Solve.
36/3 = 12/≠
X=

The probability that a student chosen at random has a cat or a dog is; P(cat or dog) = 22/25.

What is probability?

Probability is that the branch of arithmetic regarding numerical descriptions of however probably an incident is to occur, or however probably it's that a proposition is true. The likelihood of an incident could be a range between 0 and 1.

Main body:

According to the question, the total number of students is; 25.

15 of them have a cat

16 of them have a dog

while, 3 of them have neither

where, x = number if students who own a cat and a dog.

Consequently, the total number of students who own a cat, a dog, both or neither is as follows;

15-x + x + 16-x + 3 = 25.

-x = 25 - 34

In essence, x = 9

the number of students who own a cat and a dog is 9.

Therefore, probability that a student chosen at random has a cat and a dog is therefore;

P(cat and dog) = 9/25.

Therefore probability that a student chosen at random has a cat or a dog is 22/25.

To know more about probability , visit:

brainly.com/question/13604758

#SPJ1

The percentage of the variability does the model accounts for with the data is equals to the 40%.

We have an article in wear (1992, vol. 152, pp. 171-181), x = oil viscosity, y = wear volume and we have a table consists data values of x and y.

the simple linear regression model, is represented as

\(y = \beta_0 + \beta_1x \)

where,

\(\beta_0 \)

= intercept

\(\beta_1\)

= slope

The above shows all calculations of these variables.

Hence, required value is 40%.

For more information about percentage of the variability, visit :

#SPJ4

Answer:

m<DBC = 109

Step-by-step explanation:

8x-27=6x+7

8x=6x+34

2x=34

x=17

8(17)-27= 109

Answer: 109

Step-by-step explanation:

i'm not entirely sure of this answer as its been a while since ive done problems like this, however, i think the steps to solve are setting (8x-27) equal to (6x+7). Once you do that, you can solve for x. Substitute x into angle DBC to find the answer.

The time taken by the car way back if it travelled at speed 56 km/hr is 4.5 hours

According to the question,

Time taken by car to reach its destination = 4 hours

Speed of travelling to destination = 63 km/hr

Using distance-time formula

Speed = distance / time

=> distance = speed × time

Distance travelled = 63 × 4

=> 252 km

Also , Car travelled back at speed = 56 km/hr

Time taken = 252 / 56

=> 4.6 hours

Let time = t and speed = s.

S varies in opposition to t.

When the inverse variation constant k is added, it becomes

s = k/t

If s = 56, then t = 4.5.

56 = k/4.5

k = 4.5 × 56

=> k = 252 is constant of variation

To know more Distance-time formula here

https://brainly.com/question/28638965

#SPJ4

Using the normal distribution, it is found that 4.18% of the students who took the SAT math test meet this requirement.

The z-score of a measure X of a normally distributed variable that has mean given by \(\mu\) and standard deviation represented by \(\sigma\) is by the following equation:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation for the distribution of SAT scores is given as follows:

\(\mu = 528, \sigma = 117\)

The proportion above 730 is given by one subtracted by the p-value of Z when X = 730, hence:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (730 - 528)/117

Z = 1.73

Z = 1.73 has a p-value of 0.9582.

1 - 0.9582 = 0.0418.

Hence 4.18% of the students who took the SAT math test meet this requirement.

More can be learned about the normal distribution at https://brainly.com/question/4079902

#SPJ1

The aim when choosing the model parameters:

Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line

The correct option is (b)

This is incomplete question

Complete question is this:

With a linear regression, what is the aim when choosing the model parameters (aka the slope and coefficient(s))?

Choose the correct option:

Now, According to the question:

Hence, The aim when choosing the model parameters:

Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line

The correct option is (b).

Learn more about Regression line at:

https://brainly.com/question/14984940

#SPJ4

In the given figure, the length of BC is 6.66 cm and the length of DC is 5.33 cm

From  the question, we are to determine the length of BC and DC

Considering the diagram,

First, we will determine the measure of angle A

Using SOH CAH TOA

We can write that

\(sin A = \frac{4}{5}\)

sin A = 0.8

∴ A = sin⁻¹(0.8)

A = 53.13°

Now, we will determine the measure of angle C

∠A + ∠ABC + ∠C = 180° (Sum of angles in a triangle)

53.13° + 90° + ∠C = 180°

∠C = 180° - 90° - 53.13°

∠C = 36.87°

Also,

Using SOH CAH TOA

\(tan C = \frac{BD}{DC}\)

\(tan36.87 ^\circ=\frac{4}{DC}\)

\(0.7500 = \frac{4}{DC}\)

\(DC = \frac{4}{0.75}\)

DC = 5.33 cm

By the Pythagorean theorem,

/BC/² = /BD/² + /DC/²

/BC/² = 4² + 5.33²

/BC/² = 16 + 28.4089

/BC/² = 44.4089

/BC/ = √44.4089

/BC/ = 6.66 cm

Hence, the length of BC is 6.66 cm and the length of DC is 5.33 cm

Learn more on Trigonometry here: https://brainly.com/question/3642956

#SPJ1

Answer:

Hope this is helpful for you

The probability of randomly selecting someone who does not believe that some people see the future in their dreams is 39.6%.

Probability is an area of mathematics that deals with the study of chance events.

We have, A poll showed that 60.4% of Americans say they believe that some people see the future in their dreams.

Therefore, the probability of randomly selecting someone who does not believe that some people see the future in their dreams can be calculated as follows:

P(A) = 1 - P(B)

Where,

P(A) = Probability of selecting someone who does not believe that some people see the future in their dreams.

P(B) = Probability of selecting someone who believes that some people see the future in their dreams.

P(A) = 1 - P(B)

⇒ 1 - 60.4/100

⇒39.6/100

⇒ 0.396 or 39.6%

Hence, the probability of randomly selecting someone who does not believe that some people see the future in their dreams is 39.6%.

To know more about the "Probability": https://brainly.com/question/25839839

#SPJ11

Answer:

answer is 20

we know that,

perimeter of a triangle =all sides of triangle.(ie.A+B+C)

LIKEWISE..

perimeter of 1st triangle

=5+x-5+x-4

=2x-4

again,

perimeter of 2nd triangle

=16+10+x-10

=16+x

now according to question

perimeter of 1st triangle =perimeter of 2nd triangle

2x-4=16+x

2x-x=16+4

therefore ...x=20

cos(x) is bounded between -1 and 1. So,

\(-1 \le \cos\left(\dfrac{n\pi}3\right) \le 1 \implies -\dfrac1n \le \dfrac1n\cos\left(\dfrac{n\pi}3\right) \le \dfrac1n\)

As n goes to infinity, both -1/n and 1/n converge to 0, so

\(\displaystyle\lim_{n\to\infty}\frac1n\cos\left(\frac{n\pi}3\right) = \boxed{0}\)

as well.

Answer:

\(\displaystyle \lim_{n\rightarrow \infty}\left[\frac{1}{n}\cos\left(\frac{n\pi}{3}\right)\right]=0\)

Step-by-step explanation:

The squeeze theorem states that if \(g(x)\leq f(x)\leq h(x)\) for all \(x\neq c\) in some interval around \(c\) and \(\displaystyle \lim_{x\rightarrow c}g(x)=L\) and \(\displaystyle \lim_{x\rightarrow c}h(x)=L\), then it follows that \(\displaystyle \lim_{x\rightarrow c}f(x)=L\).

Essentially what this is saying is that if a function \(g\) is always smaller than or equal to function \(f\) in some interval and a function \(h\) is always greater than or equal to \(f\) in the same interval, if \(g\) and \(h\) approach the same value at some point, \(f\) must also approach that point, since it is being "squeezed", hence the name squeeze theorem.

Recall that the maximum output of cosine is 1 and the minimum output of cosine is -1. A quick check on the unit circle will confirm this.

Therefore, the function \(\displaystyle \frac{1}{n}(1)\) will always be greater than or equal to  \(\displaystyle \frac{1}{n}\cos\left( \frac{n\pi}{3}\right)\) and the function \(\displaystyle \frac{1}{n}(-1)\) will always be less than or equal to \(\displaystyle \frac{1}{n}\cos \left(\frac{n\pi}{3}\right)\).

Hence, \(\displaystyle -\frac{1}{n}\leq \frac{1}{n}\cos\left( \frac{n\pi}{3}\right)\leq \frac{1}{n}\text{ for all } x\in \mathbb{R}\).

We can easily compute \(\displaystyle \lim_{n\rightarrow \infty}\left[- \frac{1}{n}\right]\) and \(\displaystyle \lim_{n\rightarrow \infty}\left[\frac{1}{n}\right]\) with direct substitution.

Therefore, we have:

\(\displaystyle \lim_{n\rightarrow \infty}\left[- \frac{1}{n}\right]=-\frac{1}{\infty}=0\\\\\displaystyle \lim_{n\rightarrow \infty}\left[ \frac{1}{n}\right]=\frac{1}{\infty}=0\)

Since \(\displaystyle \lim_{n\rightarrow \infty}\left[- \frac{1}{n}\right]=\displaystyle \lim_{n\rightarrow \infty}\left[ \frac{1}{n}\right]=0\) and \(\displaystyle -\frac{1}{n}\leq \frac{1}{n}\cos\left( \frac{n\pi}{3}\right)\leq \frac{1}{n}\), then from the squeeze theorem, \(\displaystyle \lim_{n\rightarrow \infty}\left[\frac{1}{n}\cos\left(\frac{n\pi}{3}\right)\right]= \lim_{n\rightarrow \infty}\left[- \frac{1}{n}\right]=\displaystyle \lim_{n\rightarrow \infty}\left[ \frac{1}{n}\right]=\boxed{0}\)

The slope-intercept form of the line containing the point (5, −3) and is parallel to y = − 2/5x − 3/4 is y = -2/5x - 1.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given,  line containing the point (5, −3) and is parallel to: y = − 2/5x − 3/4

The slope-intercept form of the equation of a line

y=mx+b,

where m is the slope

b is the y-intercept

In our case Line is parallel to the Line y = − 2/5x − 3/4,

So the slope would be the same.

m = -2/5

Thus, the equation of the line:

y = -2/5x + b

Since the line passes through the point (5, -3)

-3 = -2/5 * 5 + b

b = -1

Thus the final equation of a line:

y = -2/5x - 1

Therefore, The slope-intercept form of the line containing the point (5, −3) and is parallel to y = − 2/5x − 3/4 is y = -2/5x - 1.

Learn more about Linear equations here:

https://brainly.com/question/11897796

#SPJ1

The probability of rolling a sum of 5 on a standard pair of six sided dice is 1/9.

According to the given question.

A standard pair of dice is rolled.

So, the sample sapce for rolling a pair of dice = {(1,1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4),(5, 5),(5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

⇒ Total number of outcomes = 36

And, the outcomes for getting a sum of five on a sandard pair of six sided dice = {(2, 3), (3, 2), (4, 1), (1, 4)}

⇒ Total number of favorable outcomes = 4

As we know that " probability is the ratio of total number of favorable outcomes to the total number of outcomes".

Therefore,

The probability of rolling a sum of 5 on a standard pair of six-sided dice

= 4/36

= 1/9

Hence, the probability of rolling a sum of 5 on a standard pair of six sided dice is 1/9.

Find out more information about probability here:

https://brainly.com/question/11234923

#SPJ4

Answer: 7/10

Step-by-step explanation:

Answer:

7/10 or 70/100

Step-by-step explanation:

The 7 is in the tens place!

Indexing blogs, labeling blogs and tagging entries are effective techniques for increasing people's ability to find your business blogs and wikis.

When done effectively, indexing blogs guarantees that themes are organized in an easily navigable framework that people can use to explore your content, which increases the number of people who can find your company blogs and wikis.

Labelling blogs is advantageous since it enables you to give your blog entries keywords and subjects, which makes it simpler for search engines to find your content.

By tagging entries, you can connect relevant subjects and give readers a longer means of research. All of these strategies are crucial for enhancing discoverability and ensuring that your company's blogs and wikis get viewed by the target audience.

To learn more about business blogs link is here

brainly.com/question/31313121

#SPJ4

When 100 simulation trials are run each with a sample size of 50 and a point estimate of 0.18, observing a minimum sample proportion of 0.28 and maximum sample proportion of 0.40, the margin of error of the population proportion using an estimate of the standard deviation is ±0.04.

Therefore the answer is ±0.04

Margin of error of the population proportion using an estimate of the standard deviation is calculated by the formula

ME = 2 × (max - min)/ 6

We know that the sample proportion, p is 0.18.Also we know minimum sample proportion observed is 0.28 and maximum sample proportion observed is 0.40. Therefore margin of error is

ME = 2 × (0.40 - 0.28)/ 6

ME = (0.12)/ 3

ME= 0.04

To know more on margin of error

https://brainly.com/question/10271375

#SPJ4

The cost of the chocolate for 110 bon-bons  as per given radius , density and cost is equal to $8.80 to the nearest cent.

Volume of a sphere with radius r is ,

V = ( 4/3 )πr³

Radius 'r' of each chocolate bon-bon is 0.8 cm,

Volume of each bon-bon is equals to,

V = ( 4/3 )π (0.8)³

   = 2.144 cm³

Density 'ρ' of the chocolate is 1.3 g/cm^3,

Mass 'm'  of each bon-bon is equals to,

m = ρV

   = ( 1.3 ) ( 2.144 )

   = 2.78grams

The cost of the chocolate used in each bon-bon is $0.03 per gram,

This implies,

Cost of the chocolate used in one bon-bon is ,

= ( 0.03 ) × 2.78

= 0.0834

Rounding to the nearest cent, the cost of the chocolate for one bon-bon is $0.08.

Cost of the chocolate for 110 bon-bons,

= 110 × 0.08

= 8.8

Therefore, the chocolate for 110 bon-bons would cost $8.80 to the nearest cent.

Learn more about chocolate here

brainly.com/question/29476310

#SPJ4

Answer: its 12 and 8 10 12 14 16 either of those

Step-by-step explanation:

Answer:

3rd option

Step-by-step explanation:

The equation of a line in point slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

Given

y - 4 = \(\frac{1}{4}\) (x - 8)

with m = \(\frac{1}{4}\) and (a, b) = (8, 4 )

The equation of a line in slope- intercept form is

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

y = \(\frac{1}{4}\) x + c ← is the partial equation

To find c substitute (8, 4) into the partial equation

4 = 2 + c ⇒ c = 4 - 2 = 2

y = \(\frac{1}{4}\) x + 2 ← equation in slope- intercept form

Answer:

I believe it is 3243.16 rounded 3243

If an airplane flies a total distance of 450km in 3/4 hours, the plane is traveling at an average speed of 600 kilometers per hour.

The average speed refers to the quotient of the total distance divided by the total time used by the airplane to cover the distance.

Based on the distance, time, and speed equation, we can state that there exists an equation relationship, which is given as distance = time x speed.

The total distance flown by airplane = 450 kilometers

The total time used by the airplane to travel the distance = ³/₄ hours or 0.75 hours

Thus, the average speed of the airplane is 600 kilometers per hour (450 ÷³/₄).

Learn more about distance, time, and speed at brainly.com/question/26046491.

#SPJ1

Dissociative identity disorder is a psychological condition characterized by the presence of multiple distinct identities or personality states within an individual.

Dissociative identity disorder (DID) is a psychological condition in which an individual experiences the presence of multiple distinct identities or personality states.

These identities may have their own unique traits, memories, and behaviors, and they can take control of the person's behavior and consciousness at different times.

DID, also known as multiple personality disorder, is marked by the coexistence of different identities or "alters" within the same person. These alters may vary in age, gender, mannerisms, and even voice. They often have distinct memories, skills, and emotional responses.

The development of dissociative identity disorder is believed to be a response to severe and prolonged trauma, typically experienced during childhood.

The dissociation serves as a defense mechanism, allowing the individual to compartmentalize distressing memories and experiences.

Learn more about Dissociative identity disorder

brainly.com/question/29597784

#SPJ11

Answer:

x^2 = 9

Step-by-step explanation:

If you square both 3 and -3 you get 9

This looks like a quadratic equation!

Let's first rewrite the equation in the standard form (where the coefficients of x2 and x, as well as the constant term all have absolute values greater than 0)

ax^2 + bx + c = 0

And then use the Quadratic Formula to solve for x.

x = (-b ± √[b^2 - 4ac])/2a

Where a, b, and c are the coefficients of x^2, x, and 1, respectively.

Now, we just need to substitute the constants and solve for x!

-8x^2 + 10x + 15 = 0

a = -8

b = 10

c = 15

x = (-10 ± √[100 - 4(-8)(-15)])/2(-8)

x = (-10 ± √[100 - 240])/-16

x = (-10 ± √-140)/-16

x_1 = -7/16

x_2 = -7/16

Since x must be a real number, we can disregard x_2 and therefore the value of x is -7/16.

So the value of x is -7/16!

If -7/16 isn't the answer you were looking for, then try it in decimal form.

Answer: Let's first rewrite the equation in the standard form (where the coefficients of x2 and x, as well as the constant term all have absolute values greater than 0)

ax^2 + bx + c = 0

And then use the Quadratic Formula to solve for x.

x = (-b ± √[b^2 - 4ac])/2a

Where a, b, and c are the coefficients of x^2, x, and 1, respectively.

Now, we just need to substitute the constants and solve for x!

-8x^2 + 10x + 15 = 0

a = -8

b = 10

c = 15

x = (-10 ± √[100 - 4(-8)(-15)])/2(-8)

x = (-10 ± √[100 - 240])/-16

x = (-10 ± √-140)/-16

x_1 = -7/16

x_2 = -7/16

Since x must be a real number, we can disregard x_2 and therefore the value of x is -7/16.

So the value of x is -7/16!

If -7/16 isn't the answer you were looking for, then try it in decimal form.

wich is -0.4375

Step-by-step explanation:

Answer:

6.3×10^6

Step-by-step explanation:

6.3×10^6

in standard form

Answer:

a = 3

Step-by-step explanation:

Calculate the distance d using the distance formula and equate to 4

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = (2, - 1) and (x₂, y₂ ) = (2, a)

d = \(\sqrt{(2-2)^2+(a+1)^2}\) = \(\sqrt{0+(a+1)^2}\) = \(\sqrt{(a+1)^2}\) = a + 1 then

a + 1 = 4 ( subtract 1 from both sides )

a = 3

The shapes of a cross section of the cone are circle and triangle

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

The cone

In the cone, we have the following shapes in the cross-sections

Using the above as a guide, we have the following:

the shapes of a cross section of the cone are circle and triangle

Read more about cross section at

https://brainly.com/question/10012411

#SPJ1

Answer:

\(\frac{2}{3} *\frac{15}{4}\\\)=2/3  ÷4/15=\(\frac{2}{5}\)

Step-by-step explanation:

Answer:

900 ml of milk

Step-by-step explanation:

the scale is 1:1 so just multiply by 3