Expand (1 + √2)(3-√2) ​

Answer: A gym membership cost 3 dollars a month. There is an initial fee of $5. How many months would you need to be paying for the membership to have spent 20 dollars?

Step-by-step explanation:

3x+5=20

3x=15

x=5

5 Months

The number of possible ways a person can order a two-course meal = 99

In this question, we have been given a restaurant offers 9 entrees and 11 desserts.

We need to find the number of possible combinations (ways) a person can order a two-course meal.

Here, the entrees = 9

and the desserts = 11

The entrees can be ordered in 9 ways

The desserts can be ordered in 11 ways.

a two-course meal = entrees * desserts

so,  the number of possible ways a person can order a two-course meal would be,

a two-course meal = 11 * 9

a two-course meal = 99

Therefore, in 99 ways a person can order a two-course meal.

Learn more about the possible combinations here:

https://brainly.com/question/22855614

#SPJ4

(a) The joint probability distribution of the two points will be 1/x, 0<x<1, 0<y<1

(b) The expectation of the product of the two points will be 1/6

(c) The marginal distribution of the point your friend picks will be (-1/2) lny^2

We have, X=(0,1)

Y | X=X=(0, X)

a) Let f(x,y) be the joint probability distribution of the two points will be:

f(X)=1

f(Y|X)=1/x

[tex]$$\begin{aligned}& f(x, y)=f(X) f(Y \mid X=x)=1 / x, 0 < x < 1,0 < y < x\end{aligned}$$[/tex]

b) Let E(XY) be the expectation of the product of the two points.

[tex]$$\begin{aligned}E(XY)=& \int_0^1 \int_0^x \frac{x y}{x} d y d x=\frac{1}{6} \quad \text { (Decimal : } 0.16667 \ldots \text { ) }\end{aligned}$$[/tex]

c) Let f(y) be the marginal distribution of the point your friend picks.

So, the value of f(y) will be:

[tex]$$\begin{aligned}& \mathrm{f}(\mathrm{y})= \\& \int_y^1 \frac{1}{x} d x=-\frac{1}{2} \ln \left(y^2\right)\end{aligned}$$[/tex]

d)for 0<y<1

[tex]$$\begin{aligned}& f(y) > =0 \\& \int_0^1-\frac{1}{2} \ln \left(y^2\right) d y=1\end{aligned}$$[/tex]

For more questions on Probability:

https://brainly.com/question/251701

#SPJ4

Answer:

Step-by-step explanation:

The normal distribution is defined by its mean and standard deviation, so if we know that the heights of the seedlings are normally distributed and we know certain percentiles of the distribution, we can find the mean and standard deviation.

We are given that 10% of the seedlings are taller than 15 cm, which means that 90% of the seedlings are shorter than or equal to 15 cm. This tells us that the 90th percentile of the distribution is 15 cm.

Similarly, we are given that 5% of the seedlings are shorter than 4 cm, which means that 95% of the seedlings are taller than or equal to 4 cm. This tells us that the 95th percentile of the distribution is 4 cm.

Since the normal distribution is symmetrical, the mean of the distribution is the value that separates the upper and lower halves of the distribution. In this case, the mean is the value that separates the lower 95% from the upper 5%, which means it is the value that is exactly halfway between the 95th and 90th percentiles.

To find the mean, we can add the 95th percentile (4 cm) and the 90th percentile (15 cm) and divide by 2:

mean = (4 + 15) / 2

= 19 / 2

= 9.5 cm

To find the standard deviation, we can use the fact that the normal distribution has the property that approximately 68% of the values fall within one standard deviation of the mean, approximately 95% fall within two standard deviations, and approximately 99.7% fall within three standard deviations.

Since we know that the 95th percentile (4 cm) is 2 standard deviations below the mean and the 90th percentile (15 cm) is 2 standard deviations above the mean, we can set up the equation:

4 cm = mean - 2 * standard deviation

15 cm = mean + 2 * standard deviation

Solving for standard deviation, we get:

standard deviation = (15 cm - 4 cm) / (2 * 2)

= 11 cm / 4

= 2.75 cm

So, the mean height of the seedlings is 9.5 cm and the standard deviation is 2.75 cm.

Answer:

There are many possible ranges, including  (−∞,15.051464)

 and  (15.051464,18.6844845)

 as well as  31.5±0.6270678

 (centered on the mean). Observe, in R:

> pnorm(15.051464, 31.5, 10) - pnorm(-Inf, 31.5, 10)

[1] 0.05

> pnorm(18.6844845, 31.5, 10) - pnorm(15.051464, 31.5, 10)

[1] 0.05

> pnorm(32.1270678, 31.5, 10) - pnorm(30.8729322, 31.5, 10)

[1] 0.05

In general, if you are given a small enough but otherwise arbitrary number  a∈R

 you can find a unique  b

 such that  b>a

 and

∫baϕ(x,31.5,10)dx=0.05,

where  ϕ

 is the normal density. For example, if  a=10

, then  b≈16.42

. Again in R:

> qnorm(pnorm(10, 31.5, 10) + 0.05, 31.5, 10)

[1] 16.42003

So your question doesn’t determine the answer uniquely: I’m free to choose the upper or lower bound of the interval or any particular point relative to those (e.g. the midpoint) arbitrarily.

If you had asked for a 95% interval, it would have been a reasonable assumption (but an assumption nonetheless) that you want an interval centered on the mode, median, or mean. But for a 5% interval, it’s not obvious that you want that — in practice it’s more likely that you want the upper tail or the lower tail.

That said, at a fundamental level, the answer is the same: use the cumulative distribution function and/or its inverse, as appropriate.

line k and second line h are not parallel lines because the have different slopes.

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Where x₁ - x coordinate

y₁ - y coordinate

m - slope

A line k passes through the points ​(−5​,−5​) and ​(1,37​).

Then Slope m = 37 + 5/ 1 + 5

m = 7

Now Write the equation as;

y + 5 = 7(x + 5)

y = 7x + 30

A second line h passes through the points ​(−3​,−33​) and ​(3​,9​).

Then Slope m = 9 + 3/ 3 + 33

m = 0.33

Now Write the equation as;

y + 33 = 0.33(x + 3)

Hence, line k and second line h are not parallel lines because the have different slopes.

Learn more about equations here;

brainly.com/question/25180086

#SPJ1

The percentage increase in the population of the chilrden since past year is 11.96%.

What is Percentage ?

A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.

According to the question, the town's population of children increased from 376 to 421 during the past year.

So, the increase in the population of the children is-

Increase =421-376

Increase =45

Now, the percentage increase in population of the children per year is calculated as-

Percentage Increase [tex]$=\frac{\text { Increase }}{376} \times 100 \%$[/tex]

Percentage Increase [tex]$=\frac{45}{376} \times 100 \%$[/tex]

Percentage Increase [tex]$=0.1196 \times 100 \%$[/tex]

Percentage Increase [tex]$=11.96 \%$[/tex]

Learn more about percentage here:

brainly.com/question/13450942

#SPJ4

Answer:

-3/14

Step-by-step explanation:

Step 1) Convert into -7/14 + 4/14

Step 2) -7/14 + 4/14= -3/14

Answer: 2m-6+4m

Step-by-step explanation:

The solution set of the function based on the graph is (3, 1). Option D

We know that the solution set of a function would be obtained as the points where the graph cut the axes of the graph. The graph has to do with a system in which information is presented in the x, y coordinate system.

In this kind of system, the vertical axis is the y axis while the horizontal axis is the x axis, as such we would need to plot the data points of the graph and then try to obtain the points that would correspond to the solutions of the points on the graph.

We would now need to observe the graphs so as to be able to obtain the correct presentation of the data points that would serve as the solutions of the graph as we can see the function plotted completely here.

The line cut the y axis at y =1. If we trace this point to the point that it corresponds to in the x axis we have x = 3 and we have the required points as (3, 1).

Learn more about solution set:https://brainly.com/question/11988499

#SPJ1

Answer: -8

Step-by-step explanation:

We see on the graph that there are two points located y=4. They are (7,4) ( -8,4).

So the other value other than 7 is -8!

Hence, the slope of equation is [tex]f(x)=-0.25x+2[/tex].

What is the slope of the line?

The slope is always estimated by determining the ratio of the “vertical change” to the “horizontal change” between any two different points on a line.

Suppose that the amount of water in the tank after a certain number of minutes.

Let [tex]x[/tex] be any value. So, after the [tex]x[/tex] minutes the tank has lost [tex]0.25x[/tex] gallons from the original [tex]2[/tex] .

So, the [tex]f(x)=2-0.25x[/tex] where [tex]f(x)[/tex] is the number of gallons remaining after [tex]x[/tex] minutes and here [tex]x[/tex] is the number of minutes.

[tex]f(x)=2-0.25x\\\\f(x)=-0.25x+2[/tex]

Hence, the slope of equation is [tex]f(x)=-0.25x+2[/tex].

To know more about the slope of line

https://brainly.com/question/12203383

#SPJ1

The percentage of students who live off campus and do not have a part-time job is 25.2%

The correct answer option is option C

Students who live off campus and gets a part-time job = Percentage of students who live off campus and gets a part-time job × Percentage of students who live off campus × 100

= 58% of 60% × 100

= 0.58 × 0.60 × 100

= 0.348 × 100

= 34.8%

percentage of students who live off campus and do not have a part-time job = Percentage of students who live off campus - Students who live off campus and gets a part-time job

= 60% - 34.8%

= 25.2%

Consequently, 25.2% of students live off campus and do not have a part-time job.

Read more on percentage:

https://brainly.com/question/843074

#SPJ1

If ABCD is a parallelogram and  ∠D=57° then ∠BCD =123°

What is a parallelogram ?

A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

A parallelepiped is a three-dimensional shape with parallelogram-shaped faces. The base (one of the parallel sides) and height (the distance from top to bottom) of the parallelogram determine its area. A parallelogram's perimeter is determined by the lengths of its four sides.

Using corresponding angle property int he parallelogram we can se that the ∠D is equal to exterior ∠C (57° ) because side AD and BC are parallel

and we know ∠C + exterior ∠C will be 180°

∠BCD=180° - 57°

∠BCD =123°

Learn more about Parallelogram from the link below

https://brainly.com/question/11220936

#SPJ1

Answer:

12

Step-by-step explanation:

3*4=12

The monomial that we need to add to have a square of a difference is:

-2bc

Remember that the square of a difference is written as:

(a - b)^2 = a^2 - 2ab + b^2

Here we have the two  terms:

0.01*b^2 + ... + 100c^2

We can rewrite the known terms as:

0.01*b^2 = (0.1*b)^2

100*c^2 = (10c)^2

Then our expression becomes:

(0.1*b)^2 + ... + (10c)^2

And the missing term must be:

-2*(0.1b)*(10c) = -2bc

Then the complete expression is:

(0.1b)^2 - 2bc + (10c)^2 = (0.1b - 10c)^2

Learn more about square of a difference at:

https://brainly.com/question/24524280

#SPJ1

Answer: 13/15

Step-by-step explanation:

2/3 x 5 = 10/15

1/5 x 3 =3/15

3/15 + 10/15 =13/15

Answer:

13/15

Step-by-step explanation:

2/3 = 15/3 = 10 this is because 5 and three have common factors. So I now have 10/15.
1/5 = 3/15.

3/15 + 10/15 = 13/15.

Answer: y= -2/3x + 0

Explanation: y= mx +b

Y-intercept at (o,o), so b is 0

Let's pick 2 points (-3,2) ( 0,0), so the slope is -2/3

So the equation is y=-2/3x + 0

Answer:

32

Step-by-step explanation:

we have to find the side of the bigger triangle by making a ratio

5/8=7/x

cross multiply

5x=7(8)

5x=56

/5.  /5

x=11.2

now for the other side

5/8=8/x

5x=8(8)

5x=64

/5. /5

x=12.8

we know all three sides 11.2, 12.8 and 8 so we add them

11.2+12.8+8

24+8

32

hopes this helps

Answer:

x = 3

Step-by-step explanation:

CD is an angle bisector and divides the opposite side into segments that are proportional to the other 2 sides, that is

[tex]\frac{BD}{AD}[/tex] = [tex]\frac{BC}{AC}[/tex] ( substitute values )

[tex]\frac{x}{2.25}[/tex] = [tex]\frac{4}{3}[/tex] ( cross- multiply )

3x = 4 × 2.25 = 9 ( divide both sides by 3 )

x = 3

The correct integers are;

For first diver, the elevation = - 36 feet

For second diver , the elevation = - 44 feet

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

One diver is 36 feet below the surface.

And, The other diver is 44 feet below the surface.

Now,

Since, One diver is 36 feet below the surface.

And, The other diver is 44 feet below the surface.

Hence, The correct integers to represent the surface are;

For first diver, the elevation = - 36 feet

For second diver , the elevation = - 44 feet

Thus, The correct integers are;

For first diver, the elevation = - 36 feet

For second diver , the elevation = - 44 feet

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

For the mileage of 80 miles company A will charge less than company B.

So, the inequality is m≤80.

A variety of notations are available to denote different kinds of inequalities. An inequality in mathematics is a relationship between two expressions or values that is not equal. To resolve an inequality, follow these steps: First, multiply each term by the total of the least common denominators of all the fractions to be subtracted. Step 2: Combine similar terms on both sides to simplify the inequality. Step 3: Calculate the unknown by adding or subtracting the amounts from the numbers on either side.

Charge for company A=$131

Charge for company B=$75+0.70m

75+0.70m≤131

0.70m≤56

m≤(56/0.7)

m≤80

Therefore, for the mileage of 80 miles company A will charge less than company B.

So, the inequality is m≤80.

To know more about inequality, visit:

https://brainly.com/question/28823603

#SPJ1

According to the given figure of triangle , f = 58 °

A linear pair of angles is formed when two lines intersect at a single point. The angles are said to be linear if they follow the point where the two lines intersect in a straight line.

The sum of the angles in a pair of linear equations is always 180°. These are also referred to as additional angles.

According to the given information

We are given that

a = 119°

Applying linear Pair of Angles

a + b = 180°

119° + b = 180°

b = 180° - 119°

b = 61 °

We know that

b = c = 61 °

According to Angle sum Property

b + c + f = 180°

61° + 61° + f = 180°

f = 180 - 61 -61

f = 58 °

According to the given figure of triangle , f = 58 °

To know more about Linear pair

https://brainly.com/question/17525542

#SPJ1

The statement that best describes the changes in air pressure and wind speed is C. When a high- and a low-pressure air mass are far apart, air moves slowly from high to low pressure.

The weight of air molecules pressing down on the Earth is referred to as air pressure. As you ascend from sea level into the atmosphere, the pressure of the air molecules changes. The greatest pressure exists at sea level, where the density of air molecules is greatest.

Atmospheric pressure, also known as barometric pressure, is the pressure that exists within Earth's atmosphere. The region with low pressure will always get winds from the high pressure. This means that the region of low will attract winds from the high pressure and vice versa.

Learn more about pressure on:

https://brainly.com/question/16099081

#SPJ1

Equation of line in slope-intercept form is 3y-2x= -1.

Hence, Equation of line in slope-intercept form is 3y-2x= -1.

To learn more about slope-intercept refer to:

https://brainly.com/question/1884491

#SPJ1

Answer:

153

Step-by-step explanation:

Use long division on a piece of paper I can't show photo sorry.

Anserw:

Say the averge water a person uses a day is 90 gallons 30% of the water is used outside a day. So that would mean around 27 gallons.

hope that helps :)

Step-by-step explanation:

Answer:

y = -4x-9

Step-by-step explanation:

The slope must stay the same for parallel lines, which is -4. Now we will plug the point into slope-intercept form(y=mx+b) where m is the slope and b is the y-intercept. Plugging in -4 for the slope and (-3, 3) for x and y, we get [tex]3=-4*13 + b[/tex], or [tex]3 = 12 + b[/tex]. Subtracting 12 from sides gives us that b = -9, which is the y-intercept! We know have both the slope and y-intercept, so we get that the equation is y = -4x - 9.

Hope this helps!

Answer:

There was no data provided but due to simple research i have conducted the following data

Qualifiers are in bold, italics and underlined.

Step-by-step explanations:

Chio- 3 1/5

Kevin- 3.2

Ojas- 3 8/30

Sydney- 3 13/60

Qualifiers: Chico, Kevin

let me know if this is incorrect data

The frequency distribution of the data from 103 to 107 is 2, from 108 to 112 is 4 and from 113 to 117 is 2.

Frequency distribution in a data set is the no. of times a certain data of an interval of grouped data occurs.

Temperature(°F)                              Frequency

103 to 107                                                2

108 to 112                                                4

113 to 117                                                  2

The class width of a data set is represented by the two consecutive lower limits.

learn more about frequency distributions here :

https://brainly.com/question/14926605

#SPJ1

Answer:

-60q+20

Step-by-step explanation: