four distinct fair coins are tossed. if it is known that at least one of the coins shows a head, what is the probability that all coins show heads?

A reasonable prediction for the number of times a Red or Yellow Marble Draws = (7/20) x 180 = 126.

The total number of marbles in the bag is 20 (5 red, 6 blue, 3 green, 4 black, and 2 yellow). Therefore, the probability of drawing a red or yellow marble is 7/20. Applying this probability to the 180 times a marble is drawn and replaced, we can calculate that the number of times a red or yellow marble is likely to be drawn is 126 (7/20 x 180). This can be expressed as a formula as follows: Red or Yellow Marble Draws = (Number of Red and Yellow Marbles / Total Number of Marbles) x Number of Draws. In this case, Red or Yellow Marble Draws = (7/20) x 180 = 126.

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Answer:

Step-by-step explanation:

You need to know trigonometry for this.\

You can't solve this without a scientific calculator.

TOA means Tan x = Opposite/Adjacent or in this case, 5.1/4.2

tan x = 5.1/4.2

arctant(tanx) = arctan(5.1/4.2)

x = arctan(5.1/4.2)

≈ 50.5°

arctan x is also known as tan inverse x

According to the concept of probability, the sample space for the experiment is explained below.

The term probability in math is called as the occurrence of a random event and the sample space is defined as a collection or a set of possible outcomes of a random experiment.

Here we have know that the same space of this experiment is the possible outcomes of selecting two out of the three breakfast.  

Here let us consider that the sample space is B

And the the sample space is written as.

=> {(cereal and egg), (cereal and fruit), (fruit and egg), (fruit and cereal), (egg and fruit), (egg and cereal)}

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The function that represents the total cost for the number of gigabytes is; C(x) = 50x

Some of the steps to writing a system of linear equations from word problems are;

1) Understand the problem like the words used in stating the problem and what exactly you are trying to find.

2) Translate the problem to an equation by assigning a variable (or variables) to represent the unknown.

3) Carry out the plan and solve the problem.

We  are told that her budget is $50 a month. Therefore this is like the rate for each gigabyte and if the number of gigabytes is denoted as x, then the function of the total cost is;

C(x) = 50x

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The likelihood that a student chosen at random has any siblings is 0.777. This is determined by deducting from 1 the probability of having no siblings (0.223).

1. Get the probability of 0 siblings : 0.223

2. Subtract the probability of 0 siblings from 1 :

1 - 0.223

= 0.777

3. Round the result to 3 decimal places :

0.777

The probability of a student not having 0 siblings can be calculated by subtracting the probability of having 0 siblings from 1. The probability model created from the survey results is a 2-column table with 5 rows. Column 1 is labeled number of siblings with entries 0, 1, 2, 3, 4 or more. Column 2 is labeled probability with entries

0.223, 0.532, 0.121, 0.085, 0.039.

The probability of having 0 siblings is 0.223. To calculate the probability of not having 0 siblings, we subtract 0.223 from 1. This gives us 0.777, which is the probability of not having 0 siblings. This result should be rounded to 3 decimal places, giving us 0.777 as the final answer.

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The number of ways that can she rank 9 applications should be 126.

What is the definition of combination in math?

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order.

Calculation of the number of ways:

Since A manager receives 9 applications for a specific position. She wants to narrow it down to 4.

So here we do apply the permutation here:

9*8*7*6/ 4*3*2

=126

Hence, The number of ways that can she rank 4 applications should be 126

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Answer:

B

Step-by-step explanation:

-3x + 2y =  ?  You forgot to put what this equals, but it does not matter.

3x + 6y = 9

       9y = ?

When we add -3x and 3x the x's drop out.

An answer is- More information is needed before t can be found.  So, option(D) is the correct answer.

Here initial rotation speed is given, the final rotation speed is given, and the asking for time( in a sec) is.

If we use,

A) θ=θ0+ω0t+(1/2)αt2

For this equation, we don't have any details about the value of angular displacement and angular acceleration, so it is not useful.

B) We use,

ω=ω0+αt

For this equation, we don't have any details about angular acceleration, so it is not useful.

C) We know that,

ω2=ω02+2α(θ−θ0)

In this equation, time is not included, hence it is not useful.

D) So, more information is needed.

Thus, option (D) is the correct answer.

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The complete question is:

Suppose you are asked to find the amount of time t, in seconds, it takes for the turntable to reach its final rotational speed. Which of the following equations could you use to directly solve for the numerical value of t?

A) θ=θ0+ω0t+(1/2)αt2

B) ω=ω0+αt

C) ω2=ω02+2α(θ−θ0)

D) More information is needed before t can be found.

A regular octagon is formed by cutting an isosceles right triangle from each of the corners of a square. To find the length of the side of the octagon, we can use the Pythagorean theorem to calculate the length of the hypotenuse of the isosceles right triangle.

In an isosceles right triangle, the two legs have the same length and the hypotenuse is the side opposite the right angle. Since the square has sides of length 2000, half of the side of the square is the leg of the isosceles right triangle.

So the leg of the isosceles right triangle is 2000/2 = 1000.

Applying the Pythagorean theorem to find the hypotenuse of the isosceles right triangle:

c^2 = a^2 + b^2

c = sqrt(a^2 + b^2)

c = sqrt(1000^2 + 1000^2)

c = sqrt(1000000)

c = 1000*sqrt(2)

So the length of each side of the octagon is 1000sqrt(2)

According to the given information the line integral is [tex]=\frac{8}{15}(1+125.\sqrt{10})[/tex].

Line integrals include several integrals across a curve, but definite integrals only entail a single integral over a specified interval. This is the primary distinction between the two types of integrals.

[tex]\int_C\hairsp xyds,C:x=t^2,y=2t,0\le t\le3\\x^\prime=2t\\y^\prime=2\\ds=\sqrt{\left(x^\prime\right)^2+\left(y^\prime\right)^2}\\\sqrt{{4\left(t\right)}^2+4}\\\int C\ xy\ ds\ =\int_0^3\hairspt^2\cdot2t\cdot2\cdot\sqrt{1+t^2}\mathrm{\ }dt\\t=\ \ tan\ \theta\\dt=(1+{tan}^2\theta)d\theta=({Sec}^2\theta)d\theta\ \\{=\int}_0^3\hairsp4t^3\sqrt{1+t^2}\mathrm{\ }dt\\=\frac{8}{15}(1+125.\sqrt{10})[/tex]

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Answer: The slope of the line that passes through the points (-8, -6) and (-8, 4) is undefined. This is because the line is a vertical line and the difference in y-coordinates is 0, making the denominator of the slope equation 0. The slope of a vertical line is undefined.

Step-by-step explanation:

(ii) 2.5 cm, 3.5 cm, 6.0 cm and (iii) 2.5 cm, 4.2 cm, 8 cm cannot be the sides of a triangle.

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

(i) 4.5 cm, 3.5 cm, 6.4 cm

4.5 + 3.5 = 8 > 6.4

4.5 + 6.4 =10.9 > 3.5

3.5 + 6.4 = 9.9 > 4.5

so these lengths can form a triangle.

(ii) 2.5 cm, 3.5 cm, 6.0 cm

2.5 + 3.5 = 6.0 = 6.0

2.5 + 6.0 = 8.5 > 3.5

3.5 + 6.0 = 9.5 > 2.5

so these lengths cannot form a triangle.

(iii) 2.5 cm, 4.2 cm, 8 cm:

2.5 + 4.2 = 6.7 < 8

2.5 + 8 = 10.5 > 4.2

4.2 + 8 = 12.2 > 2.5

so these lengths cannot form a triangle.

Therefore, (ii) and (iii) cannot be the sides of a triangle.

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Answer:

Step-by-step explanation:

Answer:

20° , 40° , 120°

Step-by-step explanation:

sum the parts of the ratio, 1 + 2 + 6 = 9 parts

divide the sum of the angles in a Δ , 180° by 9 to find the value of one part of the ratio.

180° ÷ 9 = 20° ← value of 1 part of the ratio, then

2 parts = 2 × 20° = 40°

6 parts = 6 × 20° = 120°

the 3 angles are 20° , 40° and 120°

No, 22/7 is not a repeating decimal. The fraction 22/7 is an estimate for pi, but since pi is an irrational number, it does not repeat and 22/7 is not an exact representation of pi.

1. The ratio of the distance around a circle to the distance across a circle through its center is represented by the number pi.

2. The number pi is a decimal that does not repeat.

3. The fraction 22/7 is sometimes used as an estimate for pi.

4. 22/7 is not a repeating decimal because pi is an irrational number, meaning it does not repeat and 22/7 is not an exact representation of pi.

No, 22/7 is not a repeating decimal. The fraction 22/7 is an estimate for pi, but since pi is an irrational number, it does not repeat and 22/7 is not an exact representation of pi.

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Answer:

if m stands for number of tickets

then amount would be

12+2.75*m

14.75m

Step-by-step explanation:

we are looking for a point to the right of (4,7), the point P is (15/2, x+3) = (15/2, 21/2).

What is polynomial ?

A polynomial is a mathematical expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

Let P = (x, y) be a point on L that is four times as far from (2, 5) as it is from (4, 7). Since L contains P, we know that y = x + 3. We also know that the distance from P to (2, 5) is 4 times the distance from P to (4, 7). Using the distance formula, we get:

(x - 2)^2 + (y - 5)^2 = 4[(x - 4)^2 + (y - 7)^2]

Plug in y = x+3 and simplify the equation as ,

(x-2)^2 + (x+3-5)^2 = 4(x-4)^2 + 4(x+3-7)^2

x^2 - 4x + 4 + x^2 - 6x + 9 = 4x^2 - 32x + 48 + 4x^2 - 24x + 36

2x^2 - 30x + 97 = 0

Solving for x, we have x = 15/2 or x = -3/1

Since we are looking for a point to the right of (4,7), the point P is (15/2, x+3) = (15/2, 21/2).

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Answer:A system of linear equations has no solution when the graphs are parallel. Infinite solutions. A system of linear equations has infinite solutions when the graphs are the exact same line.

Step-by-step explanation:

Correct option is A, the cost of the meal plan is non-linear.

The simplest approach to tell if a function is linear is to look at its graph. A linear function produces a straight line on a graph. A nonlinear function is not straight and is curved in some way. A linear function results in a straight line on a graph. As a result, non-linear functions can be of any kind. Although determining a function's linearity from its input/output table or equation is the simplest method, it is also possible to do so.

Based on the given conditions, formulate:

The definition of linear function

8-10 meals = (135-123) = (10-8) =10/2=5

10-12 meals: (155-135) = (12-10)

=20/2

= 10

12-21 meals: (220-155) = (21-12)

= 65/9

=7 2/9

5 < 7 2/9 < 10

So the cost of the meal plan is non-linear.

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Complete question -

Answer:

A) ( -10, -7)

Step-by-step explanation:

x = -10 is a vertical line going through x = -10

No matter what y is, x will be -10

Plug -10 into the first equation to find the y value

y = 2/5(-10) - 3

y = -4 - 3

y = -7

Answer: well you need to divid

Step-by-step explanation: well by dividing you get a answer so like you compare if the answer you got is for all of them and if it is not you say it is not proportional

A)  The 95% confidence interval is:

     0.58 ± 0.062

B) At the 0.01 probability value, there is neither substantial evidence of a home-field  advantage in professional football (they won and over half of the games).

Now, According to the question:

A) Confidence interval is written as

Sample proportion ± margin of error

Margin of error = z × [tex]\frac{\sqrt{pq} }{n}[/tex]

Where:

z = The z score corresponds to the amount of confidence.

p = sample proportion.

q = probability of failure

q = 1 - p

p = x/n

Where

n = the number of samples

x = the number of success

From the information given,

n = 240

x = 138

p = 138/240 = 0.58

q = 1 - 0.58 = 0.42

To determine the z score,  The confidence level from 100% to get α

α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

Thus,

1 - 0.025 = 0.975

The z -score associated with the area just on z table approximately 1.96. Therefore, the z score with a 95% confidence level is 1.96.

As a result, the 95% confidence interval becomes

0.58 ± 1.96√(0.58)(0.42)/240

Confidence interval is

0.58 ± 0.062

B) Earning more than half of the games equates to winning 120 games or more.

p = 120/240 = 0.5

The hypothesis test will be

For the null hypothesis,

P ≥ 0.5

For the alternative hypothesis,

P < 0.5

Probability of success, p = 0.5

q = probability of failure = 1 - p

q = 1 - 0.5 = 0.5

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 138

n = number of samples = 240

P = 138/240 = 0.58

We need to find the values of  the test statistic which will be the z score

z = (P - p)/√pq/n

z = (0.58 - 0.5)/√(0.5 × 0.5)/240 = 2.48

Remember that this is a two-tailed test. We would use the normal distribution table to calculate the probability potential of the property to the right of both the z score.

P value will be = 1 - 0.9934 = 0.0066

Since alpha, 0.01 > the p value, 0.0066, then we would reject the null hypothesis.

The given question is incomplete, The complete question is this:

__"During the 2000 season, the home team won 138 out of 240 regular season National Football League games. (15 points) a) Construct a 95% confidence interval for the winning proportion of the home team during this season. b) At the 0.01 significance level, is there strong evidence of a home field advantage (they win more than half of the games) in professional football? State hypotheses, calculate the test statistic and p-value, and make a conclusion in context"__

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c. The mode is the best measure to describe the typical or central value in this data set.

The data set consists of qualitative values, which means they are not in numerical form and cannot be used to calculate the mean or median. The mode is the best measure to describe the typical or central value because it identifies the value that occurs most often in the data set.

In this case, the value that occurs most often is ‘blonde’, which would be the mode. The mean and median cannot be used because they require quantitative data, such as numerical values, to be calculated.

Additionally, the data set does not have outliers, which would cause the mean to be skewed. By using the mode, we can accurately describe the typical or central value of this data set.

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Answer:

(a) Refer below for the Probability tree diagram

(b) [tex]\frac{7}{33}[/tex]

Step-by-step explanation:

(a) Probability tree diagram:

First bag:                                         Second bag

                                                       Red: [tex]\frac{7}{7 + 4}[/tex] = [tex]\frac{7}{11}[/tex]

Red: [tex]\frac{5}{12}[/tex]                                

                                                      Green:[tex]\frac{4}{7 + 4}[/tex] = [tex]\frac{4}{11}[/tex]

                                                        Red: [tex]\frac{7}{11}[/tex]

Green [tex]\frac{7}{12}[/tex]      

                                                        Green: [tex]\frac{4}{11}[/tex]      

(b) Probability that Hannah takes two green sweets:

Green sweet from first bag AND green sweet from second bag

= [tex](\frac{7}{12}).(\frac{4}{11} )[/tex]

= [tex](\frac{28}{132})[/tex]

Divide the numerator and denominator by the highest common factor (i.e  4)

= [tex]\frac{7}{33}[/tex]                                                    

The correct value of r is 2.

What is the power inverse variation?

Inverse variation is the relationship between two variables, such that if the value of one variable increases then the value of the other variable decreases.

The equation for a power inverse variation is y = kx^r,

where k is a constant, x is the independent variable, y is the dependent variable, and r is the power.

We have given the set of ordered pairs,

we can find the value of r by substituting in the known values of x and y and solving for r.

(1/2,20) => 20 = 5 * (1/2)^r => r = log(20)/log(1/2) = -2

So the answer is:

r = 2

Hence, the correct value of r is 2.

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Answer:

I don't know ooo y the same time that I can come get you if you want to

Step-by-step explanation:

your teacher gave you even the formula. so, what is still not clear ?

in regular words, the slope of a line is the ratio

y coordinate difference / x coordinate difference

when going from one point on the line to another.

so, we have here (-2, 1) and (3, 2).

x changes by +5 (from -2 to 3).

y changes by +1 (from 1 to 2).

so, the slope is +1/+5 = 1/5

Step-by-Step Explanation:

We know,

[tex] \cos(angle) = \frac{base}{hypotenuse} [/tex]

Here, angle = 60°, base = 5, hypotenuse = x

Therefore,

[tex] \cos(60) = \frac{5}{x} \\ = > \frac{1}{2} = \frac{5}{x} \\ = > x = 5 \times 2 \\ = > x = 10[/tex]

Answer:

10

Hope it helps.

The solution for x in triangle is,

⇒ x = 10

We have to given that;

A triangle is shown in figure.

Since, A triangle is a three-sided polygon with three vertices, three angles that add up to 180 degrees, and three sides.

Now, We can use the trigonometry formula to find the value of x as;

⇒ cos a = Base / Hypotenuse

Substitute a = 60°, base = 5 , hypotenuse = x in above equation,

⇒ cos 60° = 5 / x

⇒ 1 / 2 = 5 / x

⇒ x = 5 × 2

⇒ x = 10

Thus, The solution for x in triangle is,

⇒ x = 10

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In grade 7, one common method to solve absolute value equations is by isolating the absolute value on one side of the equation and then solving for the two possible solutions.

Here is a step-by-step process to solve an absolute value equation:

Isolate the absolute value on one side of the equation by adding or subtracting the same value to both sides of the equation.

For example, |x| = 3 can be rewritten as x = 3 or x = -3

Split the equation into two separate cases, one for when the value inside the absolute value sign is positive, and one for when it is negative.

Solve each case separately.

Check your solutions by plugging them back into the original equation and making sure they are valid solutions.

Write your answer in interval notation if the solutions are continuous or list them as individual values if they are not.

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The type of data that would be used to describe the number of students enrolled at Evergreen Valley College is quantitative - discrete.

What is algebra ?

Algebra is a branch of mathematics in which arithmetic operations and other formal manipulations are applied to abstract symbols rather than specific numbers. Geometry is the branch of mathematics that deals with the shape of objects, their spatial relations, and the properties of the space the objects are in.

It's going to be quantitative because the number of students at a college can only take on certain numerical values, those that are into jurors continuous. All values can be taken by quantitative variables. Maybe 479.4, not just 479 or 480.

The type of data that would be used to describe the number of students enrolled at Evergreen Valley College is quantitative - discrete.

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Answer:

Quantitative discrete due to the fact that’s the current quantity