unit 11 probability and statistics homework 2 answers

Answer: [tex]x\leq -1[/tex]

Step-by-step explanation: The closed point indicates that it can be equal to that number. The arrow is going back on the number line, meaning it is going to be less. Thus, it is less than or equal to -1.

t = price of bag of takis

w = water price

10t + 2w = 32

4t + 6w = 18

get both equations in terms of w

2w = 32 - 10t

6w = 18 - 4t

multiply first equation by -3

-6w = -96 + 30t

6w = 18 - 4t

add

0 = -78 + 26t

78 = 26t

t = 3

price of taki bag is 3 dollars

plug into any of the formulas and solve for w

6w = 18 - 4(3)

6w = 18 - 12

6w = 6

w = 1

price of water is 1 dollar

make sure this is correct by plugging into one of the formulas and verifying if true

4t + 6w = 18

4(3) + 6(1) = 18

18 = 18

answers are correct

takis are 3 dollars

waters are 1 dollars

hope this helps :)

- jeron

comment if you have questions

look up "solving linear equations" for more information

The graph of the linear function y = 36 - 4x that represents this situation is given by the image shown at the end of the answer.

To graph the linear function, these three steps are taken:

The slope-intercept definition of a linear function is presented as follows:

y = mx + b.

In which the coefficients are detailed as follows:

Initially, he has 36 overdue activities, hence the intercept is of:

b = 36.

And thus the coordinates of the y-intercept are given as follows:

(0,36).

Each day, he can do 4 activities, meaning that the number of remaining activities decays by 4, and thus the slope is of:

m = -4.

Thus the definition of the function is presented as follows:

y = -4x + 36.

The x-intercept of the function is the value of x when the output variable assumes a value of 0, hence it is obtained as follows:

-4x + 36 = 0

4x = 36

x = 9.

Thus the coordinates of the x-intercept are given as follows:

(9,0).

Finally, a line is traced connecting the y-intercept (0,36) and the x-intercept (36,0).

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Answer: 13,900

Step-by-step explanation:

To round numbers to the nearest hundred, you always look at the place one down which is the tens place. The tens place is 5.

The options for 856 to round to is either 800 or 900.

The rule is that 0-4 rounds down, 5-9 rounds up. Since the tens place is 5, it will round up to 900.

Therefore, the answer would be 13,900.

Answer:

The answer is 60

Step-by-step explanation:

160 × 3/8 = 480/8 = 60

Thus, 60 new houses have been sold this year.

The amounts in each mutual fund are $500 and $1800. By using a system of equations, the required values are evaluated.

The system of equations is a set of one or more equations that intersects at locations called solutions of the system.

The system of equations is solved for solutions in three different methods. They are the Elimination method, Substitution method, and Graphing method.

It is given that, an investor invested $2300 in two mutual funds.

Consider the amount invested in two mutual funds as fund1 = x and fund2 = y.

So, we can write the equation for the total investment is

x + y = 2300 ...(1)

The percentage of profit earned from the fund1 = 6% = 0.06

The percentage of profit earned from the fund2 = 4% = 0.04

The total profit for the investor = $102

Then, the equation from this statement is

0.06x + 0.04y = 102 ...(2)

Then the system of equations is

x + y = 2300 ...(1)

0.06x + 0.04y = 102 ...(2)

Applying the substitution method to solve the obtained system of equations.

So, from (1), we can write x = 2300 - y

Then, equation (2) becomes

0.06(2300 - y) + 0.04y = 102

⇒ 6(2300 - y) + 4y = 10200

⇒ 13800 - 6y + 4y = 10200

⇒ 13800 - 2y = 10200

⇒ 2y = 13800 - 10200 = 3600

∴ y = 3600/2 = $1800

So, the value of x is x = 2300 - 1800 = $500

Thus, the amount of investment in two mutual funds is $500 and $1800.

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The value of the double integral ∫∫[tex]\frac{y^{2} }{x^{2} +y^{2} }[/tex] dA is 131.95.

We know that in polar coordinates, the circle become r = 4 and r = 16. These are the limits on the radius. Clearly the limits on the angle are

0 ≤ θ ≤ 2π.

Therefore we get,

∫∫ [tex]\frac{y^{2} }{x^{2} + y^{2} }[/tex] dA = ∫ ∫ r²sin²θ / r² dr dθ

                  = ∫ sin²θ dθ ∫ r dr

                  = [ [tex]\frac{1}{2}[/tex]θ - [tex]\frac{1}{4}[/tex]sin(2θ)]₀²ⁿ[ [tex]\frac{1}{2}[/tex] r²]₄¹⁰

                  = [tex]\frac{1}{4}[/tex] (2π)(10² - 4²)

                  = 42π

∫∫ [tex]\frac{y^{2} }{x^{2} + y^{2} }[/tex] dA = 131.95.

What is Polar coordinates?

When each point on a plane of a two-dimensional coordinate system is decided by a distance from a reference point and an angle is taken from a reference direction, it is known as the polar coordinate system.

Polar coordinates are useful in calculating the equations of motion from a lot of mechanical systems. Polar coordinate means the magnitude and direction of a vector.

Polar coordinate system of locating points in a plane with reference to a fixed point O and a ray from the origin usually chosen to be the positive x-axis.

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The missing measures of the named angles are:

w = 62°

z = 57°

y = 57°

x = 61°

b = 24°

a = 132°

c = 156°

d = 156°

e = 132°

f = 24°

g = 24°

h = 156°

i = 156°

To find the measures of each of the named angles in the figure above, note the following:

Therefore:

w = 62° [alternate interior angles are congruent]

z = 180 - 123 = 57° [angles on a straight line]

y = 180 - 62 = 57° [angles on a straight line]

x = 180 - 62 - 57 = 61° [triangle sum theorem]

b = 24° [base angles of isosceles triangle]

a = 180 - 2(24) = 132°

c = 180 - 24 = 156°

d = 180 - 24 = 156°

e = a = 132°

f = g = 1/2(180 - e)

Plug in the value of e:

f = g = 1/2(180 - 132)

f = g = 24°

h = i = 180 - 24 = 156°

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The probability that a student in the 6th-period class watched more than 1 hour of TV is approximately 0.600.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

The table in the image shows the results of a survey of students in two math classes.

Did You Watch More Than One Hour of TV Last Night?

                           Yes           No

3rd period class   6            10

6th period class   9            6

To find P(more than 1 hour of TV | 6th period class), we need to find the probability that a student in the 6th period class watched more than 1 hour of TV given that we know they are in the 6th period class.

We can use the formula: P(A|B) = P(A and B) / P(B)

We are trying to find P(A|B), where:

A = "more than 1 hour of TV"

B = "6th period class"

We can find P(A and B) by looking at the table.

There were 15 students in the 6th-period class and 9 of them watched more than 1 hour of TV, so P(A and B) = 9/15.

We can find P(B) by looking at the table. There were 15 students in the 6th-period class, so P(B) = 15/15 = 1.

Plugging these values into the formula, we get: P(A|B) = (9/15) / 1 = 0.6

Rounded to the nearest thousandth, this is: 0.600

Thus, the required probability is approximately 0.600.

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Answer:

Yes

Step-by-step explanation:

The pair of congruent angles needs to be included between the congruent sides. Since this is not the case, more information is needed.

The correct response is yes, the additional information is needed to show that ΔDEF is congruent to ΔGHJ by SAS congruency rule is whether the sides DE and GH, are congruent

The SAS (Side-Angle-Side) congruency postulate states that two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle.

The specified information for each triangle, starting from the indicated angle, and calling the sides in a clockwise direction, we get;

∠E, side EF and side DF in triangle ΔDEF are congruent to angle ∠H, side HJ, and side GJ

Therefore, the information from the diagram in the question are a nonincluded angle and two sides, SSA, which is not a condition for congruency.

The additional information needed to prove ΔDEF is congruent to ΔGHJ, by SAS are the sides DE and GH, which makes the angle ∠E and ∠H included angles.

Therefore, additional information is required;

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Answer:

The equation of the line in slope-intercept form is: y = 1/3x + 2

To derive this equation, we first need to identify the slope of the line, which is given as 1/3. We then use the point (0,2) to find the y-intercept, which is 2. Finally, we substitute these values into the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. In this case, we have m = 1/3 and b = 2, so the equation of the line is y = 1/3x + 2.

Alternatively, we could use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. In this case, we have (x1, y1) = (0,2) and m = 1/3, so the equation of the line is y - 2 = 1/3(x - 0), which simplifies to y = 1/3x + 2. This is the same result as before, but using a different method to derive the equation.

Step-by-step explanation:

The probability of getting a full house is 0.001441 or 0.14%.

When you dealt five cards from a thoroughly shuffled standard check of cards then for the probability of getting a full house we need to know the total number of full house combinations and possible cards hands.

This is calculated by taking the number of possible full house combinations (3,744) and dividing it by the total number of possible 5-card hands (2,598,960). This can be written as :

Mathematically, this can be expressed as:

P(Full House) = 3,744 / 2,598,960 = 0.001441 or 0.14%

Therefore the probability of getting a full house is 0.001441 or 0.14%

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Answer:

60 hours to lose 120 gallons of water.

Step-by-step explanation:

Make a spreadsheet of the data with 3 columns.  The first will contain the hours and the second will contain the gallons of water lost.  (attached).  It would be useful to have a water loss rate, such as gallons lost per hour.  So in the third column, take the gallons of water for that line and divide it by the hours for that same line.  Do this for each of the line entries, as shown.  The first thing to note is that they are all the same.  Perfect! (and important).  This means we can use the rate of 2 gallons per hour and multiply it by the number of hours to find the total water lost:

   (Rate[gal/hr])x(Time[hr]) = Gallons water lost

The question is how mush time until 120 gallons are lost.  The unknown is the hours, which we'll call x.  Now we can set up the equation and solve for x:

(Rate[gal/hr])*(Time[hr]) = Gallons water lost

(2 gal/hr)*(x) = 120 gallons water

x = 60 hours to lose 120 gallons of water.

The predicted strength of a weld with diameter of 51 is -503.16.

Given that diameter of weld is 51.

And we have to find predicted strength of a weld.

We know that the equation of predicted strength is,

strength = -941.6 + (8.598 × D)

where D id diameter = 51

⇒ strength = - 941.6 + (8.598 × 51)

   strength = -941.6 + 438.4

   strength = -503.2

Therefore predicted strength of a weld is -503.2 i.e option (b) -503.16.

A prediction equation predicts a value of the response variable for given values of the factors. The Delphi Survey technique is a popular method used in prediction. There are two types of prediction methods: qualitative and quantitative.

The Least square Regression Line is the line that makes the vertical distance from the data points to the regression line as small as possible. It is called a "least squares" because the best line of fit is one that minimizes the variance.

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Answer:

[tex]$\frac{5}{8}$[/tex]

Step-by-step explanation:

The pair of 1st line is vertical opposite angle and 2nd one is adjacent angles.

What is vertical opposite angle ?

When 2 lines meet one another, then the other angles, shaped thanks to intersection ar known as vertical angles or vertically opposite angles. A try of vertically opposite angles ar continuously adequate to one another. Also, a angle and its adjacent angle are supplementary angles, i.e., they add up to a hundred and eighty degrees.

Main body:

1st pair of line intersect each other , so ∠1 = ∠2 by using vertical opposite angle.

2nd pair of line also intersect each other , so ∠3 ,∠4 are adjacent angles.

Hence ,pair of 1st line is vertical opposite angle and 2nd one is adjacent angles.

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The connection test is performed prior to making any ends in view of the tests for the primary impacts. The effect of one factor on the population mean when two factors interact is determined by the specific value or level of the other factor.

Before drawing any conclusions based on the tests for the main effects, the interaction test is carried out. The effect of one factor on the population mean when two factors interact is determined by the specific value or level of the other factor.

There may be an interaction if the plot's lines don't line up in the same direction. A collaboration demonstrates that the method for the Y information at the levels of the main X variable are different at each level of the second X variable. The interaction's strength increases with the number of nonparallel lines.

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Answer:10

Step-by-step explanation:

Answer:

$37.50

Step-by-step explanation:

75% of $50:

0.75x50=$37.50

1024/3 units³ is the required volume of the given solid using the triple integral theorem.

As the name implies, triple integrals are 3 sequential integrations, used to determine a volume or to integrate into a 4th dimension, over 3 other independent dimensions.

∭Ef(x,y,z)dV=∬D[∫u2(x,y)u1(x,y)f(x,y,z)dz]dA.

So, we must use the triple integral formula in rectangular coordinates to get the volume of the solid (v):

[tex]V=\iiint d y d x d z[/tex] ...(1)

The solid is restricted by the following intervals:

[tex]y \in\left[x^2, 16\right], x \in[-4,4], z \in[0,4][/tex]

Then, this triple integral is now characterized as:

[tex]V=\int_0^4 \int_{-4}^4 \int_{x^2}^{16} d y d x d z[/tex]

Now we continue to integrate again to get the volume:

[tex]\begin{aligned}& V=\int_0^4 \int_{-4}^4\left(16-x^2\right) d x d z \\& V=\left.\int_0^4\left(16 \cdot x-\frac{x^3}{3}\right)\right|_{-4} ^4 d z \\& V=\frac{256}{3} \int_0^4 d z=\frac{1024}{3}\end{aligned}[/tex]

Therefore, 1024/3 units³ is the required volume of the given solid using the triple integral theorem.

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Complete question:
Use a triple integral to find the volume of the given solid. The solid is bounded by the parabolic cylinder y = x2 and the planes z = 0, z = 4, y = 16.

Answer: 7

Step-by-step explanation: I got 7. Here's how I got it:

Use the process of elimination. The 2 cannot be divided by 3, because the number (3) we are dividing by, is greater than the primary number (2). If we divided 3 by 2, we would result in a decimal. Then, I took an estimate. I got rid of the 3 because that number would be a low number to divide by 3.

Then I started plugging in numbers:

(6*2) + 5 + 1 + 4 = 22

As we know, 22 is NOT a product of 3.

So, it has to be 7, but I'll prove my answer:

(7*2) + 5 + 1 + 4 = 24

And yes, 24 can be divided by 3 8 times. I hope this helps.

Clarification: I multiply 6 and 7 by 2 because both numbers would go into the 2 boxes.

Answer:

Mr. Callaway needs 120 ounces of seed to seed both lawns

Step-by-step explanation:

2400/40 = 60 ounces per square foot

3000 divided by 60 = 50 ounces

So, Mr. Callaway needs 50 ounces to cover a 3000-square-foot lawn

4200 divided by 60 = 70 ounces

So, Mr. Callaway needs 70 ounces to cover a 4200-square-foot lawn

50+ 70 = 120 ounces

So, Mr. Callaway needs 120 ounces to seed both lawns.

If you can, please give me a Brainliest; thank you, and have a good day!

Answer:

120 ounces pf grass seed

Step-by-step explanation:

[tex]\frac{40}{2400}[/tex] = [tex]\frac{x}{3000}[/tex]  Cross multiply and solve for x

120000 = 2400x  Divide both sides by 2400

\[tex]\frac{120000}{2400}[/tex] = [tex]\frac{2400x}{2400}[/tex]

50 = x

It will take 50 ounces of grass seed to cover 3,000 square foot lawn.

[tex]\frac{40}{2400}[/tex] = [tex]\frac{x}{4200}[/tex]  Cross multiply and solve for x

168000 = 2400x  Divide both sides by 2400

70 = x  

It will take 70 ounces of grass seed to cover 4200 square foot lawn.

50 + 70 = 120

The approximation for the function g(4.2) is 12.44

From the table, we know that g'(4) = 2.2

g (4) = 12

Using the line tangent to the graph of g at x=4 ,

g (4.2)  = g (4 ) + (4.2 -4 )2.2

           = 12 + 0.44

           = 12.44

The approximation for the function g(4.2) is 12.44. So ,option A is correct.

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Answer:

[tex]x = 15 $^{\circ}$ ; z = 74$^{\circ}$[/tex]

Step-by-step explanation:

First, combine all like terms. Like terms are terms that have the same amount of the same variables:

[tex]m$\angle$(5x - 1) + m$\angle$(7x + 1) = 180$^{\circ}$\\\\[/tex]

[tex]m$\angle$(5x + 7x) + (1 - 1) = 180$^{\circ}$[/tex]

[tex]12x + 0 = 180$^{\circ}$[/tex]

Next, isolate the variable, x. Divide 12 from both sides of the equation:

[tex]12x = 180\\\frac{12x}{12} = \frac{180}{12}\\ x = \frac{180}{12}\\ x = 15 $^{\circ}$[/tex]

Next, plug in 15 for x in one of the given expressions. If you choose the right one (7x + 1), you will solve using the straight angle theorem. If you choose the bottom one (5x - 1), you will solve using the vertical angle postulate. Both will give you the same answer for x.

Firstly, if you want to solve using the straight angle theorem. The straight angle theorem is defined that all straight angles are 180 degrees. Solve using the straight angle theorem. Set both angle measurements equal to 180°:

[tex](z) + (7x + 1) = 180[/tex]

Plug in 15 for x and solve for the parenthesis:

[tex]z + 7(15) + 1 = 180 $^{\circ}$\\[/tex]

First, multiply 7 with 15:

[tex]z + (7 * 15) + 1 = 180 $^{\circ}$\\z +105 + 1 = 180$^{\circ}$\\[/tex]

Next, simplify by combining like terms:

[tex]z + (105 + 1) = 180 $^{\circ}$\\z + 106 = 180$^{\circ}$[/tex]

Next, isolate the variable, z, by subtracting 106 from both sides of the equation:

[tex]z + 106 = 180 $^{\circ}$\\z + 106 (-106) = 180 (-106)\\z = 180 - 106\\z = 74$^{\circ}$[/tex]

Your answer:

[tex]x = 15 $^{\circ}$ ; z = 74$^{\circ}$[/tex]

~

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Answer:

4(2)^(2/3)   or   4∛(4)

Step-by-step explanation:

Rules of Exponents..

16^(2/3)

= (2^4)^(2/3)

= 2^(8/3)

= 2^(2 + 2/3)

= 2^2 · 2^(2/3)

= 4(2)^(2/3)   or   4∛(4)

A range of values estimated to have a high probably of containing the population value is called Confidence interval.

A confidence interval is a range of values that is likely to contain the true value of a population parameter, such as a mean or proportion. The degree of confidence associated with a confidence interval is the probability that the population parameter falls within the range of the confidence interval.

Population parameter : In statistics, a population parameter is a numerical measure of a population, such as its mean, variance, or proportion of a certain characteristic. It is usually estimated from a sample of the population and is usually not known precisely.

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Answer:

Step-by-step explanation:

Answer:

11.25. or 11.3 miles

Step-by-step explanation:

Because Ash Ave. and Maple are parallel, this means that you have a pair of similar right triangles. Therefore, you can set up a proportion and solve for the length of Ash Ave.

6 miles/9 miles = 7.5 miles/x miles

x=11.25 miles

If the bookstore sells 15 pencils, the ratios of pens to pencil written as fraction is 2 / 3.

Proportional relationships are relationships between two variables where their ratios are equivalent.

A proportional relationship is one in which two quantities vary directly with each other.

Therefore, proportional relationship can be represented as follows:

y ∝x

y = kx

where

Therefore,

4 = 6k

k = 4 / 6

k = 2 / 3

Therefore, let's find the number of pen sold when the bookstore sells 15 pencils.

y = 15 × 2 / 3

y = 30 / 3

y = 10

Therefore, if the bookstore sell 15 pencils the ratio of pen to pencil is 10 / 15 = 2 / 3

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If they keep running at the same pace, they will eventually meet at the same end of the course after 30 minutes.

The rate at which distance and time change is what is meant by speed. It has the aspect of temporal and spatial distance. The basic unit of distance with the basic unit of time are combined to form the SI unit of speed. This means that the SI unit of speed is the metre per second.

The way that the issue is described is vague.

I believe what is being said here is that they continue to jog at the same speed.

Half a mile per ten minutes is Diane's speed.

2/3 miles per 10 minutes is Jack's speed.

The numerator and denominator (top and bottom of the ratio) must be multiplied by the factor between 10 minutes and an hour (60 minutes) in order to convert this to a standard miles per hour format.

60/10 = 6.

In order to convert the above speeds to miles per hour, we must multiply both speeds by 6.

Diane: (1/3 divided by 6)/hour equals 2 miles/hour

Jack: (4 miles per hour) = (2/3 x 6) / hour

Diane will complete one length in the time it takes Jack to complete a round trip (back) because he runs twice as fast as she does.

Running a mile at a speed of two miles per hour takes Diane 30 minutes.

Running 2 miles (back and forth) at a speed of 4 miles per hour will take Jack 30 minutes.

So after 30 minutes they will meet again at his starting point.

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According to the Central Limit Theorem, the mean of the sampling distribution of means will be equal to The mean of the Original Population.

Central Limit theorem:

The central limit theorem (CLT) is a statistical concept that states that the sample mean distribution of a random variable assumes an approximately normal or normal distribution when the sample size is large enough. Simply put, the theorem states that the mean sampling distribution approaches a normal distribution as the sample size increases, regardless of the shape of the original population distribution.

For example:

An investor wants to estimate the return on the ABC stock market index, which consists of 100,000 shares. Due to the large size of the index, the investor cannot analyze each stock individually and instead chooses to use a random his sample to obtain an estimate of the index's total his return. Investors select a sample of stocks. Each sample contains at least 30 strains. Samples should be random and previously selected samples should be replaced by subsequent samples to avoid bias.

If the average return of the first sample was 7.5%, the average return of the next sample could be 7.8%. Due to the nature of random sampling, each sample will produce different results. As you increase the sample size for each selected sample, the sample means begin to form their own distribution.

The distribution of the sample mean approaches a normal distribution as the value of n increases. The average return of the index example stocks estimates the return of the entire index of 100,000 shares, and the average returns follow a normal distribution.

According to the central limit theorem, if a large sample is chosen from an unknown population with mean μ and standard deviation σ, the sampling distribution of the sample mean follows a normal distribution.

The mean and standard deviation of this sampling distribution are:

                        μₐ = μ

                      σₐ = σ/√n

This standard deviation of the sampling distribution of the mean is called the standard error.

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