Solve for the unknown 7/G = 35/50

the probability that a subject would guess more than 20 correct in a series of 36 trials

p(X > 20.5)

= p(z > 0.83)

= 0.2033

Probability is a branch of mathematics that quantifies the likelihood of an event occurring or the likelihood of a statement being true. Probability is a number between 0 and 1, with 0 generally indicating impossibility and 1 indicating certainty. that an event will occur.

A simple example is tossing a fair (unbiased) coin. Since the coin is fair, the two outcomes (heads and tails) are equally likely. The probability of heads is the same as the probability of tails. Since no other outcome is possible, the probability of heads or tails is 1/2 (also written as 0.5 or 50%).

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To find the terminal point P(x, y) on the unit circle determined by the value of t, we can use the trigonometric functions sine and cosine.

In this case, t = 6π/11.

The x-coordinate of the point P can be found using the cosine function:

x = cos(t) = cos(6π/11)

The y-coordinate of the point P can be found using the sine function:

y = sin(t) = sin(6π/11)

To calculate the values, we can use a calculator or reference table for the sine and cosine of 6π/11.

The terminal point P(x, y) on the unit circle determined by t = 6π/11 is given by:

P(x, y) ≈ (0.307, 0.952)

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Answer:

see below

Step-by-step explanation:

Assuming the comma means and

a) P(A , E) = P(A) * P(E) = .1 * .5 = .05

b) P( A, L, E) =  P(A) * P(L) *P(E) = .1 *.4* .5 = .002

C This means that it snows in Abbostford, Lehtbridge and Estevan today  is .002 or .2%

Answer:

50.1

Step-by-step explanation:

let the height = h

so because that angle is 62 so it's supplemental angle in left triangle is 28°

in any triangle, the tangent of an angle is opposite/adjacent

so height/28 = tan28° =0.53

so height = 14.8

in any triangle, the sine of an angle is opposite/hypotenuse

so height / x = sin 38°

so x = 14.8 / sin 38° = 14.8/0.296 =50.1

Answer:

R and Z

Step-by-step explanation:

A point that "touches" the circle once.

Answer:

x = 4.75

Step-by-step explanation:

Yes, it is true that an alternative hypothesis states that the direction one expects to see in the difference between treatments while the null hypothesis does not.

Null and alternative hypothesis are the two statistical hypotheses and research hypothesis is another name for the alternative hypothesis. Whenever there is difference in the outcomes of interest then it is an alternative hypothesis. And the null hypothesis is the statement of equality. The null hypothesis and alternative hypothesis both are complementary to each other.

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Number 3 is the answer

The distance by which the cage will drop is; 25.12m.

According to the task content, the diameter of the winch drum is; 6m.

On this note, it follows that the radius of the drum is; 6/2 = 3m.

The drop in the cage height is therefore;

C = 2 πr = 2 × 3.14 × 4

C = 25.12m.

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The similar photo should be 4.5 inches wide.

Direct variation of a quantity {y} with respect quantity {x} means that the value of {y} increases as the the value of {x} increases. Mathematically -

y = Kx

K = y/x

where -

{K} is scale factor. It also tells by how many times is {y} greater than {x}.

Given is that Gwen scans a photo that is 4 inches wide by 6 inches long into her computer. Now, she scales the length down to 3 inches.

We can write -

y₁/x₁ = y₂/x₂

6/4 = 3/x₂

x₂ = 6 x 3/4

x₂ = 6 x 0.75

x₂ = 4.5

Therefore, the similar photo should be 4.5 inches wide.

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Peter watches 805 American movies and 460 Chinese movies.

Let x represent the number of American movies and y represent the number of Chinese movies and let z represent the total number of movies.

Since he watches 345 more American movies than Chinese movies. Hence:

x = y + 345

x - y = 345    (1)

Also:

x + y = z

x + y - z = 0  (2)

The ratio of Chinese movies to American movies is 4:7. Hence:

(4/11)z = y

-y + (4/11)z = 0   (3)

Solving equations 1, 2, and 3, simultaneously gives:

x = 805, y = 460 and z = 1265

Hence, Peter watches 805 American movies and 460 Chinese movies.

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Answer: 5

Step-by-step explanation:

Answer:

-54y+27y²

Step-by-step explanation:

-9y(6-3y)

-9y x 6=-54y

-9y x -3y=27y²

-54y+27y² or

27y²+ -54y

Solution :

Given that the expression is :

\($10^3 \times 0.006$\)

This can be written as,

\($\Rightarrow 10^3 \times \frac{6}{1000}$\)

\($\Rightarrow 10^3 \times \frac{6}{10^3}$\)

\($\Rightarrow 10^0 \times 6$\)

a). Therefore the exponent in the power of 10

     = 0

b). Factors of 10 in \($10^3$\)

    = 10 x 10 x 10

    = 1000

    = \($10^3$\)

   So there are 3 factors of 10 in \($10^3$\)

c). If we compare the exponent of power of 10 in 1000 and factors of 10 in 1000, then both of them will be same.

  But in part a), we are finding exponent in the power of 10 in the expression  which is equal to 0. And in part b), we are finding the factor of 10 in 1000, which is equal to 3, as 10 x 10 x 10 = 1000.

d). The value of the expression \($10^3 \times 0.006$\) is 6.

Answer:

5

Step-by-step explanation:

on day 1 you had 20 pieces and each day you lose 2 pieces. so that means your equation is y=-2x+20. So x = number of days, and y = pieces of candy. Plug in 10 for y, minus 20 to both sides, divide by -2 to each side. Then your answer is 5.

The coordinate of the triangle after the dilation is (3, 3), (6, 3), (3, 6)

From the question, we have the following parameters that can be used in our computation:

(5, 5), (10,5), (5, 10)

Scale factor = 3/5

The coordinate of the triangle after the dilation is calculated as

Image' = triangle * Scale factor

Substitute the known values in the above equation, so, we have the following representation

(5, 5), (10,5), (5, 10) * 3/5

Evaluate

(3, 3), (6, 3), (3, 6)

Hence, the image is (3, 3), (6, 3), (3, 6) and it is attached

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The equations N1/dt = r1N1[(K1 - N1 - ON2)/K1] and ON2/dt = r2N2[(K2 - N2 - BN1)/K2] describe models for population dynamics. These models are used to understand how populations of organisms change over time, based on factors like birth rates, death rates, and available resources.

In these equations, N1 and N2 represent the population sizes of two interacting species. The variables r1 and r2 are the intrinsic growth rates of these species, or the rates at which they reproduce in the absence of limiting factors. K1 and K2 represent the carrying capacities of the environment for each species, or the maximum population sizes that can be sustained by available resources.
The terms ON2 and BN1 represent the effects of interspecific interactions on population growth. ON2 refers to the negative impact of species 2 on the growth rate of species 1, and BN1 refers to the negative impact of species 1 on the growth rate of species 2. These interactions can take many forms, such as competition for resources or predation.
By manipulating these equations, scientists can make predictions about how populations will change over time, and test these predictions against real-world data. These models are particularly useful for understanding how species interact in complex ecosystems, and how human activities like habitat destruction and climate change are affecting these ecosystems.

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Step-by-step explanation:

the radius of the circular base is 7/2=3.5 cm

the surface of the base is πr^2=π*(3.5)^2=38.465

volume of the cylinder is surface of the base*high

38.465*30=1153.95

the cuboid volume=8^2*x=64x

64x=1153.95

x=1153.95/65=18.03 cm=18 cm

Therefore, The expression for the total number of baseball cards Kala has now is 62 + b, where b represents the additional cards she got today.

The total number of baseball cards Kala has now, we can start with the number she had yesterday, which is 62. We know she got b more cards today, so we can add that to the initial amount: 62 + b. This expression represents the total number of baseball cards Kala has now. The value of b will determine how many more cards she has today compared to yesterday.
To represent Kala's total number of baseball cards now, we need to use the information given about her previous card count (62) and the new cards she acquired today (b). Since she gained more cards, we will add the two amounts together.
Total baseball cards = 62 + b
Kala has (62 + b) baseball cards now.

Therefore, The expression for the total number of baseball cards Kala has now is 62 + b, where b represents the additional cards she got today.

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Answer:

Domain; -5,9

Range; -3,-1

Answer:

C 0.0361

Step-by-step explanation:

The probability that the color of the first car is silver and the color of the second car is also siver is 0.0361.

Given that,

Based on the above information, the calculation is as follows:

\(= 0.19\times 0.19\)

= 0.0361

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The probability of randomly selecting a nickel and then a dime, given that there are four nickels and five dimes in the pocket, is 4/9 or approximately 0.444.

To calculate the probability, we consider the total number of possible outcomes and the favorable outcomes. There are a total of 9 coins in the pocket (4 nickels + 5 dimes). The probability of selecting a nickel first is 4/9 because there are four nickels out of the nine coins. After placing the first nickel on the counter, there are now eight coins left in the pocket, including four nickels and four dimes. The probability of selecting a dime second is 4/8 or 1/2 because there are four dimes out of the remaining eight coins.

To find the combined probability, we multiply the probabilities of the individual events. Thus, the probability of selecting a nickel and then a dime is (4/9) * (1/2) = 4/18 = 2/9. Therefore, the answer is approximately 0.222, which is not one of the provided answer choices.

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Answer:

y = 2x − 5

Step-by-step explanation:

i took the quiz

The eye color of people on commercial aircraft flights is not a random variable.

What is random variable?

Random variables are variables that can take on different values based on the outcome of a random event or experiment.

However, eye color is a characteristic of individuals and does not vary randomly within a specific context, such as being on a commercial aircraft flight. Eye color is determined by genetic factors and does not change during a flight or as a result of being on a flight.

Eye color is a categorical variable that represents the color of an individual's eyes, such as blue, green, brown, or hazel. While it is not a random variable in the context of commercial aircraft flights, it can still be observed and recorded as a characteristic of the passengers on the flight.

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The solution for the system of equations shown in this graph is (-2, 1)

In this question, we need to determine the solution for the system of equations shown in this graph.

From given graph of system of equations we can observe that the  system of equations represent lines intersected at point.

This means that the system of equations has a solution.

The point of intersection of given line is (-2, 1)

Therefore, the solution for the system of equations shown in this graph is (-2, 1)

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A function h such that f(x) = (h ◦ g3)(x) is h(x) = 1 - 2cos^2(x) - sin(x).

We want to find a function h such that f(x) = (h ◦ g3)(x), where g3(x) = 3x.

First, we need to express f(x) in terms of g3(x):

g3(x) = 3x

=> sin(g3(x)) = sin(3x)

=> sin(g3(x)) = 3sin(x) - 4sin^3(x)

Using this expression, we can rewrite f(x) as:

f(x) = 2sin^2(x) - sin(x) - 1

=> f(x) = 2(1-cos^2(x)) - sin(x) - 1

=> f(x) = 2 - 2cos^2(x) - sin(x) - 1

=> f(x) = 1 - 2cos^2(x) - sin(x)

Now we can substitute g3(x) into f(x) to obtain:

f(g3(x)) = 1 - 2cos^2(3x) - sin(3x)

Let h(x) = 1 - 2cos^2(x) - sin(x), then:

f(g3(x)) = h(3x)

Therefore, the function h(x) such that f(x) = (h ◦ g3)(x) is                            h(x) = 1 - 2cos^2(x) - sin(x).

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Interval notation for increasing and decreasing functions is written as (x, y) where x < y for increasing functions, and (x, y) where x > y for decreasing functions.

To write interval notation for increasing and decreasing functions, you need to analyze the behavior of the function's graph.

For an increasing function, as you move from left to right along the x-axis, the y-values of the function's graph increase. In interval notation, you would write this as:

(x, y) where x < y

For example, if the function is increasing from -3 to 5, the interval notation would be (-3, 5).

On the other hand, for a decreasing function, as you move from left to right along the x-axis, the y-values of the function's graph decrease. In interval notation, you would write this as:

(x, y) where x > y

For example, if the function is decreasing from 7 to -2, the interval notation would be (7, -2).

It's important to note that for both increasing and decreasing functions, the parentheses indicate that the endpoints are not included in the interval.

Remember, when using interval notation, always write the x-value first and then the y-value. This notation helps us understand the direction and range of a function.

In conclusion, interval notation for increasing and decreasing functions is written as (x, y) where x < y for increasing functions, and (x, y) where x > y for decreasing functions.

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