand City whose main source of news is television, we need to use the proportion of adults in the sample who selected television as their main source of news and apply it to the entire population of 46,000 adults.

The proportion of adults in the sample who selected television as their main source of news is:

135/361 = 0.374

To get the predicted number of adults in Grand City whose main source of news is television, we multiply this proportion by the total population:

0.374 x 46,000 = 17,204

Rounding this to the nearest whole number, we get:

17,204 adults

Therefore, we predict that approximately 17,204 adults in Grand City have television as their main source of news.

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The total number of revolutions per minute tire makes when the car is traveling at a speed of 90 mi/hr and the tire has a diameter of 22 inches is equal to approximately 1375.09.

Diameter of a car tire = 22 inches

Speed of a car = 90mi/hr

Let us first convert the speed from miles per hour to inches per minute,

Since the diameter of the tire is given in inches.

90 mi/hr

= 90 × 5280 ft/hr

= 475200 ft/hr

= 475200 × 12 in/hr

= 5,702,400 in/hr

= 95,040 in/min

Number of revolutions the tire makes per minute,

Distance the tire travels in one revolution.

The circumference of a circle is given by,

C = πd

where C is the circumference and d is the diameter.

So the distance the tire travels in one revolution is,

d = π(22 in)

  = 69.115 in

Now, the number of revolutions per minute  is ,

=distance traveled per minute / distance traveled in one revolution

⇒ revolutions per minute = 95,040 in/min / 69.115 in/rev

⇒revolutions per minute ≈ 1375.09 rev/min

Therefore, the tire makes approximately 1375.09 revolutions per minute with tire of diameter of 22 inches.

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This is because, in this scenario, the total cost per hour (-$432/hour) is the lowest compared to the costs of having two or three workers (-$864/hour and -$1,066/hour, respectively).

To determine the optimal maintenance crew size for servicing the machines at Three-Guys Vending Inc., we need to consider the average rate of breakdowns, downtime costs, and worker costs for each crew size.

The breakdowns are distributed in a Poisson manner, and the service rates are distributed exponentially.
1. Average breakdown rate: 3 machines/hour
2. Downtime cost: $230/hour per machine
3. Worker cost: $28/hour per worker.
Crew Size Scenarios:
A. One worker: services 5 machines/hour
B. Two workers: service 7 machines/hour together
C. Three workers: service 8 machines/hour together
First, we'll calculate the downtime and worker costs for each scenario:
A. One worker:
Downtime cost = (3 breakdowns/hour - 5 services/hour) x $230 = -$460/hour
Worker cost = 1 x $28 = $28/hour
Total cost = -$460 + $28 = -$432/hour
B. Two workers:
Downtime cost = (3 breakdowns/hour - 7 services/hour) x $230 = -$920/hour
Worker cost = 2 x $28 = $56/hour
Total cost = -$920 + $56 = -$864/hour.
C. Three workers:
Downtime cost = (3 breakdowns/hour - 8 services/hour) x $230 = -$1,150/hour
Worker cost = 3 x $28 = $84/hour
Total cost = -$1,150 + $84 = -$1,066/hour
From the calculations above, the optimal maintenance crew size for servicing the machines is one worker.

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Answer: a1 = 3 and an = an-1 + 3(-1)n

Step-by-step explanation:

* start off with the first term being a1 = 3

* add on 3 to get to 6 as the second term

* add on -3, to get back to 3 once more

*  add on the general term 3*(-1)^n (bc the pattern continues like, forever)

* term is found by a(n) = a(n-1) + 3*(-1)^n

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