Manipulate the triangle so angle A measures
approximately 92º.
Manipulate the triangle so angle B measures
approximately 51°.
Notice the straight line p.
What must the measurement of angle C be for p to
remain a straight line?
Angle C should measure approximately ?

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:

g=24

Step-by-step explanation:

g/4 -5 = 1

g/4 = 6

g = 24

Answer:

\(g=24\)

Step-by-step explanation:

When given the following equation,

\(\frac{g}{4}-5 = 1\)

Solve for the variable (g) using inverse operations,

\(\frac{g}{4}-5=1\)

Add (5) to both sides

\(\frac{g}{4}=6\)

Multiply both sides by (4)

\(g=24\)

Toshi's actual results were significantly different from his prediction. Specifically, his actual success rate of 80% was lower than his predicted success rate of 95%.

Probability is a way to gauge how likely or unlikely something is to happen. It is denoted by a number between 0 and 1, with 1 denoting a certain event and 0 denoting an impossibility.

Toshi's prediction was that he would perform the card trick successfully 95% of the time. This means that out of 100 card tricks, he expects to perform the trick successfully in 95 of them. We can represent this mathematically by:

P(success) = 0.95

This is the probability of success for one card trick.

Toshi actually performed the card trick 30 times and was successful in 24 of them. We can represent this as:

P(actual success) = 24/30 = 0.8

This is the proportion of successful card tricks that Toshi actually performed.

To compare Toshi's prediction with his actual results, we can use probability theory. The probability of getting exactly x successes in n trials when the probability of success is p is given by the binomial distribution formula:

P(x) = (n choose x) * pˣ * \((1-p)^(n-x)\)

In this case, we can use the formula to calculate the probability of getting exactly 24 successes in 30 trials if Toshi's prediction of 95% success rate is accurate. This is given by:

P(24 successes) = (30 choose 24) * 0.95²⁴ * 0.05⁶ ≈ 0.0045

This means that if Toshi's prediction is accurate, the probability of getting exactly 24 successes in 30 trials is very low (less than 0.5%).

Therefore, we can conclude that Toshi's actual results were significantly different from his prediction. Specifically, his actual success rate of 80% was lower than his predicted success rate of 95%.

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The value of x is equal to 15°

In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

By substituting the given parameters, we have the following:

3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.

3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.

23x + 15 = 360°.

23x = 360 - 15

23x = 345

x = 345/23

x = 15°.

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The introduction of international trade can impact the IS curve by altering the components of aggregate demand. An increase in international trade can resulting in higher output levels and potentially lower interest rates.

The IS curve represents the equilibrium in the goods market, where aggregate demand (AD) equals aggregate output (Y) in a closed economy.

However, the introduction of international trade changes the components of aggregate demand.

With increased international trade, exports and imports become significant components of aggregate demand. An increase in exports raises aggregate demand, leading to higher output levels.

This results in an upward shift of the IS curve, indicating a more expansionary monetary and fiscal policy is needed to maintain equilibrium.

The rise in international trade can also affect interest rates. Increased exports can boost domestic income, leading to higher savings. This increase in savings can potentially lower interest rates, as the supply of loanable funds in the economy rises.

Consequently, a rise in international trade can lower interest rates, further contributing to the expansionary effect on the IS curve.

Overall, the introduction of international trade alters the components of aggregate demand, leading to an expansionary effect on the IS curve, resulting in higher output levels and potentially lower interest rates.

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y=k/x is the equation represents relation between x and y and value of y is 16 when x is 21.

Two or more expressions with an Equal sign is called as Equation.

Given that y is inversely proportional to x.

When y is 7 and x is 9

y=k/x

k is the proportional constant and y=k/x is the equation connecting y and x.

We have to find the value of y when x is 21

9/7=21/y

Apply cross multiplication

9y=21×7

9y=147

Divide both sides by 9

y=147/9

y=16.3

Hence, y=k/x is the equation represents relation between x and y and value of y is 16 when x is 21.

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The ratios that are equivalent to the ratio 8 : 6 are 40 : 30 and 56 : 42

From the question, the ratio is given as

Ratio = 8 : 6

For ratios to be equivalent, each term of the ratio must be multiplied or divided by the same number

An equivalent of the ratio is

Ratio = 8n : 6n

Where n is a real number

Take for instance, we set n = 5

So, we have the following representation

Ratio = 8 * 5 : 6 * 5

Evaluate the products

So, we have the following representation

Ratio = 40 : 30

Take for instance, we set n = 7

So, we have

Ratio = 8 * 7 : 6 * 7

Evaluate the products

So, we have the following representation

Ratio = 56 : 42

So, we have the following representation

40 : 30 and 56 : 42

Hence, the equivalent ratios are 40 : 30 and 56 : 42

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Expression  \((12h^3 + 48h^2 - 54h)\) can be divided exactly by (6h) to give the expression  \(2h^2 + 8h - 9\) .

What is a expression ?

In mathematics, an expression is a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. An expression can represent a mathematical relationship, a quantity, or a value. Expressions can be simple or complex and can involve one or more variables.

To divide \((12h^3 + 48h^2 - 54h)\) by (6h), we can simplify the expression by factoring out the common factor of 6h from each term in the numerator.

\(6h(2h^2 + 8h - 9)\)

Therefore, the final answer is:

\((12h^3 + 48h^2 - 54h)\div (6h) = 2h^2 + 8h - 9\)

The result can also be written in factored form as \(2h^2 + 8h - 9\) .

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Answer:

90

Step-by-step explanation:

Hope this helps!

Answer:

9×10=90

Step-by-step explanation:

hope it helps ....

Answer:

  (a)  15 -18i

Step-by-step explanation:

You want the simplified form of the expression -2i(5- i) + (17- 8i).

For many purposes, the value i in a complex number can be treated in the same way a variable would be treated. When simplifying an expression involving i, any instances of i² can be replaced with the real value -1.

  -2i(5- i) + (17- 8i) = -10i +2i² +17 -8i

  = -2 +17 +(-10 -8)i

  = 15 -18i

__

Additional comment

Your scientific or graphing calculator can probably help you evaluate such expressions.

Answer:

1

Step-by-step explanation:

Answer:

63pi

Step-by-step explanation:

the formula for the volume of a cylinder is pi r^2 h

r=radius

h=height

3=r

7=h

pi((3)^2)7

63pi units^3

Hope that helps :)

Answer:

197.92

Step-by-step explanation:

To find the volume of a cylinder use V=πr2h.

Then fill in the equation with known information

V=π(3²)(7)

V= 197.92

If there are any units your answer will need them.

The correct option is A, the lower quartile (Q1) and it is 75.

We must comprehend the quartiles of the box plot in order to calculate the number below which 25% of the data lies.

A box plot's interquartile range (IQR), which contains the middle 50% of the data, is represented by the box.

The median, which splits the data into two equally sized half, is shown by the line inside the box.

Here, the box has a line at 79 and spans from 75 to 82.

Accordingly, the lower quartile (Q1) and the upper quartile (Q3) are both situated near the box's boundary, which is 75 and 82, respectively.

The line inside the box, which is 79, is the median (Q2).

The first quartile (Q1) or the 25th percentile must be identified in order to establish the number below which 25% of the data lies.

The first quartile in a box plot symbolizes the number below which 25% of the data is found.

Since Q1 is located at the lower boundary of the box, which is 75, 25% of the data lies below the score of 75.

Hence the correct option is A.

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Answer:

Its the first option.

Step-by-step explanation:

y = 3x - 9 on the boundary.

Any points on this line must satisfy this equation.

Try (0, -9) and (3,0):-

-9 = 3(0) - 9 = -9 so the first point is on the boundary.

(3, 0):

0 = 3(3)  - 9

= 9 -9 = 0    so this point is on the line also.

Answer: 72.97 Minutes

Step-by-step explanation: We have two cars, A and B, traveling along a straight road. Car A is moving at a constant speed of 77.0 km/h, while car B is moving at a constant speed of 114 km/h. At the starting point (t=0), car B is 45.0 km behind car A.

To figure out how long it takes for car B to catch up and overtake car A, we need to consider their relative speeds. The relative speed is the difference between the speed of car B and the speed of car A.

Relative speed = Speed of car B - Speed of car A

Relative speed = 114 km/h - 77.0 km/h

Relative speed = 37.0 km/h

So, car B is moving 37.0 km/h faster than car A. Now, we need to determine the time it takes for car B to cover the initial distance between them, which is 45.0 km.

To calculate time, we use the formula: Time = Distance / Speed. In this case, the distance is 45.0 km, and the speed is the relative speed of 37.0 km/h.

Time = 45.0 km / 37.0 km/h ≈ 1.2162 hours

Now, let's convert the time to minutes by multiplying it by 60 (since there are 60 minutes in an hour).

Time = 1.2162 hours * 60 minutes/hour ≈ 72.97 minutes

Therefore, it takes approximately 1.2162 hours or 72.97 minutes for car B to catch up and overtake car A.

Hope this helps!

Answer: Part A - 113°

Step-by-step explanation:

A. 6x-5 = 5x+7 -> x = 12

6x-5 -> 6(12)-5 = 72-5 = 67

180-67 = 113

Answer:

with what life

Step-by-step explanation:

The simplified expression of (5.1)(5.1^2)^4 is (5.1)^9

The expression is given as:

(5.1)(5.12)4

Rewrite the expression properly as follows:

(5.1)(5.1^2)^4

Rewrite the expression properly as follows:

(5.1)(5.1^2)^4 = (5.1) * (5.1^2)^4

Apply the power law of indices

(5.1)(5.1^2)^4 = (5.1) * (5.1^8)

Apply the power law of indices

(5.1)(5.1^2)^4 = (5.1)^(1 + 8)

Evaluate the sum

(5.1)(5.1^2)^4 = (5.1)^9

Hence, the simplified expression of (5.1)(5.1^2)^4 is (5.1)^9

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0.2x + 2.7x - 8.1 = 6.9 + 1.1x

Combine like terms on left side:

0.2x + 2.7x = 2.9x

Now you have:

2.9x -8.1 = 6.9 + 1.1x

Subtract 1.1x from both sides:

1.8x - 8.1 = 6.9

Add 8.1 to both sides:

1.8x = 15

Divide both sides by 1.8:

X = 8.3333 ( round as needed) or as a fraction = 8 and 1/3

Answer:

8.3recurring

Explanation:

0.2x+2.7x =2.9x

rewrite the questions

2.9x-8.1=6.9+1.1x

like terms together. Therefore:

2.9x-1.1x = 1.8x

8.1 will go to the other side of the equal sign. Therefore:

8.1+6.9 = 15

Therefore: 1.8x = 15

x =15/1.8 which is equal to 8.3recurring

Answer:

\(\sqrt{100}+\sqrt{36}=16\)

-------------------------

Solution:-

\(\sqrt{100}+\sqrt{36}\)

\(\sqrt{100} =10}\)

\(\sqrt{36} =6\)

\(=10+6\)

\(=16\)

✩✩✩✩✩✩✩

hope it helps...

have a great day!!

Answer:

hope it is helpful to you

SOLUTION

To find the perimetr of the triangle IJK, we need to obtain the value of x.

The triangles above are similar triangles, using the ratioof similar triangle, we have

Substituting the values, we have

Then take cross product of the equation above, we have

Then, the perimeter of the triangle is sum of all the sides

Therefore

The perimeter of triangle IJK is 180.4 unit

Answer: 112.5

Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.

simplifyyyyyyyyyyyyyyyyyy

Answer:

8, 1:3

Step-by-step explanation:

There are 8 shapes in each row and if you take 12:36 and divide by 12, you can get 1:3, which is its simplest form.

The mean absolute deviation for the Jumping Jackrabbits was of 3.8, which was lower than the 6.8 for the Leaping Lizards, hence they had more consistent scores.

For the Jumping Jackrabbits and the Leaping Lizards, the mean and the MAD are given as follows:

M = (70 + 65 + 72 + 80 + 73)/5 = 72

MAD = (|70 - 72| + |65 - 72| + |72 - 72| + |80 - 72| + |73 - 72|)/5 = 3.6.

M = (61 + 47 + 70 + 63 + 54)/5 = 59

MAD = (|61 - 59| + |47 - 59| + |70 - 59| + |63 - 59| + |54 - 59|)/5 = 6.8.

The mean absolute deviation for the Jumping Jackrabbits was of 3.8, which was lower than the 6.8 for the Leaping Lizards, hence they had more consistent scores.

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The value of c that satisfies the Mean Value Theorem for the function f(x) = 2 - 3x² on the interval [-6, 5] is c = -37/66.

In mathematics, slope refers to the steepness or incline of a line on a graph.

(A) To find the average or mean slope of the function on the interval [-6, 5], we need to use the formula:

average slope = (f(5) - f(-6)) / (5 - (-6))

where f(x) = 2 - 3x². We can evaluate f(5) and f(-6) by substituting these values into the function:

f(5) = 2 - 3(5)² = -73

f(-6) = 2 - 3(-6)² = -110

Substituting these values into the formula, we get:

average slope = (-73 - (-110)) / (5 - (-6)) = 37/11

Therefore, the average slope of the function on the interval [-6, 5] is 37/11.

(B) By the Mean Value Theorem, we know that there exists a c in the open interval (-6, 5) such that f'(c) is equal to the mean slope calculated in part (A).

To find c, we need to first find f'(x), which is the derivative of f(x) with respect to x:

f'(x) = d/dx (2 - 3x²) = -6x

Now we need to solve the equation f'(c) = 37/11 for c:

-6c = 37/11

c = -(37/11) * (1/6) = -37/66

Therefore, the value of c that satisfies the Mean Value Theorem for the function f(x) = 2 - 3x² on the interval [-6, 5] is c = -37/66.

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