How do you know if an equation of a line is a vertical line?

The probability that it will be a king or a diamond is 4/13

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here, we have

There are 52 cards, of which 4 are kings.

There are 52 cards, of which 13 are diamonds.

But there are only 3 cards that are kings which are not diamonds, and only 12 cards that are diamonds but not kings, there’s one card that is both a king and a diamond.

So, there are 3/52+12/52=15/52 chances of drawing a card that is king or diamond but not both.

There are 3/52+12/52+1/52=16/52 chances of drawing a card that is king or diamond or both.

Hence, the probability that it will be a king or a diamond is 4/13.

To learn more about the probability from the given link

https://brainly.com/question/24756209

#SPJ4

The expression which represents the perimeter of the rectangle is 2x + 14

The following expressions represent the descriptions respectively;

6x

(x - 5)

(x + 2.99)

The total cost of membership of each gym is represented by;

Gym A total cost = 80 + 25m

Gym B total cost = 40m

Length= x + 3

Width = 4

Perimeter of a rectangle= 2(length + width)

= 2{(x + 3) + 4}

= 2(x + 3 + 4)

= 2(x + 7)

Perimeter of the rectangle = 2x + 14

Area of the rectangle= length × width

= (x + 3) × 4

Area of the rectangle = 4x + 12

If x = 7

Area of the rectangle = 4x + 12

= 4(7) + 12

= 28 + 12

= 40 square units

If x is the cost of each apple, the total cost of 6 apples = 6x

Adam is x years old. John is 5 years younger.

So, John's age = (x - 5) years

Ben spent x dollars on a book and $2.99 on a pack of pencil.

Ben spent a total of x + 2.99

Gym A total cost:

80 + 25m

Gym B total cost:

40m

Where,

number of months= m

If m = 6 months

Gym A total cost:

80 + 25m

= 80 + 25(6)

= 80 + 150

= $230

Gym B total cost:

40m

= 40(6)

= $240

Therefore, the gym which is the best deal for 6 months is gym A

Read more on algebraic expression:

https://brainly.com/question/4344214

#SPJ1

a. The common ratio is 2.

Given that the sum of the first five terms of the geometric series is 33, we use the formula for the sum of terms of a geometric series, S

Sₙ = a(rⁿ - 1)/(r - 1) where a = first term and r = common ratio

Since n = 5, the first 5 terms, and S₅ = 33

Sₙ = a(rⁿ - 1)/(r - 1)

33 = a(r⁵ - 1)/(r - 1) (1)

Also, when n = 10, the sum of the first 10 terms is S₁₀ = -1023

So, -1023 = a(r¹⁰ - 1)/(r - 1) (2)

Dividing (2) by (1), we have

-1023/33 = a(r¹⁰ - 1)/(r - 1) ÷ a(r⁵ - 1)/(r - 1)

-31 = (r¹⁰ - 1)/(r⁵ - 1)

-31(r⁵ - 1) = r¹⁰ - 1

-31r⁵ + 31 = r¹⁰ - 1

r¹⁰ - 1 + 31r⁵ - 31 = 0

r¹⁰ + 31r⁵ - 32 = 0

Let r⁵ = y

(r⁵)² + 31r⁵ - 32 = 0

y² + 31y - 32 = 0

Factorizing, we have

y² + 32y - y - 32 = 0

y(y + 32) - (y + 32) = 0

(y - 1)(y - 32) = 0

y - 1 = 0 or y - 32 = 0

y = 1 or y = 32

r⁵ = 1 or r⁵ = 32

r = ⁵√1 or r = ⁵√32

r = 1 or r = 2

Since for a geometric series, r ≠ 1, r = 2.

So, the common ratio is 2.

ii. The first term of the series.

The first term of the series is 33/31

Using (1)

33 = a(r⁵ - 1)/(r - 1) (1) where r = 2,

33 = a(2⁵ - 1)/(2 - 1) (1)

33 = a(32 - 1)/1

33 = 31a

a = 33/31

So, the first term of the series is 33/31

b. Find the general term of the series. Simplify your answer. ​

The general term of the geometric series is (33/62) × 2ⁿ

The general term of a geometric series is Uₙ = arⁿ⁻¹

With a = 33/31 and r = 2,

Uₙ = arⁿ⁻¹

Uₙ = (33/31) × 2ⁿ⁻¹

Uₙ = (33/31) × 2ⁿ/2

Uₙ = (33/62) × 2ⁿ

So, the general term of the geometric series is (33/62) × 2ⁿ

Learn more about geometric series here:

https://brainly.com/question/17445865

You have to write an expression that involves exponents to represent the shaded area in square inches of the diagram. Use your expression to calculate the shaded area in square inches.

a. the derivative of the function y = (ln(x))^14 + ln(x^14) is dy/dx = (14(ln(x))^13)/x + 14ln(x). b. the derivative of the function y = ^√[(7x^2)/(x^2 + 2)] is y' = (7x^3 + 14x - 7x^2) / (2(x^2 + 2)^2 * √(7x^2/(x^2 + 2))).

(a) To differentiate the function y = (ln(x))^14 + ln(x^14), we can use the power rule and the chain rule. The power rule states that if we have a function of the form f(x) = x^n, then the derivative is given by the formula f'(x) = nx^(n-1). Additionally, the derivative of ln(x) with respect to x is 1/x.

Let's differentiate the given function step by step:

y = (ln(x))^14 + ln(x^14)

Using the power rule, we have:

dy/dx = 14(ln(x))^13 * (1/x) + (14/x) * ln(x^14)

Simplifying further, we get:

dy/dx = (14(ln(x))^13)/x + 14ln(x)

Therefore, the derivative of the given function y = (ln(x))^14 + ln(x^14) is dy/dx = (14(ln(x))^13)/x + 14ln(x).

(b) For y = ^√[(7x^2)/(x^2 + 2)], we can use the chain rule and the power rule to find the derivative. The power rule states that if we have a function of the form f(x) = x^n, then the derivative is given by the formula f'(x) = nx^(n-1).

Let's differentiate the given function step by step:

y = ^√[(7x^2)/(x^2 + 2)]

Rewriting the square root as a fractional exponent, we have:

y = (7x^2/(x^2 + 2))^(1/2)

Using the chain rule, we can differentiate the function as follows:

dy/dx = (1/2)(7x^2/(x^2 + 2))^(-1/2) * d/dx (7x^2/(x^2 + 2))

Now, let's differentiate the expression inside the parentheses:

d/dx (7x^2/(x^2 + 2)) = [(d/dx)(7x^2)(x^2 + 2) - (7x^2)(d/dx)(x^2 + 2)] / (x^2 + 2)^2

Expanding and simplifying the expression, we get:

d/dx (7x^2/(x^2 + 2)) = (14x(x^2 + 2) - 2(7x^2)) / (x^2 + 2)^2

= (14x^3 + 28x - 14x^2) / (x^2 + 2)^2

Substituting this back into the chain rule, we have:

dy/dx = (1/2)(7x^2/(x^2 + 2))^(-1/2) * (14x^3 + 28x - 14x^2) / (x^2 + 2)^2

Simplifying further, we get:

y' = (7x^3 + 14x - 7x^2) / (2(x^2 + 2)^2 * √(7x^2/(x^2 + 2)))

Therefore, the derivative of the given function y = ^√[(7x^2)/(x^2 + 2)] is y' = (7x^3 + 14x - 7x^2) / (2(x^2 + 2)^2 * √(7x^2/(x^2 + 2))).

Learn more about derivative here

https://brainly.com/question/31399608

#SPJ11

Answer:

Step-by-step explanation:

sin 75°

sin(30°+45°)

sin30°*cos45°+cos30°sin45°

1/2*1/\(\sqrt{2}\) + \(\sqrt{3}\)/2*1\(\sqrt{2\)

1/2\(\sqrt{2}\)+\(\sqrt{3}\)/2\(\sqrt{2}\)

1+3/2\(\sqrt{2}\)

cos(-75°)

-cos(180°-105°)

-cos(-105°)

cos 105°

cos(45°+60°)

cos45°cos60°-sin45°sin60°

1/\(\sqrt{2}\) *1/2-1/\(\sqrt{2}\) *\(\sqrt{3}\) /2

1/2\(\sqrt{2\)-\(\sqrt{3\)/2\(\sqrt{2}\)

1-\(\sqrt{3}\)/2\(\sqrt{2}\)

sin(75)

=0.96

cos(-75)

=0.25

Answer:

\(2.64^{2}\)

Step-by-step explanation:

conjugate is the opposite i math so the opposite of finding the square root is giving it a root \(\sqrt{7}=2.64...^{2}\)

Answer:

the student in question bought 3 large notebooks and 3 small notebooks

Step-by-step explanation:

the easiest way to explain how to do this is by recognizing that the student bought $54 worth of notebooks- which is not divisible by 10 easily. that means, we should subtract 8 from 54 until we get a number that IS divisible

54 - 8 = 46 (one small notebook)

46 - 8 = 38 (two small notebooks)

3 8 - 8 = 30 (three small notebooks)

then, divide 30 by 10 to see how many large notebook the student bought.

30/10 = 3

the student in question bought 3 large notebooks and 3 small notebooks

The probability that a flight between New York City and Chicago is less than 135 minutes is 0.6667, or approximately 0.67. This means there is a 67% chance that a randomly selected flight will take less than 135 minutes.

In the given problem, we are told that the time to fly between the two cities follows a uniform distribution, with a minimum of 120 minutes and a maximum of 150 minutes. In a uniform distribution, the probability of an event within a certain range is proportional to the length of that range. Therefore, to find the probability of a flight being less than 135 minutes, we need to calculate the length of the range from 120 to 135 minutes and divide it by the length of the entire distribution, which is 150 - 120 = 30 minutes.

The length of the range from 120 to 135 minutes is 135 - 120 = 15 minutes. Dividing this by the length of the entire distribution gives us 15/30 = 0.5, or 50%. However, since the distribution is continuous and the probability of exactly 135 minutes is zero (as the distribution is uniform), the probability of a flight being less than 135 minutes is slightly greater than 0.5. Thus, the correct answer is approximately 0.67.

Learn more about length here: https://brainly.com/question/32060888

#SPJ11

Answer:

y=(x+4)²-19

Step-by-step explanation:

f(z)/g(z) → f'(zo)/g'(zo) as z → zo  of derivative to show that f(z) lim.

Let us use definition (3), Sec. 19, to give a direct proof that dw = 2z when w = z².

We know that dw/dz = 2z by the definition of derivative; thus, we can write that dw = 2z dz.

We are given w = z², which means we can write dw/dz = 2z.

The definition of derivative is given as follows:

If f(z) is defined on some open interval containing z₀, then f(z) is differentiable at z₀ if the limit:

lim_(z->z₀)[f(z) - f(z₀)]/[z - z₀]exists.

The derivative of f(z) at z₀ is defined as f'(z₀) = lim_(z->z₀)[f(z) - f(z₀)]/[z - z₀].

Let f(z) = g(z) = 0 at z = zo and f'(zo) and g'(zo) exist, where g'(zo) ≠ 0.

Using definition (1), Sec. 19, of the derivative, we need to show that f(z) lim ?

z~20 g(z) f'(zo) g'(zo).

By definition, we have:

f'(zo) = lim_(z->zo)[f(z) - f(zo)]/[z - zo]and g'(zo) =

lim_(z->zo)[g(z) - g(zo)]/[z - zo].

Since f(zo) = g(zo) = 0, we can write:

f'(zo) = lim_(z->zo)[f(z)]/[z - zo]and g'(zo) = lim_(z->zo)[g(z)]/[z - zo].

Therefore,f(z) = f'(zo)(z - zo) + ε(z)(z - zo) and g(z) = g'(zo)(z - zo) + δ(z)(z - zo),

where lim_(z->zo)ε(z) = 0 and lim_(z->zo)δ(z) = 0.

Thus,f(z)/g(z) = [f'(zo)(z - zo) + ε(z)(z - zo)]/[g'(zo)(z - zo) + δ(z)(z - zo)].

Multiplying and dividing by (z - zo), we get:

f(z)/g(z) = [f'(zo) + ε(z)]/[g'(zo) + δ(z)].

Taking the limit as z → zo on both sides, we get the desired result

:f(z)/g(z) → f'(zo)/g'(zo) as z → zo.

To know more about derivative visit:

https://brainly.com/question/25324584

#SPJ11

The rate of change and the initial values is solved to be 0.15 and 22 respectively

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

c = y intercept

The equation as described in the problem of the service charges of a phone company is represented using linear function as as follows

C(t) = 22 +0.15t,

m = rate of change = $0.15

the rate of change is 0.15

the initial value is the y intercept, value of y(c(t)) when x (t) is zero

C(t) = 22 +0.15 * 0

C(t) = 22

the initial value is 22

Learn more on  linear models at :

https://brainly.com/question/29650903

#SPJ1

Hello!

1/6 ≈ 0.167

the answer is 0.167

The complete question is

"Find the general solution of the given differential equation

y''-y=0, y1(t)=e^t , y2(t)=cosht

The function \(y(t)=e^t\)  is the solution of the given differential equation.

The function y(t)=cosht is the solution of given differential equation.

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

\(y_1(t) = e^t\)

Given differential equations are,

y''-y = 0

 So that,  

\(y' (t) = e^t, y'' (t) = e^t\)

Substitute values in the given differential equation.

\(e^t -e^t=0\)

Therefore, the function \(y(t)=e^t\)  is the solution of the given differential equation.

Another function;

\(y(t)=cosht\)  

So that,  

\(y"(t)=sinht\\\\y"(t)=cosht\)

Hence, function y(t)=cosht is solution of given differential equation.

Learn more about function here:

https://brainly.com/question/2253924

#SPJ1

Step-by-step explanation:

let the numbers are:

a, b, and c

the equation would be:

a+b+c = 131

c = 4a

b = a+5

=>

a + a+5 +4a = 131

6a +5 = 131

6a = 131-5

6a = 126

a= 126/6

a = 21

b = a+5 = 21+5

b = 26

c = 4a = 4(21)

c = 84

Answer:

1/5 cup of grapes for each cup of apples

Step-by-step explanation:

Divide: 3 divided by 15=0.2

0.2 as a fraction is 2/10

2/10 simplified=1/5

(I was gonna put picture of my work, but I'm too lazy, lol)

Hope this helped!! :)

Stay safe and have a wonderful day/night!!!!!

Brainliest?!?!

Answer:

3rd one

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

sorry if its wrong

Answer:

24496

Step-by-step explanation:

40912 * (1-5%) ^10 = 24495.5

becuase they are humans, so round up to 24496

Answer:

To calculate the surface area and volume of a cylinder, we can use the following formulas:

a) Surface Area of a Cylinder:

The surface area of a cylinder consists of two circles (top and bottom) and the curved surface area.

The formula for the surface area of a cylinder is:

SA = 2πr² + 2πrh

Where:

SA = Surface Area

r = Radius of the base (half the diameter)

h = Height of the cylinder

Given that the diameter is 16 yards, the radius is half of that, so r = 8 yards. The height is 20 yards.

Substituting the values into the formula, we get:

SA = 2π(8)² + 2π(8)(20)

= 2π(64) + 2π(160)

= 128π + 320π

= 448π

So, the surface area of the cylinder is 448π square yards.

b) Volume of a Cylinder:

The formula for the volume of a cylinder is:

V = πr²h

Using the same values for the radius (r = 8 yards) and height (h = 20 yards), we can calculate the volume:

V = π(8)²(20)

= 64π(20)

= 1280π

The volume of the cylinder is 1280π cubic yards.

The fraction which is equivalent to 6/12 is 1/2

What does a fraction mean?

In the first place, fraction is a numerical quantity or relationship where one number is expressed in terms of another.

In order to determine the equivalence of 6/12 in fraction , we need reduce 6/12 to the lowest term, since 6 is common to 6 and 12 and that 6 divided by gives 1 and 12/6 gives 2, which means that we are left 1/2

The correct fraction which is equivalent to 6/12 is 1/2

Find out more about fraction on:https://brainly.com/question/5243429

#SPJ1

Full question:

A group of 12 students goes on a school field trip, 6 are in third grade. which fraction is equivalent to 6/12?

(A) 1/3

(B)1/4

(C) 1/6

(D) 1/2

The probability of experiencing a flood equal to or greater than the 25-year flood at a specific location depends on several factors, including historical flood data and statistical analysis.

The 25-year flood is a term used in hydrology to refer to a flood event that has a 4% chance of occurring in any given year. To calculate the probabilities of having at least one flood of this magnitude, we can use the concept of the complementary cumulative distribution function (CCDF).

In the next year, the probability of having at least one flood equal to or greater than the 25-year flood can be estimated by subtracting the probability of no such flood from 1. Assuming floods follow a Poisson distribution, the probability of no flood is given by the equation P(0) = exp(-λ), where λ is the average number of floods per year. Thus, the probability of having at least one flood can be calculated as P(at least one) = 1 - P(0).

Over the next 25 years, we can calculate the probability of no flood of this magnitude occurring by using the same equation but with λ multiplied by the number of years (25). Therefore, the probability of having at least one flood equal to or greater than the 25-year flood over this period can be estimated as P(at least one) = 1 - P(0) = 1 - exp(-25λ).

For any 5-year period, we can calculate the probability of no flood using the equation P(0) = exp(-5λ). Thus, the probability of having at least one flood during this time frame can be estimated as P(at least one) = 1 - P(0) = 1 - exp(-5λ).

Learn more about probability here : brainly.com/question/32117953

#SPJ11

The correct answer is the Beta-binomial model. Bayesian analysis is a statistical approach that incorporates prior knowledge or beliefs about a parameter of interest and updates it based on observed data using Bayes' theorem.

In the case of a binary choice, where the outcome can be either yes or no, Bayesian analysis seeks to estimate the probability of success (yes) based on available information.

The Beta-binomial model is a commonly used model in Bayesian analysis for binary data. It combines the Beta distribution, which represents the prior beliefs about the probability of success, with the binomial distribution, which describes the likelihood of observing a specific number of successes in a fixed number of trials.

The Beta distribution is a flexible distribution that is often used as a prior for modeling probabilities because of its ability to capture a wide range of shapes. The Beta distribution is characterized by two parameters, typically denoted as alpha and beta, which can be interpreted as the number of successes and failures, respectively, in the prior data.

The binomial distribution, on the other hand, describes the probability of observing a specific number of successes in a fixed number of independent trials. In the context of Bayesian analysis, the binomial distribution is used to model the likelihood of observing the data given the parameter of interest (probability of success).

By combining the prior information represented by the Beta distribution and the likelihood information represented by the binomial distribution, the Beta-binomial model allows for inference about the probability of success in a binary choice.

The other options mentioned, such as the Normal-normal model and the Gaussian model, are not typically used for binary data analysis. The Normal-normal model is more suitable for continuous data, where both the prior and likelihood distributions are assumed to follow Normal distributions. The Gaussian model is also suitable for continuous data, as it assumes that the data are normally distributed.

In summary, the Beta-binomial model is the appropriate model for Bayesian analysis of a binary choice because it effectively combines the Beta distribution as a prior with the binomial distribution as the likelihood, allowing for inference about the probability of success in the binary outcome.

Learn more about Bayes' theorem at: brainly.com/question/33143420

#SPJ11

Answer:

Eli has the faster speed than Jess.

Answer:

C. 12°

Step-by-step explanation:

Angle-180°

192°-180°

=12°

Answer:

0

Step-by-step explanation:

-2-(-4)-2

We can break down the problem first. The beginning of the problem is...

-2-(-4)

Two negatives make a positive. An equivalent way to say this is

-2+4

-2+4=2

Next, we can solve for the last part. At the end of the equation, you have to subtract 2, so that's what we'll do!

2-2=0

The answer to this is 0!

I hope you understood the explanation...have an amazing day!!!! :3

Answer:

y = 2x - 9

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 2 , then

y = 2x + c ← is the partial equation

To find c substitute (2, - 5) into the partial equation

- 5 = 4 + c ⇒ c = - 5 - 4 = - 9

y = 2x - 9 ← equation of line

In a family with three children, assuming each child is equally likely to be a boy or a girl, we can analyze the sample space and calculate the probabilities of different events. The sample space consists of eight possible outcomes indicating the genders of the three children. The events of interest include exactly one child being a girl, at least two children being girls, and no child being a girl.

(a) The eight elements in the sample space, representing all possible genders of the three children, are as follows:

1. BBB (Three boys)

2. BBG (Two boys and one girl)

3. BGB (One boy and two girls)

4. BGG (One boy and two girls)

5. GBB (One girl and two boys)

6. GBG (One girl and two boys)

7. GGB (Two girls and one boy)

8. GGG (Three girls)

(b) Now let's calculate the probabilities of the given events:

(i) The event of exactly one child being a girl can be represented as {BGG, GBG, GGB}. The probability is 3/8 since there are three favorable outcomes out of the eight possibilities in the sample space.

(ii) The event of at least two children being girls can be represented as {BGG, GBB, GBG, GGB, GGG}. The probability is 5/8 since there are five favorable outcomes out of the eight possibilities.

(iii) The event of no child being a girl can be represented as {BBB}. The probability is 1/8 since there is only one favorable outcome out of the eight possibilities.

By analyzing the sample space and defining the events of interest as sets, we can determine the probabilities associated with each event based on the principles of probability theory.

Learn more about outcomes here:

https://brainly.com/question/30718240

#SPJ11

Answer: = 1

Step-by-step explanation:

Answer:

x=1

Step-by-step explanation:

8(x-4)=4(x-7)

we can expand the brackets

8x-32=4x-28

8x-4x=-28+32

4x=4

x=1