"a fair coin is tossed 5 times. what is the probability of exactly 4 heads?"

The probability that the student answers the question on the first or second try is 0.60.

Given

P(A) = 0.2

[tex]\rm P(B|A^c)=0.5[/tex].

The conditional probability of an event is when the probability of one event depends on the probability of occurrence of the other event.

When two events are mutually exclusive.

Then,

[tex]\rm P(A\cap B)=0[/tex]

The first probability is;

[tex]\rm P(A^C)=1-0.2=0.8[/tex]

Therefore,

The probability that the student answers the question on the first or second try is;

[tex]\rm P(A\cup B)= P(A) +P(B)-P(A \cap B)\\\\ P(A\cup B)= P(A) +P(B|A^C) \times P(A^C)-P(A \cap B)\\\\ P(A\cup B)= 0.2+0.5 \times 0.8 -0\\\\P(A\cup B)=0.2+0.40\\\\ P(A\cup B)=0.60[/tex]

Hence, the probability that the student answers the question on the first or second try is 0.60.

To know more about Conditional probability click the link given below.

https://brainly.com/question/10739947

Answer:

x=3 y=3

Step-by-step explanation:

The sum of the squares of two numbers is 18, and the product of those two numbers is 9, you just need to create an equation:

So the sum of the squares is 18, the first number will be represented as X and the second as Y:

[tex]x^{2}+ y^{2} =18[/tex]

And the other one is that the product of the two numbers is 9:

[tex]xy=9[/tex]

We have a system of equations here, we clear X from the first one:

[tex]x=\frac{9}{y}[/tex]

And instert that value of x in the first one:

[tex]x^{2}+ y^{2} =18\\(\frac{9}{y} )^{2}+ y^{2} =18\\81=y^2(18-y^2)\\y^4-18y^2+81=0\\(y^2-9)(y^2-9)=0\\Y^2-9=0\\y^2=9\\y=3[/tex]

By solving this equation we get that the first number is 3.

The second number is solved by inserting the value of Y into one of the equations, in this case we will use the second:

[tex]xy=9\\x=\frac{9}{y} \\x=\frac{9}{3} \\x=3[/tex]

So we get that x and y are both 3.

In the question it must be 10 instead of 101010, y instead of yyy and x instead of xxx.

Since, Enrique earns 10 points for each question that he answers correctly on a geography test.

We have to write an equation for the number of points, 'y' Enrique scores on the test when he answers 'x' questions correctly.

So, Number of points scored = Points scored for one question [tex] \times [/tex] Number of questions answered correctly.

So, Number of points scored = [tex] 10 \times x [/tex]

[tex] y=10 \times x [/tex]

y = 10x is the required equation.

The inequality 5 + 7l ≤ 60 represents the scenario where a student has a 60-minute free trial of a game that requires 5 minutes to set up and 7 minutes to play each level, where 'l' denotes the number of levels the student can play.

The subject of this question is about setting up an inequality to represent a scenario. The student has a 60-minute free trial of a game and it takes 5 minutes to set up the game and another 7 minutes to play each level. Let's denote 'l' as the number of levels the student can play. The total time spent both setting and playing the game cannot exceed 60 minutes. Therefore, the inequality to determine the maximum number of levels the student can play would be: 5 + 7l ≤ 60.

To explain this further, the '5' is the time spent setting up the game and '7l' is the total time spent playing the levels. As we want to find out the maximum number of levels that can be played within a constraint of 60 minutes, thus we use the less than or equal to symbol ('≤').

https://brainly.com/question/30231017

#SPJ3

Answer:

Option D [tex]\$50+\$31.5x[/tex]

Step-by-step explanation:

Let

x------> the number of days

y----> the cost of renting a car

we know that

For [tex]x<7\ days[/tex]

[tex]y=\$50+\$35x[/tex]

For [tex]x\geq 7\ days[/tex]

The rate is equal to

[tex]0.90*\$35=\$31.5[/tex]

so

[tex]y=\$50+\$31.5x[/tex]

In this problem. the car has been rented for more than a week

therefore

[tex]x> 7\ days[/tex]

The cost of renting a car is equal to

[tex]y=\$50+\$31.5x[/tex]

In a mathematical proof, missing statements and reasons are usually concluded from the given statements and the relevant geometric postulates or theorems. They could include establishing the congruency of angles or declaring the parallelism of lines.

Without the concrete steps of the proof or the reasoning proposed, it is difficult to provide the exact missing statements and reasons. However, in a general mathematical proof, common reasons used include 'definition of congruent angles', 'definition of parallel lines', 'alternate interior angles theorem', etc.

For instance, if we have a proof that involves stating two angles are congruent, the missing statement might be 'Angle A is congruent to Angle B', and the missing reason could be 'Definition of Congruent Angles' or 'Angle Bisector Theorem', if an angle bisector comes into the picture.

Another missing statement might be 'Segment AB is parallel to Segment CD', with the reason being 'Corresponding Angles Postulate', or 'Alternate Interior Angles Theorem', if the proof involves parallel lines.

https://brainly.com/question/26697247

#SPJ6

Answer:

AB and CD are intersecting lines but are not perpendicular.

See attached image.

Step-by-step explanation:

which means the other asymptote is the line .

Final answer:

The probability of rolling an even number or a prime number on a six-sided die is 5/6, considering the unique favorable outcomes of 2, 3, 4, 5, and 6 against the total possible outcomes.

Explanation:

The question asks, "What is the probability of rolling an even number or a prime number on a number cube?" To answer this, first identify the outcomes on a six-sided die which are even and those that are prime.

Even numbers on a die: 2, 4, 6. Prime numbers on a die: 2, 3, 5. Notice that 2 is both even and prime, and it only needs to be counted once. Therefore, the unique favorable outcomes are 2, 3, 4, 5, 6.

The die has a total of 6 sides, making the total number of possible outcomes 6. The probability of rolling an even number or a prime number is therefore the number of favorable outcomes (5) divided by the total number of outcomes (6), which simplifies to 5/6.

To find the sum of the geometric series, we use the formula: Sn = a1 * (r^n - 1) / (r - 1). Substituting the given values and solving, we find that the sum is 16,383.

To find the sum of a geometric series, we can use the formula Sn = a1 * (r^n - 1) / (r - 1), where Sn is the sum of the series, a1 is the first term, r is the common ratio, and n is the number of terms.

In this case, a1 = 3, r = 4, and an = 49,152. We can use the formula to find n, which is the exponent.

49,152 = 3 * (4^n - 1) / (4 - 1)

49,152 = 3 * (4^n - 1) / 3

16,384 = 4^n - 1

4^n = 16,385

n = log4(16,385)

n ≈ 7

Now, we can substitute the values into the formula for Sn.

Sn = 3 * (4^7 - 1) / (4 - 1)

Sn = 3 * (16,384 - 1) / 3

Sn = 3 * 16,383 / 3

Sn = 16,383

Therefore, the sum of the geometric series is 16,383. So the correct answer is Sn = 16,383.

The correct answer is [tex]\( S_n = 65,535 \)[/tex].

To find the sum of a geometric series, you can use the formula:

[tex]\[ S_n = a_1 \frac{(r^n - 1)}{r - 1} \][/tex]

Where:

- [tex]\( S_n \)[/tex] is the sum of the series,

- [tex]\( a_1 \)[/tex] is the first term,

- [tex]\( r \)[/tex] is the common ratio,

- [tex]\( n \)[/tex] is the number of terms.

Given [tex]\( a_1 = 3 \), \( r = 4 \), and \( a_n = 49,152 \)[/tex], we need to find [tex]\( n \)[/tex]. The formula for the [tex]\( n^{th} \)[/tex] term in a geometric series is [tex]\( a_n = a_1 \times r^{(n-1)} \)[/tex]. In this case, [tex]\( 49,152 = 3 \times 4^{(n-1)} \)[/tex]

Let's solve for n:

[tex]\[ 4^{(n-1)} = \frac{49,152}{3} \][/tex]

[tex]\[ 4^{(n-1)} = 16,384 \][/tex]

[tex]\[ n-1 = \log_4(16,384) \][/tex]

[tex]\[ n-1 = 7 \][/tex]

[tex]\[ n = 8 \][/tex]

Now that we have [tex]\( n = 8 \)[/tex], we can use it in the sum formula:

[tex]\[ S_n = 3 \frac{(4^8 - 1)}{4 - 1} \][/tex]

[tex]\[ S_n = 3 \frac{(65,536 - 1)}{3} \][/tex]

[tex]\[ S_n = 3 \frac{65,535}{3} \][/tex]

[tex]\[ S_n = 65,535 \][/tex]

Therefore, the correct answer is [tex]\( S_n = 65,535 \)[/tex].

Answer: all real numbers

Step-by-step explanation:

The given function is : [tex]g(x) = 52x[/tex], which is polynomial function with degree one.

We know that the domain of a polynomial is the entire set of real numbers because for any real number r the polynomial function exists.

Therefore, the domain of the given function [tex]g(x) = 52x[/tex] is the set of real numbers.

Answer:

14

Step-by-step explanation:

Let the legs of the triangle each have length $x$ (they are equal because it is an isosceles right triangle). Then

x^2 + x^2 = (14√2)^2 = 14^2 × (√2)^2 = 14^2 × 2, so x^2 = 14^2. Given that x must be positive, we have x = 14. So, the value of each leg is 14

(Hope this helped you!)

A good guess for the real root of the polynomial [tex]f(x) = x^3 - 6x^2 + 11x - 6[/tex] that is neither 1, even, nor negative, would be a positive odd integer such as 3 or 5, considering the constraints and the Rational Root Theorem.

The real root of the cubic equation [tex]f(x) = x^3 - 6x^2 + 11x - 6[/tex] that is neither 1, even, nor negative would most likely be a positive odd number (since all positive even numbers are, by default, also excluded). Considering the smallest odd numbers greater than 1 are 3 and 5, and given that we're working with integers, a good guess for the real root would be either 3 or 5. However, one can apply the Rational Root Theorem which states that any rational root, expressed in its lowest form p/q, must have p as a factor of the constant term and q as a factor of the leading coefficient. In this case, the possible rational roots could be

divisors of 6 (constant term) over divisors of 1 (leading coefficient), which gives us only divisors of 6 itself

since the leading coefficient is 1. Among those divisors, the ones that fit the criteria of being neither 1, even, nor negative, would be 3 or positive odd integers.